Novel Nanostructures and Materials for Strong LightâMatter

Perspective Cite This: ACS Photonics XXXX, XXX, XXX-XXX

pubs.acs.org/journal/apchd5

Novel Nanostructures and Materials for Strong Light−Matter Interactions Denis G. Baranov,*,†,‡ Martin Wersal̈ l,† Jorge Cuadra,† Tomasz J. Antosiewicz,†,§ and Timur Shegai*,† †

Department of Physics, Chalmers University of Technology, 412 96 Gothenburg, Sweden Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia § Centre of New Technologies, University of Warsaw, 02-097 Warszawa, Poland ‡

ABSTRACT: Quantum mechanical interactions between electromagnetic radiation and matter underlie a broad spectrum of optical phenomena. Strong light-matter interactions result in the well-known vacuum Rabi splitting and emergence of new polaritonic eigenmodes of the coupled system. Thanks to recent progress in nanofabrication, observation of strong coupling has become possible in a great variety of optical nanostructures. Here, we review recently studied and emerging materials for realization of strong light−matter interactions. We present general theoretical formalism describing strong coupling and give an overview of various photonic structures and materials allowing for realization of this regime, including plasmonic and dielectric nanoantennas, novel two-dimensional materials, carbon nanotubes, and molecular vibrational transitions. In addition, we discuss practical applications that can benefit from these effects and give an outlook on unsettled questions that remain open for future research. KEYWORDS: strong coupling, Rabi splitting, excitons, quantum emitters, nanophotonics

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INTRODUCTION Interaction between photons and quantum emitters (QEs) is a fundamental aspect of electromagnetism and quantum optics that underlies an incredibly wide spectrum of observable phenomena ranging from spontaneous emission to lasing and more sophisticated effects. The strength of interaction between matter and an optical cavity is usually characterized by the Rabi frequency, which reflects the rate of energy exchange between matter and an electromagnetic mode.1 The weak side of this interaction, manifested in spontaneous emission of quantum emitters,2,3 underlies operation of incoherent light sources ranging from fluorescent lamps to light emitting diodes. During the past decades, a lot of effort has been devoted to theoretical studies and engineering of nanostructures that enable acceleration of spontaneous emission via the Purcell effect.4−8 Strong coupling is a distinct regime of light−matter interaction, when the Rabi frequency exceeds the rate of electromagnetic mode damping. This regime of interaction manifests itself in coherent oscillations of energy between matter and a photonic subsystem. In the frequency domain, this leads to modification of the spectroscopic response of the system such that two new normal modes emerge. This is known as vacuum Rabi splitting. Beside fundamental interest, strong coupling between light and matter enables realization of such profound effects as Bose−Einstein condensates9 and superfluidity.10 Strong coupling also holds a great potential for demanding applications such as single-photon switches,11−13 all-optical logics,14,15 and control of chemical reactivity.16−19 © XXXX American Chemical Society

The possibility of reaching the strong coupling regime crucially depends on the characteristics of two ingredients involved in any light-matter interaction: an optical cavity and QEs. The magnitude of Rabi splitting is proportional to the transition dipole moment of the QEs forming the excitonic subsystem and this fact makes certain emitters predisposed for realizations of strongly coupled systems. On the other hand, Rabi splitting is proportional to the value of the vacuum electric field and the visibility of Rabi splitting also benefits from a large Q-factor of the cavity. For this reason, certain combinations of optical cavities and quantum emitters exhibit more favorable properties for observation of the strong coupling regime than others. In recent years, strong coupling has been obtained with the use of many novel material platforms, whose electronic and optical properties need to be understood in detail to ensure optimum performance of envisioned applications. The aim of this Perspective is to provide a broad overview of these novel nanostructures. We present the theoretical basis underlying the phenomenon of Rabi splitting, review various nanophotonic structures and novel materials that can be employed for realization of this regime, and discuss open challenges and Special Issue: Strong Coupling of Molecules to Cavities Received: Revised: Accepted: Published: A

June 26, 2017 September 12, 2017 October 9, 2017 October 9, 2017 DOI: 10.1021/acsphotonics.7b00674 ACS Photonics XXXX, XXX, XXX−XXX

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Figure 1. Schematic illustration of weak and strong coupling between an optical cavity and a TLS. (a) Weak coupling results in spontaneous decay of the QE at a rate γ accompanied by emission of a photon. (b) Strong coupling results in Rabi oscillations of the QE population inversion at a rate Ω. (c) Jaynes-Cummings ladder of a strongly coupled QE-cavity system. The ground state of the system is not affected by the interaction, while energies of the excited states split by the Rabi splitting (Ω = 2g for the two lowest dressed states |1, ±⟩).

σ̂†) is the QE dipole moment operator, and , is the vacuum electric field. Skipping the counter-rotating terms âσ̂ and â†σ̂† in the commonly made rotating wave approximation, we write the resulting Hamiltonian in the Jaynes-Cummings (JC) form:

potential implications of strong coupling to various optical and electronic effects that remain largely unexplored.

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THEORETICAL BACKGROUND

Let us begin by briefly recalling the general theory describing interaction of a QE, such as an atom, a molecule, a quantum dot, or a semiconductor exciton, with a single electromagnetic mode of an optical cavity. The simplest model of a QE capturing effects inherent to real optical emitters is a two-level system (TLS) with the ground |g⟩ and excited |e⟩ energy states separated by the transition energy ℏω0 with ℏ being the reduced Planck constant. The Hamiltonian of such an emitter is ℏω0σ̂†σ̂ with σ̂ = |g⟩⟨e| being the lowering operator. The QE is characterized by a transition dipole moment deg = ⟨e|qr̂|g⟩, with q being the elementary charge. When a QE is coupled to an optical cavity, two distinct scenarios may be realized. In the first case, known as the weak coupling regime, the excited QE undergoes exponential decay into the ground state at a rate γ, accompanied by spontaneous emission of a photon, Figure 1a. The presence of the cavity in this scenario modifies the local density of optical states and, according to the Fermi golden rule,1 the resulting decay rate. In this case, the process of spontaneous decay may be calculated classically, and the enhancement of the decay rate, known as the Purcell factor, can be computed from the electromagnetic Green tensor of the structure.4−7 In the second case, that is, strong coupling, coherent energy exchange between the QE and the cavity mode occurs. The rate of this exchange, Ω, is faster than any decay process in the system, and thus the dynamics of the system is drastically different from the weak coupling case, Figure 1b. To correctly describe the physics of a strongly coupled system, both the QE and the optical cavity should be quantized.1 The single-mode cavity is described by the standard Hamiltonian ℏωâ†â, where ω is the mode frequency and â is the photon annihilation operator. The emitter-cavity interaction is mediated via the electric dipole term, d̂·Ê (rd), where Ê (rd) = ,(a†̂ + a)̂ is the electric field operator at the position of the emitter, d̂ = deg(σ̂ +

/̂ = ℏω0σ ̂†σ ̂ + ℏωa†̂ a ̂ + ℏg (σ â †̂ + σ ̂†a)̂

(1)

where g is the coupling constant given by g = −deg, /ℏ. In the absence of coupling, g = 0, the eigenstates of the system are the direct product of the atomic eigenstates |g⟩, |e⟩, and the cavity Fock states |n⟩. Assuming resonant interaction, ω0 = ω, this Hamiltonian results in the well-known spectrum of dressed light−matter, or polaritonic, states1 |n , ±⟩ =

|g , n⟩ ± |e , n − 1⟩ , n≥1 2

(2)

with the corresponding energy spectrum given by En± = nℏω0 ± g n , n ≥ 0

(3)

Coupling modifies the spectrum of the system, Figure 1c, opening a gap of Ω = E+ − E− = 2g n between the upper and lower polaritonic states of the coupled system, referred to as the Rabi splitting. At the same time, the global ground state of the system |g⟩ ⊗ |0⟩ is not affected in the JC picture of interaction, resulting in E0 = 0 energy of the ground state. The anharmonic structure of the energy levels depicted in Figure 1c, known as the JC ladder, gives rise to an intriguing optical effect of a photon blockade,20 which is a signature of quantum light−matter interaction. Photon blockade arises when a strongly coupled system absorbs a resonant photon exciting the system to the first polaritonic state |1, ±⟩. Due to the anharmonicity of the JC ladder, the presence of this excitation blocks absorption of a second photon of the same energy, enabling nonlinear response with a single photon.21−23 Coupling described by the JC Hamiltonian is inherent to all interacting photon−QE structures. However, Rabi splitting can be blurred out by spontaneous decay and dephasing in the system. In order to describe the crossover between the two B

DOI: 10.1021/acsphotonics.7b00674 ACS Photonics XXXX, XXX, XXX−XXX

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dispersive materials with special emphasis placed on metal cavities.33 The challenge thus lies in the fact that these are modes of nonconservative systems (via radiative and/or dissipative losses) and subsequently the field used to obtain V diverges, as shown in Figure 2a. However, while the correct

scenarios, we need to introduce losses associated with incoherent processes. This can be done phenomenologically by introducing complex energies of the QE, ω0 − iγQE, and the cavity, ω − iγcav. The resulting eigenenergies in the single excitation subspace, n = 1, may be found by diaganolizing the following non-Hermitian Hamiltonian (for n ≥ 2, such an approach fails to describe eigenstates, and a rigorous dissipative approach is required instead1): ⎞ ⎛ ω0 − iγQE g ⎟ /loss = ⎜⎜ g ω − iγcav ⎟⎠ ⎝

(4)

where γcav and γQE are the phenomenological cavity and emitter amplitude decay rates, resulting in 2γcav and 2γQE full widths at half-maximum of the cavity and the QE, respectively. Upon diagonalization this Hamiltonian yields energies of the two states ω + ω0 i − (γQE + γcav) E± = 2 2 1 ± g 2 + (δ − i(γQE − γcav))2 (5) 4 where δ = ω − ω0 is the detuning. In the resonant case ω = ω0, the Rabi splitting between these two states is Ω=

Figure 2. (a) Quasinormal mode of an open cavity with exponentially divergent fields outside. Reprinted with permission from ref 31. Copyright 2013 APS. (b) Electric field intensity (top) and energy density (bottom) distribution of a plasmonic mode of a sphere. Reprinted with permission from ref 30. Copyright 2010 OSA. (c) Dependence of the mode volume of a nanotriangle dimer on the gap separation. The insets illustrate in a logarithmic scale the evolution of the energy density which determines the magnitude of the mode volume with strongly amplified and localized values leading to small mode volumes.

4g 2 − (γQE − γcav)2 . This splitting becomes real-valued 24,25

when the expression under the square root sign is positive: 2g > |γQE − γcav|. However, fulfilling this condition does not guarantee observation of two spectral peaks. In order to resolve the two states, the Rabi splitting Ω additionally must exceed the polariton full width at half-maximum, which in the notation of eq 4 reads:24,26,27 Ω > γQE + γcav

(6)

Under the condition of eq 6, the strong coupling regime can be actually observed, for example, in the dark field (DF) or in photoluminescence (PL) spectra. As eq 6 suggests, observation of strong coupling requires an appropriate combination of two factors: the coupling constant g and the QE’s and cavity’s line widths. Ideally, one would combine large g with small line widths (large Q-factors), however, these are not fully independent parameters. Properties of a given QE can be tuned by external stimuli to some degree. In the case of solid-state QEs, their line width γQE is often broadened by dephasing caused by, for example, electron− phonon interaction.28 Cooling the system to cryogenic temperatures reduces the degree of dephasing and narrows the QE line width,29 making the conditions for observation of Rabi splitting more favorable. A greater flexibility is, however, offered by appropriately structuring the optical cavity. The coupling strength g between a single QE and a cavity is defined by the QE transition dipole moment deg and the cavity vacuum electric field , . The latter can be expressed through the mode volume V as30−32 ,=

ℏω/2εε0V

method of evaluating V is a subject of current research,30−32,34−36 the exact procedure is not important for the following discussion on the influence of V on Rabi splitting. With this in mind, we proceed to discuss how the choice of cavity and resulting mode volume impacts the viability of achieving the strong coupling regime. Early experiments on strong coupling of single emitters to resonators37−39 were accomplished with the use of high-Q dielectric cavities whose mode volume is inevitably bounded by the diffraction limit ∼(λ/2n)3. This impacts the vacuum field and, consequently, the coupling strength. For example, a cavity with a mode volume of 0.1 μm3 resonant at 1.5 eV has g ≈ 4 μeV per 1 D of a QE’s transition dipole moment (see Table 1). Such small coupling strengths necessitate large Q-factors for both the cavity and QE. This is turn requires cryogenic cooling to reduce the dephasing that is otherwise too high for QEs at elevated temperatures. For a given QE the obvious route to increase g lies in eq 7 − decreasing the mode volume − although due to the square root dependence a one order increase of g requires a two order decrease of V. Dielectric cavities cannot be made arbitrarily small due to the diffraction limit. The required decrease, however, can be achieved in metallic systems which support plasmon resonances, as the resonance is to a large extent determined by the permittivity of the nanoparticle. In the simplest case of a metal nanosphere with permittivity ϵc in a medium with ϵm in the quasistatic approximation the resonance condition is given by ϵc + 2ϵm = 0. The field of the resonance is

(7)

where ε0 is the vacuum permittivity. The mode volume, initially introduced by Purcell to quantify enhancement of spontaneous decay,4 is now a central parameter describing cavities. For dielectric ones it is typically correct to use V = ∫ ε|E|2d3r/max(ε|E|2), although only when losses (radiative or otherwise) are negligible. Additional complications arise for C


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Table 1. Summary of Experiments on Single Quantum Emitters Strongly Coupled to Dielectric and Plasmonic Cavitiesa nanocavity 38

photonic crystal cavity DBR cavity39 microdisk cavity51 Ag dimer105 Ag bow-tie nanoantenna103 Au nanosphere on Au film104 Au@Ag nanorods107

λ, nm

Q

V, μm3

QE type

deg, D

Ω, meV

Ω/deg, meV/D

Ω/γcav

1180 940 744 600 670 660 580

6000 7300 12000 ∼10 ∼5 ∼10 12

0.04 0.3 0.07 ∼2 × 10−7b ∼10−6c ∼4 × 10−8 ∼7 × 10−8d

InAs QD In0.3Ga0.7As QD GaAs QD R6G CdSe/ZnS QD methylene blue J-aggregate

29 60 92 5.4 5−15 3.8 ∼35

0.17 0.16 0.4 200 240 80−95 78

0.006 0.0027 0.004 29 48 24 ∼2.2

1.3 0.7 2.2 ∼1.9 ∼1.8 ∼0.85 0.45

a

The data on experiments with dielectric cavities is adopted from ref 24. bThe mode volume is probably overestimated, see discussion in the text. The mode volume was estimated for a bowtie nanoantenna in vacuum and is probably overestimated, see discussion in the text. dThe mode volume is probably underetimated, see discussion in the text. c

related to the phenomenon of superradiance.43 Indeed, the second term in eq 9 resembles the form of a superradiant Dicke state, which leads to an N times faster decay of the excited state. In addition to two bright states, the single excitation subspace also contains (N − 1) dark states orthogonal to |1, ±⟩.44,45 The wave function of these states can be written in the general form 1 as |D⟩ = 2 (σ1̂ † − σĵ†)|G⟩, j > 1. As one can see, these states do not couple to the photonic component, and their energies are identical and equal to the energy of uncoupled emitters ℏω0. These states are referred to as dark states since the transition dipole moment between the global ground state |G⟩ and any of these states is zero and, as a result, they cannot be populated by an external pump. Obviously, any linear superposition of the dark states in the form given above is also a solution of the TC Hamiltonian, with the same energy and a preserved dark nature. Because of this superposition, several authors discuss coherent properties of the dark states,45,46 a point to which we come back later. Having briefly overviewed the basic theoretical approaches of describing the phenomenon of strong coupling, we shall now consider various material platforms and nanostructures that have been recently utilized for realization of systems exhibiting Rabi splitting.

shaped by the geometry and size of the nanoparticle, thus for small single nanoparticles the mode volume follows the geometrical one.30 This is excellently seen for the example of a spherical particle, shown in Figure 2b, where almost all energy of the mode is tightly confined in the particle. Even smaller mode volumes can be achieved by arranging two particles in a dimer geometry. This is illustrated in Figure 2c, which presents an exemplary gap-size evolution of the mode volume of an Ag bowtie nanoantenna. In the present example this decrease spans close to 2 orders of magnitude; however, it can, in principle, be even greater. To a large extent it is determined by the dimensions of the nanometer-sized gap and for sharp enough tips can be comparable to or smaller than 100 nm3. Although utilizing small-V cavities allows one to enhance the vacuum electric field, employing a single QE is often not sufficient to realize Rabi splitting because the coupling constant g of a typical emitter to a notoriously lossy plasmonic nanocavity γcav is usually orders of magnitude smaller than the line width of the latter. In order to increase the splitting further, an ensemble of identical QEs may be coupled to a cavity. The spectrum of the system changes qualitatively when more than one QE is involved in the interaction. A system of N emitters coupled to the same electromagnetic mode is described by the Tavis-Cummings (TC) Hamiltonian,40,41 which is a generalization of the JC Hamiltonian: /̂ T − C =

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REVIEW OF NANOSTRUCTURES AND MATERIAL PLATFORMS Experimental studies of strong coupling and vacuum Rabi splitting began in the 1980s with pioneering works on coupling between ensembles of Rydberg atoms and microwave cavities.47−49 They were followed by experiments with single atoms and quantum dots (QDs) coupled to diffraction limited Fabry−Perot cavities,50 photonic crystal cavities,38 distributed Bragg reflector (DBR) cavities,39 and whispering gallery mode cavities.51 The results of these experiments on QEs coupling with diffraction-limited cavities were summarized in a number of comprehensive review papers.24,52 Another possibility to reach the strong coupling regime involves the use of propagating surface plasmon polaritons (SPPs)53−55 (see also ref 27 for a review). In this case, coupling occurs between excitations of QEs and propagating SPPs, what leads to modification of the SPP dispersion and splitting of the reflection dip in the Kretschmann configuration.53,54 Recent progress in nanofabrication enabled observation of strong light−matter coupling in a great variety of optical nanostructures, incorporating subwavelength cavities and novel excitonic materials with intriguing optoelectronic properties. Below we review examples of such structures reported to date. Plasmonic Nanoantennas. Plasmonics offers a straightforward way to increase the Rabi frequency and reach strong

∑ ℏω0σĵ†σĵ + ℏωa†̂ a ̂ + ℏ ∑ gj(σĵ a†̂ + σĵ†a)̂ j

j

(8)

The global ground state of the system |G⟩ = |g, ..., g⟩ ⊗ |0⟩ is not affected by the interaction (although we should note here that inclusion of the quickly rotating terms σ̂jâ and σ̂†j â† would modify the ground state of the system42). The structure of excited states, however, is substantially different. For N identical QEs identically coupled to the cavity (gj ≡ g), in the most interesting and relevant single excitation case, Hamiltonian (eq 8) has two bright dressed states |g , ..., g ⟩|1⟩ ± |1, ±⟩ =

1 N

∑j σĵ†|g , ..., g ⟩|0⟩ 2

(9)

with eigenenergies given by ω± = ω0 ± N g. In fact, at large N and weak excitations (far below saturation of all TLSs), such an ensemble behaves as a giant harmonic oscillator41 giving rise to N in the effective Rabi splitting. Unlike in the JC ladder case, here, higher excitations (still within the limit n ≪ N) are harmonic and do not induce the effect of photon blockade. It is also worth noting that formation of bright states is closely D


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Figure 3. Strong light−matter coupling using individual plasmonic nanoantennas. (a) Rabi splitting in an isolated silver nanoprism coupled to Jaggregate. Reprinted with permission from ref 81. Copyright 2015 APS. (b) Rabi splitting in dark-field scattering spectra of a plasmonic dimer strongly coupled to J-aggregates. Reprinted with permission from ref 82. Copyright 2013 ACS. (c) Rabi splitting in dark-field scattering and PL measurements of a silver nanoprism strongly coupled to J-aggregates. Reprinted with permission from ref 83. Copyright 2017 ACS.

properties for future applications as well as steer the research field in an appropriate direction. One of the pioneering studies exploiting plasmonic nanostructures for Rabi splitting demonstrated strong coupling between plasmons and QEs in a system comprised of arrays of spherical nanovoids coated with an organic J-aggregate film.75 Hereafter, a myriad of both theoretical and experimental demonstrations of systems exhibiting strong plasmon-exciton coupling with nonlinear optical dynamics followed. Reports on strong coupling in Au/J-aggregate systems,76,77 ultrafast energy transfer between molecular assemblies and surface plasmons,78 real-time observations of ultrafast plasmon-exciton Rabi oscillations,79 and ultrafast manipulation of strong coupling in molecular aggregate hybrid nanostructures80 are only a few examples of recent demonstrations within this field. Studies on plexcitonic (plasmon−exciton) systems have been performed on a variety of nanostructures and have given further insight into both fundamental understanding of the governing microscopic dynamics as well as possible future applications.84−86 Emphasis has, in many cases, been put on exploring intriguing changes in system properties between similar structures in a weak-, strong- and even ultrastrong coupling regimes.87,88 Also, strong coupling of localized surface plasmons to excitons in light-harvesting complexes from purple bacteria has been studied,89 indicating that strong plasmon−exciton coupling is sensitive to the specific presentation of the pigment molecules. Strong plasmon-exciton coupling has been demonstrated in systems with various geometries and materials of both plasmonic and excitonic nature. Gold and silver structures such as nanoshells and core−shells,84,86,90 nanostars,91 sharp tips and platelets,92,93 and nanoantennas of more complicated geometries94 are only a handful of prominent examples where signs of strong coupling have appeared. With all this at hand, there have lately also been studies on suggesting simple

coupling by confining light down to subwavelength scales with the use of metallic nanoparticles and nanocavities.56,57 These systems have been intensively studied from a theoretical perspective. Generally speaking, coupled nanoparticle-emitter systems exhibit Fano-like scattering spectra with the regimes of enhanced or suppressed scattering.58−60 Interestingly, interference of radiation from a QE and a cavity occurs, despite a very small volume of the QE compared to that of the nanoparticle. Remarkably, the coupled system exhibits an intensity-dependent response due to the saturation of the TLS,58 opening the way toward active quantum metamaterials with a switchable response. Resonant fluorescence and spontaneous emission from coupled systems were also studied theoretically, revealing a rich variety of spectral features.59,61,62 Observation of Rabi splitting in plasmonic systems was preceded by numerous studies reporting often so-called “coherent” coupling of molecular or excitonic resonances to plasmonic cavities.63−68 Such coherent coupling in the weak regime of interaction is characterized by a Fano-like profile of the scattering spectrum.69,70 Unfortunately, due to the presence of two peaks in scattering, this regime is often confused with true Rabi splitting.71−73 In the coherent coupling regime, the scattering dip is the result of destructive interference between the plasmon and the QE in far field;74 splitting between the two peaks can still be significantly smaller than the plasmon line width 2γcav. In the strong coupling regime, in contrast, two newly formed polariton modes do split apart at a distance exceeding the polariton line width γQE + γcav. In recent years, a plethora of experimental results on plasmon-exciton strong coupling in various systems have been reported. The coupling mechanisms, and hence the optical properties, are rather diverse between the cases where a single cavity excitation is coupled to many or a few QEs. This is important to grasp in order to exploit and harvest suitable E


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Figure 4. Single quantum emitter Rabi splitting at room temperature. (a) Scattering spectra of a silver bowtie antennas with one, two, and three CdSe/ZnS QDs in the gap exhibiting Rabi splitting. Reprinted with permission from ref 103. Copyright 2016 Springer. (b) Top: sketch of a single methylene-blue molecule placed in the gap of a plasmonic nanocavity. Bottom: Coupling strength g for samples with various numbers of molecules. Reprinted with permission from ref 104. Copyright 2016 Springer.

dynamics in the presence of metal oxidation have also been observed.101 To our knowledge, all previous demonstrations of strong coupling on a single particle level have relied on extracting parameters of the hybrid systems from dark-field (DF) scattering data. Several claims have been made that true strong coupling is reached only when the scattering data is accompanied by signs of polariton splitting in absorption72 or photoluminescence (PL).24 Furthermore, in case of individual QDs coupled to a bowtie nanoantenna, even splitting in the absortion spectrum cannot grant strong coupling, as it can be confused with the Fano regime.71−73 In this respect, it would be extremely interesting to observe convincing Rabi splitting data not only in elastic DF scattering, but also in absorption or PL of individual hybrid nanostructures. The first experimental demonstration of this kind on a single nanoparticle level was made recently.83 Strongly coupled (Ω ≈ 400−500 meV, observed in DF) plasmon−exciton systems, formed by single crystalline silver nanoprisms embedded in J-aggregate TDBC, possess signs of polaritons both in DF and PL, Figure 3c. Similar optical features have been reported previously,90,102 but have instead relied on extracting PL data from ensembles of nanoantennas rather than single nanoparticles. One of the cornerstones for exploiting plasmonic nanostructures as tools for future optical nonlinearities (including those down to a single photon) is the ability to achieve strong coupling between a plasmonic mode and a single quantum emitter. Since the quantum mechanical nature of excitons is prominent only when they are few in numbers, the quantum properties of hybrid systems solely rely on the amount of emitters that strongly couple to the cavity. Inasmuch as the coupling strength between cavity and emitter scales with the mode volume of the cavity field as g ∼ 1/V , several attempts have been made to further confine optical modes of plasmonic nanostructures. Recently there have been several studies claiming realization of strong coupling in plasmonic structures at the single emitter

approaches to design plexcitonic nanostructures for various applications.95 Finally, a useful approach for enhancing plasmon-exciton coupling based on transformation optics was developed by Li et al.96 The technique allows to accurately estimate the coupling strength for emitters within nanometric gaps between plasmonic nanoparticles and design nanocavities with more favorable properties in the context of light-matter coupling. All this indicates that a lot of knowledge has been acquired since the first pioneering works on the subject. Strong coupling between a single nanoparticle and molecular excitons was recently demonstrated in hybrid systems composed of various silver and gold nanostructures and Jaggregated TDBC molecules, Figure 3a.81,97 Analysis of the experimental data obtained by Zengin et al.81 furthermore suggested that the coupling was the result of interactions between a single plasmonic nanoparticle and no more than ≈80 excitons. Moreover, as a result of the very compressed mode volume of a thin nanoprism, a strong coupling figure-of-merit Q/ V of around 6 · 103 μm−3/2 was reported, which is comparable to state-of-the-art photonic crystals cavities. Despite the enhanced electric field near the surface of a single metal particle, the mode is mostly concentrated in the interior of the nanoparticle,30,81 cf. Figure 2b. Indeed, this fact is responsible for the limits on decreasing the mode volume as well as unfavorable overlap conditions between the mode and a QE.73 A sound approach is to form a dimer structure out of two nanoparticles, Figure 3b. This forces a qualitative change of the mode which not only produces a very strongly enhanced electric field in the gap, but also localizes the mode within the gap region both inside and outside of the metal.26,73,82 In order to push strong coupling dynamics even further, such as to ultraviolet regimes of the electromagnetic spectrum, studies on plasmonic aluminum nanostructures and molecular excitons have also been performed.98,99 Coupling effects between plasmons and interband transitions in magnetic nickel nanoantennas100 as well as effects on the strong coupling F


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limit. Probably, the first known demonstration of this kind was reported by Itoh et al. in 2014.105 The presence of single R6G molecules in the gap between two silver particles was monitored by means of Raman spectroscopy. For selected dimers, the maximum splitting of 200 meV was detected. We note that the value of the mode volume of ≈2 × 10−7 μm3 obtained by the authors of ref 105 is probably an overestimation, as when used with eq 7 it does not yield 200 meV single-molecule splitting observed in the experiment. Also, there was only indirect evidence of a single molecule presence in the gap; therefore, such large splitting may originate from collective coupling of a few molecules. Similar results have been reported by Santhosh et al.103 and Hartsfield et al.106 in 2015. Hartsfield et al.106 studied a gold nanosphere on a glass substrate coupled to a single CdSe/ZnS quantum dot and observed Fano features in the scattering spectrum. Although pronounced Rabi splitting was not reached because of significant detuning between the QD transition and the nanoparticle resonance, it was noticed that the response of the hybrid structure becomes strongly anisotropic for in-plane polarization in contrast to a bare nanosphere on a substrate. Santhosh et al.103 reached strong coupling by placing a single CdSe/ZnS QD in the gap of a bow-tie silver nanoantenna, Figure 4a. In this study, the authors have employed a double exposure electron beam lithography process in order to place a QD precisely at the bowtie nanoantenna hot spot. Vacuum Rabi splitting up to 240 meV was achieved for single QDs, which is the record value reported up to date (see Table 1). We note, however, that the mode volume of an Ag bow-tie nanoantenna with a gap of 20 nm is on the order of 1000 nm3, which is quite an optimiztic estimation as the mode volume of the dimer is only slightly reduced in comparison to the geometrical one with the mode still occupying a significant part of the inside of the metal, as shown in Figure 2c. This imples that the coupling strength of 120 meV observed in this work requires a transition dipole moment of ≈50 D. This number is 3−4× higher than the actual transition dipole moment of CdSe QDs (see Table 2). This discrepancy can be potentially explained by a reduction of the mode volume of the bow-tie nanoantenna induced by the high background refractive index of the QD.73 In the study of Chikkaraddy et al.104 a single molecule of methylene blue (transition dipole moment deg = 3.8 D) was positioned inside a sphere-on-film nanocavity, Figure 4b, and oriented along the vacuum-field lines by exploiting a barrel

shaped host molecule. To establish an ultraconfined mode volume (≈40 nm3), a gap-plasmon mode between a gold nanosphere on top of a gold film was utilized. With these parameters fulfilled, the authors observed Rabi splitting when the cavity field was coupled to only a few molecules, Figure 4b. Finally, strong coupling between J-aggregates and Au/Ag nanorods at the quantum optics limit was claimed in a recent study.107 While only the mean number of J-aggregates ⟨N⟩ coupled to a nanorod was monitored, observations suggested that the strong coupling condition can be satisfied with ⟨N⟩ ≈ 1.38. We note that the mode volume of 71 nm3 quoted by the authors is probably an underestimation, as frequency dispersion of metal was not taken into account for calculation of the mode volume, what would significantly increase the estimation. We also note that in small metallic nanostructures nonlocal effects, such as screening and Landau damping, arise inevitably. There are early theoretical efforts to estimate the impact of these effects on Rabi splitting,108 which demonstrated that coupling remains largely unaffected contrary to expectations. However, this issue remains to be the subject of ongoing debate. To facilitate comparison of Rabi splitting in plasmonic and dielectric structures, we provide Table 1, which summarizes the most essential parameters of the strong coupling regime reached in experiments with dielectric and plasmonic cavities with single emitters. A striking contrast between dielectric and plasmonic realizations is evident − while Rabi splitting in dielectric structures is measured in hundreds of μeV, plasmonic structures exhibit hundreds of meV splitting, that is, nearly 3 orders of magnitude stronger, due to extremely confined optical modes. This allows for observation of vacuum Rabi splitting down to the quantum optical limit using plasmonic nanoantennas even at room temperature. In the same Table 1, we also provide several important strong coupling measures, such as Rabi splitting per Debye (Ω/deg) and Rabi splitting versus cavity line width. We observe that plasmonic cavities dominate over photonic counterparts in terms of Ω/deg, due to confined optical modes. Along the same lines, within plasmon cavities− tight gap antennas dominate in this respect. However, in terms of Ω/γcav photonic and plasmonic cavities are well comparable. This is a consequence of very high quality factor of photonic cavities in comparison to plasmonic counterparts. Concluding this section, we note that plasmonic nanostructures, especially single gapped plasmonic nanoantennas, provide the ultimate confinement of electromagnetic field and are possibly the best candidates for realizations of truly subwavelength strongly coupled systems and single-photon nonlinearities. We anticipate that future work in this direction should shed more light on the previous observations103,104,106 and finally reach the true quantum mechanical nature of these interactions. Diffractive Arrays and Metasurfaces. Although single metallic nanoparticles and small clusters thereof are an important platform in the context of the quantum optical regime of nanoantenna-single QE interaction, reaching strong coupling with just a single emitter remains a challenging task. The difficulties lie both in fabrication and measurement methodologies. In this respect another type of plasmonic resonators, that is periodic arrays of nanoparticles, can be an interesting class of photonic nanostructures to consider. An important aspect here is that periodically arranged nanoparticles give rise to hybridization of localized plasmonic resonances and the diffractive modes of the array.109 These

Table 2. Summary of Transition Dipole Moments and Sizes of QEs Employed for Experiments on Rabi Splitting

a

quantum emitter

deg, D

diameter, nm

InAs QD24 GaAs QD24 Cs atom24 methylene blue104 rhodamine 800151 CdSe QD152,153 carbon nanotube154 WSe2154 WS2154,155 MAPbI3154

29 92 8 3.8 4 5−15 12 7 50 46

25 44 0.5 ≈1 ≈1 2−8 ∼1 × 100b ≈1a ≈3 ≈1a

Estimated as a characteristic Wannier-Mott exciton. diameter, ∼100 nm in length.

b

1 nm in G


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Figure 5. Surface lattice resonances for Rabi splitting. (a) Left: Schematic of a lattice of plasmonic nanoparticles coupled with atoms. Right: Extinction spectrum as a function of a pseudomomentum of the SLR with molecular excitons where the avoided crossing is observed. Adopted with permission from ref 110. Copyright 2014 ACS. (b) Condensation of polaritons in the ground state of a dye-coupled SLR indicating polariton lasing. Reprinted permission from ref 111. Copyright 2017 OSA.

Figure 6. Strong light−matter coupling in systems incorporating TMDCs. (a) Arrangement of atoms in a 2D TMDC material of the form MX2 with M being a transition metal atom and X being a chalcogenide atom. (b) Monolithic DBR cavity with a MoS2 monolayer embedded at the antinode of the electromagnetic field used for strong coupling. Reprinted with permission from ref 157. Copyright 2015 ACS. (c) Left: Structure for realizing electrically tunable organic−inorganic polaritons formed by DBR mirror and glass substrate. Electric bias applied to WS2 causes shift of the excitonic peak and modifies the resulting polariton composition. Right: The resulting weight coefficients of the Wanier-Mott (purple curve) and Frenkel (orange curve) excitons vs applied dc voltage. Reprinted with permission from ref 161. Copyright 2016 Springer. (d) Schematic of the MoS2 monolayer−plasmonic lattice integrated with a field-effect transistor. Reprinted with permission from ref 163. Copyright 2016 ACS. (e) Temperature-dependent dark-field scattering spectra from gold nanorods on a WS2 monolayer with the gray arrow showing the evolution of the exciton energy. Reprinted with permission from ref 165. Copyright 2017 ACS. (f) Helicity-resolved PL spectra from cavity-coupled WS2 monolayer under circularly polarized excitation. Reprinted with permission from ref 166. Copyright 2017 ACS.

in several configurations.110,116−118 Interestingly, the composition and the effective mass of the resulting polariton state can be manipulated by adjusting geometrical factors of the lattice, thus the interaction between polaritons can be increased.117,118 Recently, polariton lasing from a strongly coupled plasmonic diffractive array-dye molecules structure has been claimed, see Figure 5b.111 SLRs offer an alternative testbed for polaritonic devices. In contrast to individual nanoantennas, polariton states of plasmonic lattices have a delocalized spatial behavior, which allows to employ them for coherent energy transfer on the scale of the lattice. The first step toward this was achieved by demonstrating thermalization of plasmon exciton polaritons using SLR.119 Probing the first order correlation function through spatial coherence of a SLR coupled to dye molecules

collective modes, referred to as surface lattice resonances (SLRs), offer advantages with respect to pure plasmonic counterparts such as a higher quality factor due to Fano interference of the plasmon and the diffractive modes, and dispersion of the modes due to two-dimensional geometry. Combining plasmonic arrays supporting SLRs with excitons allows one to boost the emission of the excitonic transition. In this context, lasing action has been demonstrated in the near-IR and visible regions using an array of Au nanoparticles or metal hole arrays together with organic dyes.112−114 More recently, lasing in the visible range has been achieved by exploiting both the dipolar and quadrupolar resonances of periodically arranged Ag disks what results in lasing action into bright and dark modes of the SLR.115 Rabi splitting in diffractive arrays of plasmonic nanoparticles coupled with ensembles of QEs, Figure 5a, has been observed H


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explore the lasing behavior of these structures, statistical properties of light should be measured. From a theoretical standpoint, these extended materials can not be treated as single isolated QEs (excitons), but rather present an ensemble of those. However, as we have established, such ensembles of QEs obey the same behavior and exhibit Rabi splitting Ω that is proportional to the square root of the number of involved emitters N. Rabi splitting is determined by the concentration of excitons and the mode volume of a cavity: a macroscopic cavity can cover a large area and involve many excitons in the interaction (but that would come at a price of reduced vacuum field , , eq 7), while a cavity with a small mode volume may involve only a single exciton. Both may exhibit similar coupling strengths, however, quantum effects will only be observed in the smaller cavity. The concentration of excitons in TMDCs, however, can not be controlled: it is completely defined by the material properties. Another factor to consider is the polarization of the transition dipole moment in TMDCs, which is dominantly in-plane for monolayers,150 but can be outof-plane for multilayers. For this reason, attractive nanocavities such as nanoparticle-on-a-film104 can not be employed as they produce an electric field mostly in the out-of-plane direction, which will not interact with the electronic transition of a monolayer. Like electronic transitions in molecules and quantum dots, excitons in TMDCs can be characterized by their size and transition dipole moment. For convenience, we summarize in Table 2 transition dipole moments and sizes of several important classes of quantum emitters that have been employed for realizing strong light-matter coupling. In a given experiment, knowledge of the transition dipole moment and measured Rabi splitting allows one to estimate the number of excitons N involved in the interaction, provided the mode volume of the cavity and resulting vacuum field can be obtained. We note that it is possible to find several alternative measures characterizing the strength of the optical transition in the literature. This can be the transition dipole moment−the quantity used to calculate the strength of interaction−and therefore the most useful for the purposes of this perspective. But it also can be the oscillator strength f, absorption crosssection σabs, or molar extinction coefficient κ. All these measures have similar physical meanings and scale as the squared transition dipole moment |deg|2, for example, f = 2mω0|deg|2/(e2ℏ), with m being the electron mass (note that in many-electron systems the oscillator strength f can exceed unity156). Demonstration of Rabi splitting with TMDCs has been reported for a variety of photonic cavities. Monolithic microcavities formed by DBRs have shown hybridization of the cavity photons with MoS2 monolayer at room temperature, Figure 6b.157 Such demonstration opens up the possibility to realize polaritonic devices at room temperature.158 Electrically tunable microcavities together with van der Waals heterostructures have also shown strong coupling, although only at cryogenic temperatures.159 Such structures offer the advantage of tuning the photon-exciton detuning at will, which allows controlling the polariton composition, that is, making it more excitonic- or photonic-like. The layered nature of TMDCs makes them ideal candidates to be incorporated in such geometries as metal/DBR structures that give rise to Tamm plasmons.160 The versatility of these materials was shown by combining organic molecules with WS2 monolayers, Figure 6c, what allowed to tune electrically the

has shown the presence of correlations even for very excitonlike polaritons.120 Another interesting platform for exploration of strong lightmatter interaction is presented by plasmonic metasurfaces− periodic arrangements of resonant meta-atoms with subwavelength separation.121 In contrast to diffractive arrays, subwavelength separation ensures that only the zeroth diffraction order is open. Rabi splitting was observed for a near-IR intersubband transition in a semiconductor heterostructure coupled to a metasurface of plasmonic nanoantennas.122 An attractive advantage of this hybrid structure is that the intersubband transition energy can be finely controlled during the fabrication process or external bias using the Stark effect. Another study was carried out with cesium atoms coupled to a nanoslit metasurface.123 Although the regime of Rabi splitting was not identified, the authors observed strong modification of the atomic response induced by the plasmon resonance of the nanostructure. Transition Metal Dichalcogenides. Plasmonics serves as an excellent platform for confining the optical field using nanoresonators, what is one ingredient for reaching vacuum Rabi spitting. Another one is a material supporting electronic transitions. Until recently, excitons in semiconductors and organic molecules have been considered the main candidates for this role.27 As a result of progress in material science, many novel excitonic materials were explored in the context of strong light-matter coupling and have shown favorable characteristics. Possibly the most prominent of recent examples is presented by atomically thin transition metal dichalcogenides (TMDCs).124−127 These are an emergent class of twodimensional bandgap materials. A monolayer of TMDC is formed by a hexagonal layer of transition metal atoms hosted between two hexagonal lattices of chalcogenide atoms, Figure 6a. These materials are particularly interesting in the atomic monolayer limit, when their bandgap becomes direct enabling enhanced interaction of the dipole transition with light.128,129 Owing to this behavior, these materials represent a great opportunity in the context of various optoelectronic applications, such as photodetection and light harvesting,130−134 ultrafast modulation,127 light emission,135 and other device applications.136 A large exciton binding energy of these materials is especially favorable for working in the strong coupling regime. First, it allows observation of excitonic effects even at room temperatures. Second, larger binding energies are beneficial for oscillator strength,137 hence leading to larger Rabi splitting with a fixed vacuum field. Accelerated spontaneous emission as well as modified PL were reported for TMDCs monolayers coupled to photonic crystals,138 tunable microcavities,139 and hyperbolic metamaterials.140 Plasmonic nanoparticles have also been employed as cavities for modification of the PL spectra.141−145 Depending on the size and the shape of the nanoparticle, the modification can lead to enhancement, no modification or quenching of the PL, demonstrating the importance of choosing the correct parameters of the plasmonic resonator to control the interaction.146 Lasing in the weak-coupling regime has been demonstrated using excitonic transitions of TMDC monolayers as a gain medium in high Q-factor cavities such as photonic crystal cavities and microdisk resonators supporting whispering gallery modes.147−149 In these reports, characterization of emitted light only encompassed spectroscopic properties, such as line width narrowing and threshold behavior. Yet, to fully I


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Figure 7. (a) Schematic representation of a unit cell of a perovskite. A and B are cations; X is an anion. (b) Illustration of two-dimensional inorganic perovskite positioned in the DBR microcavity, and angle-resolved PL spectrum measured above lasing threshold. Reprinted with permission from ref 178. Copyright 2017 ACS. (c) Angle-resolved reflectivity and PL spectra from carbon nanotubes inside Fabry−Perot cavity exhibiting Rabi splitting. Reprinted with permission from ref 179. Copyright 2016 Springer.

fields around a nanoantenna to define a small region/volume from which excitons may interact with the plasmon. However, the electric field in this region needs to contain a significant component parallel to the 2D material and should be localized in an area smaller than the effective exciton area. TMDCs exhibit great capabilities for tuning of their response. One is presented by electrostatic tuning, which affects the spectral position of the exciton resonance.165 For the case of MoS2 such tuning not only allows to control the composition of the polariton, but also shows signatures of a charged exciton being involved in the coupling, as was demonstrated in ref 164 for a MoS2 monolayer coupled with a plasmonic array assembled in a field-effect transistor, Figure 6d. This type of charged polariton possessing the fermionic nature presents higher nonlinearities than the bosonic counterpart. Temperature is another parameter that should be considered as a way of tuning the TMDCs’ excitons and plasmon−exciton interaction.170 Due to large binding energies of excitons in TMDCs, tuning can be performed from liquid helium temperatures up to room and even higher temperatures, allowing to strongly modify the polariton composition, Figure 6e.165,171 Intriguing interaction between plasmons in single Ag nanoprisms and charged excitons−trions was demonstrated via cooling the system down to liquid nitrogen temperatures.168 Such hybrid electrically charged polaritonic states may have profound implications for charge transport and optoelectronic devices by boosting the carrier mobility in a manner similar to predicted exciton transport enhancement mediated by a cavity.172,173 An alluring property of TMDCs is the ability to form excitons in different valleys of a TMDC monolayer with a welldefined helicity.125−127 This degree of freedom is inherited by polaritons in microcavities, as was evidenced by measuring helicity-resolved polariton emission from TMDCs strongly coupled with planar cavities, Figure 6f.166,174,175 This property of polaritons can be exploited for optical spin-valley Hall effect, valley switching, and bistability. Concluding the discussion of TMDCs, we note that these materials due to their monolayer composition, high oscillator strength, valley degree of freedom, and capabilities for tuning

polariton composition, namely, the contribution of WanierMott excitons, typical for TMDC, and of Frenkel exciton in organic molecules.161 This work opens possibilities to observe hybrid polaritons whose energy can be stored in different excitonic materials. Carrier separation would be easier in these mixed polaritons, a sought-after property for solar cell applications. SLRs in Au and Ag diffractive arrays have also been employed to attain strong coupling with excitons in WS2162 and MoS2163,164 monolayers, respectively. Demonstration of strong coupling between TMDCs and cavities that possess large mode volumes, where collective excitations take place, presents an initial step toward investigation of many-body phenomena involving excitonpolaritons, such as superfluidity10 and Bose−Einstein condensation.9 To that end, interaction of the cavity photons with a Fermi sea of electrons and excitons (polarons) was observed in a MoSe2 monolayer integrated in a field-effect transistor, allowing to study fundamental problems in many-body physics.167 At the single nanoparticle level, strong coupling has been recently demonstrated at room temperature between excitons in WS2 and Au nanorods,165 WS2 and Ag nanoprisms,168 and, finally, WeS2 and Ag nanorods.169 Estimations made in refs 165 and 168 indicated that the number of excitons involved in the interaction with single nanoantennas is of the order of 10. Thus, TMDCs have a potential for reaching strong coupling with just a single exciton; however, even isolation of a single exciton in these materials still presents a challenge. For other materials, isolation of a single QE requires careful manipulation, for example, as in the case of quantum dots in bow-tie gaps,103 or stochastic assembly of molecules in particle-on-mirror geometry.104 However, such approaches are not viable for TMDCs due to the mismatch between the in-plane dipole moment of the exciton and local field in the above listed hotspots and the fact that, as clearly shown for WS2, its exciton is not localized to a single unit cell, but rather extends well beyond it. As it is not clear how the exciton would change in a patterned nanometer-sized TMDC nanostructure, instead of utilizing, for example, top-down patterning of TMDC to isolate a single exciton, it may be viable to use the electromagnetic J


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Figure 8. Strong coupling to vibrational transitions. (a) Schematic representation of the strong coupling between an optical cavity mode and a molecular vibration resulting in formation of hybrid polariton states. Reprinted with permission from ref 189. Copyright 2016 ACS. (b) Left: illustration of CO vibrational transitions coupled to IR microcavity. Right: calculated spectrum of transmission through the cavity filled with polyvinyl acetate molecules. Points denote the dispersion of the upper and lower polaritons. Reprinted with permission from ref 186. Copyright 2015 Springer. (c) Splitting in the Raman spectrum of a polyvinyl acetate film coupled to an IR cavity indicating the strong vibrational coupling regime. Reprinted with permission from ref 190. Copyright 2015 Wiley.

properties like carrier transport or recombination.183 Very recently, combining a perovskite nanoplatelet with a DBR cavity has enabled observation of polariton lasing, Figure 7b, which was evidenced by macroscopic ground state occupation and the buildup of long-range spatial coherence.178 Carbon nanotubes are another example of excitonic material for strong light-matter interaction. High oscillator strength and large exciton binding energy make them a favorable material for realization of strongly coupled systems in the near-IR region. The possibility of formation of hybrid light-matter states involving carbon nanotubes was recently confirmed in experiments with diffraction-limited planar microcavities, Figure 7c,179 and plasmonic crystals.184 Such coupled systems hold the potential for novel optoelectronic devices and polariton lasing. Indeed, polariton thermalization and emission, a precursor of polariton lasing, has been recently observed in electrically pumped planar microcavities.185 Vibrational Transitions. In the above examples, the strongly coupled structures incorporated excitonic materials that employ electronic transitions of molecules, quantum dots, or semiconductors. In general that does not need to be the case, as any type of optical transition that is associated with a given oscillator strength can be used for reaching the strong coupling regime. Indeed, recently strong coupling between optical cavities and vibrational transitions of molecules has gained considerable interest. These represent mid-IR transitions between ground and excited states of molecules associated with vibrational motion of interatomic bonds. In a fashion similar to electronic systems, coupling these transitions to a mid-IR cavity should result in formation of vibropolariton hybrid states, Figure 8a. A substantial difference with respect to electronic transitions is that the latter are well approximated as two-level systems, while vibrational oscillations due to their

are a very promising class of excitonic structures for the development of novel strongly coupled systems with intriguing behavior. Furthermore, their monolayer nature and high mechanical resistance allows these materials to be integrated in flexible devices. Perovskites and Nanotubes. Perovskites are another class of interesting two-dimensional excitonic materials. These are organic−inorganic halide semiconductor compounds of the form ABX3, where A is an organic cation, B is a metallic cation, and X is the halide anion, Figure 7a; their band gap can be easily tuned by changing the halide anion X.176 These materials draw enormous attention for their high absorption and are becoming a building-block for optoelectronics and photovoltaic research.177 Nevertheless, despite these remarkable properties great efforts need to be made to increase their stability at ambient conditions. Due to their high transition dipole moment and low binding energy, perovskites also represent considerable interest in the context of Rabi splitting.180 Similarly to TMDCs, perovskites are extended materials that should be treated as ensembles of QEs. But unlike TMDCs, the effective concentration of these QEs can be controlled at the fabrication stage via choosing appropriate initial concentrations of the compounds and spincasting conditions. Layered perovskites have been combined with metallic Fabry−Perot cavities, which results in the hybridization of the cavity photon and the perovskite exciton.181 More complex geometries like metallic gratings covered by perovskites have shown strong coupling between excitons and surface plasmon polaritons in the grating.182 Moreover, an exciton and its image exciton in the metal was shown to form a biexciton that also strongly couples to light. Nanopatterning a perovskite has also led to the observation of photoinduced strongly coupled polarons that can affect K


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Figure 9. Our expectations for novel nanocavities and potential applications of the strong coupling regime in optoelectronic processes. (a) Realization of strong coupling between a QE and a graphene nanoflake antenna. (b) Enhancement of exciton transport between plasmonic hotspots in the strong coupling regime. (c) Illustration of enhancement of charge transport reported in ref 215. Copyright 2015 Springer. (d) Modification of chemical reactivity via coupling vibrational transition to an optical cavity. (e) Illustration of photon blockade with a plasmonic nanoantenna.

the recent work of Dunkelberger et al.195 pump−probe infrared spectroscopy of the cavity-coupled CO bond in a W(CO)6 molecule was performed in order to measure polariton lifetime. Another recent work reported observation of strong coupling between surface plasmon polaritons and molecular vibrations in organic polymer films.196 A quantum mechanical approach for interaction between an optical cavity and vibrational transitions was developed by del Pino et al.197 Dark vibrational polariton states were shown to be almost completely decoupled from bright polaritons that behave like a single isolated oscillator. In addition, the impact of material absorption and cavity design on strong vibrational coupling was studied.198 On the basis of simple theoretical calculations, a criterion for selecting molecules appropriate for strong vibrational coupling was established. The strong coupling regime modifies the spectrum of vibrational excitations of a molecule and, as a result, the strength of the chemical bond between atoms f ∼ meffν2, with ν being the frequency of the lowest excited (hybrid) vibrational state. Since many chemical reactions start with breaking an interatomic bond, Rabi splitting of vibrational transitions may have profound implications for chemistry, providing an additional tool for probing and controlling chemical reactivity, similarly to strong coupling of an electronic transition to the vacuum field, which has been shown to modify chemical reaction rates.16 Supporting evidence for this hypothesis has come recently from experiments on a deprotection reaction of a simple alkynyl-silane, where its SiC vibrational bond was strongly coupled to an IR microfluidic cavity. The reaction rate at different temperatures was clearly shown to be reduced by coupling to the cavity. Ultrastrong coupling of vibrational transitions in molecular liquids, the regime characterized by Rabi frequency comparable to the transition frequency, was reached with Rabi splitting of about 1/4 of the transition frequency.199 Measurements revealed contributions to the counter-rotating terms in the Rabi Hamiltonian on the polariton states spectrum, what is not captured in the JC or TC picture. Moreover, an energy gap in the resulting polaritonic spectrum was observed, which is

bosonic nature can occupy higher energy levels. However, as long as we limit ourselves to low excitations, only the first excited state is populated, and the physics of the system is similar to that of two-level quantum emitters. To describe this interaction, the standard IR absorption selection rules apply, which upon the Taylor decomposition of the dipole moment ⟨p̂⟩ requires the first derivative with respect to the nuclear coordinate Q to be nonzero in order for the vibrational transition to be allowed. The dipole moment expectation value reads ⟨p ̂⟩ = ⟨p ̂⟩0 +

( ) Q , where the subscript 0 denotes ∂⟨p ̂⟩ ∂Q

0

that the value is taken at the equilibrium position. As a result, the coupled system is characterized by the coupling constant g given by186 ⎛ ∂⟨p ̂⟩ ⎞ ℏg = ,⎜ ⎟Q ⎝ ∂Q ⎠0 zpf

(10)

Here, , is the cavity vacuum field as previously, and Q zpf = ℏ/(2m * × ω) is the zero-point fluctuation amplitude of the molecular oscillator with m* being the reduced mass. We should emphasize here that in contrast to surfaceenhanced Raman scattering, where optical modes of plasmonic cavities interact efficiently with the Raman dipole,187,188 in the vibrational coupling picture the vibrational transitions themselves couple to long-wavelength mid-IR modes. The pioneering observations of vibrational strong coupling were reported by Shalabney et al.186 for an ensemble of polyvinyl acetate molecules placed between two Au−Ge mirrors, Figure 8b. The cavity mode was coupled to the CO bond of the molecules, which has a vibrational transition at frequency of 1740 cm−1. Linear transmission measurements revealed a Rabi splitting of ≈20.7 meV for normal incidence, Figure 8b. This observation was followed by similar experimental studies of strong vibrational coupling of chemical bonds in poly(methyl methacrylate),191 organometallic complexes,189 proteins,192 and various molecular liquids.193 Strong coupling of vibrational modes of two different organic materials placed in the same microcavity has also been observed.194 In L


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quantum emitters has not been employed for studies of Rabi splitting yet. After acceptance of the manuscript we became aware of the recent study [Nano Lett. 2017, 17, 5521−5525] demonstrating strong coupling between graphene quantum dots and a planar microcavity. Recently studied van der Waals metal−organic frameworks214 thanks to high exciton binding energy, long lifetime, and relatively narrow line width also offer an interesting playground for realizations of strong light− matter coupling effects. Promising applications for strong light−matter coupling are beginning to be explored. Strong coupling between QEs and cavities was shown to have implications for various optical and electronic processes. In particular, efficient second-harmonic generation from porphyrin molecules strongly coupled to a planar cavity was demonstrated recently.216 The SHG spectrum exhibited two peaks corresponding to two polaritonic states; interestingly, emission intensity of the lower cavity polariton was significantly larger than that of the upper polariton. The underlying nature of such enhancement, however, has not been discussed. Other nonlinear processes such as third harmonic generation217 and four-wave mixing are likely to exhibit interesting behavior in the strongly coupled regime. Another set of exciting applications for strong light-matter coupling involves exploiting exciton transport in nanophotonic systems.173,218 It was theoretically predicted that exciton diffusion can be enhanced by coupling QEs both to planar Fabry−Perot microcavities172,173 and plasmonic nanoparticles.218 In the latter case, the presence of hotspots at the surface of a plasmonic particle enables efficient transport of excitons between these subwavelength hotspots with an ultrafast (∼10 fs) rate, Figure 9b. These predictions are expected to have possible implications for excitonic transistors and heat transport. An unsettled question is whether this effect explains the recent observation of charge transport enhanced by strong coupling to the vacuum field, Figure 9c, whose underlying physical mechanism remains unclear.215 There are intriguing opportunities to employ Rabi splitting for biological applications.219 For example, as a recent observation of strong coupling between excitonic states of chlorosomes of photosynthetic bacteria and an optical cavity suggests,220 it may be possible to create “living polaritons” and study the effect of strong light−matter interaction on bacterial growth. In addition, previous results on strong coupling between living species and microcavities have been performed in the visible range. However, most electronic transitions in biologically relevant molecules happen in the UV. For this reason, we anticipate a demonstration of strong coupling in the UV region, which can be done for instance by usage of aluminum-based plasmonic or photonic cavities. As we note above, strong vibrational coupling may offer novel opportunities for controlling chemical reactivity, Figure 9d. Only recently in experiment with the deprotection reaction of an alkynyl-silane it was demonstrated that this phenomenon can actually affect the rate of chemical reactions.221 However, the full potential of strong vibrational coupling in controlling chemical reactivity remains to be explored. We also envision that more comprehensive investigation of the so-called dark polaritons45,46 may reveal novel physical effects. It is still not entirely clear what role these light-matter states play in the behavior of strongly coupled systems. Theoretical efforts have shown that these states, despite not having a photonic component in their wave functions, may exhibit a delocalized macroscopic character, similar to bright

absent in the usual strong coupling regime and is a clear signature of ultrastrong coupling.200 On the other hand, strong coupling between an electromagnetic mode and vibrational transitions may be also manifested in the Raman spectrum of the system.201,202 Strong vibrational coupling leads to modification of the Raman spectrum, whose main observable signature is the emergence of two polariton sidebands in the Raman spectrum. Such splitting of the Raman emission was observed in an experiment employing a polyvinyl acetate film coupled to an IR Fabry− Perot cavity, Figure 8c.190 Finally, strong vibrational coupling was shown to have very interesting consequences on the operation of Raman lasers. In a conventional Raman laser an input pump beam is converted into coherent Stokes emission at slightly smaller energy, while the excess of energy is incoherently radiated in the form of phonons. In the strongly coupled Raman laser studied by del Pino et al.203 this excess is stored in the vibropolariton mode, which is converted into an additional coherent beam at mid-IR frequencies, creating a device analogous to an optical parametric oscillator. In closing this section, we emphasize that vibropolariton strong coupling seems to be an interesting route to explore. We anticipate to see demonstrations of strong vibropolariton coupling in open cavities and in coherent devices spanning not only mid-IR but also the THz range.

■

DISCUSSION AND OUTLOOK Realization of strongly coupled light−matter systems is not limited to the above-mentioned materials. Looking ahead, we expect realizations of hybrid light-matter states in a wider variety of platforms allowing stable, reproducible and tunable optical behavior. There are examples of other optical nanoresonators that can be employed for designing strongly coupled systems. One such example that has not been addressed above is presented by high-index dielectric nanoantennas that support Mie resonances.204 Due to relatively large mode volumes of Mie resonances,205 these nanoantennas have not received significant attention in the context of strong coupling. Nevertheless, Rabi splitting was recently observed in heterostructures formed by silicon nanosphere coated with Jaggregate.206 A highly intriguing open question is represented by realization of strong coupling between a QE and a graphene nanoflake resonator, as depicted in Figure 9a. Owing to excitation of extremely localized surface plasmons in mid-IR, graphene nanodisks behave as nanocavities with an ultrasmall mode volume and a large vacuum field.207,208 In light of these properties, in a number of theoretical efforts the feasibility of reaching the strong coupling limit with an extended excitonic system209 and even with a single emitter207,210 was predicted. Although strong coupling of phonon modes in hexagonal boron nitride to a graphene metasurface has been recently observed,211 realization of single-emitter strong coupling still presents an important challenge. On the other hand, graphene quantum dots, flakes of graphene with small (few nanometers) lateral dimensions, represent an emerging class of excitonic materials whose transition frequency can be tuned in a wide range spanning from the UV down to the near-IR range via adjusting lateral size of the flake.212 Theoretical studies have predicted large oscillator strengths of such quantum dots in the near-IR region of the order of 1, corresponding to a transition dipole moment of ≈10 D.213 To the best of our knowledge, this class of M


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polaritons.45 In addition, it is believed that dark polaritonic states, although being “invisible” in elastic scattering (such as DF measurements), may exhibit PL and explain features of PL spectra of coupled systems.222 In systems containing N ≫ 1 QEs the density of dark states is usually very high near the bare transition frequency. Therefore, if one finds a way to employ these states for efficient light−matter interaction, that would be a very important step toward practical applications of collective strong coupling. On the other hand, interesting theoretical results were obtained for interaction of QEs with dark modes of a spherical nanoparticle. Interaction of QEs placed very close to a metallic surface usually result in nonradiative loss into high-order modes of the nanoparticle known as quenching. However, this conclusion applies only in the weak coupling regime. As was shown by Delga et al.,223 collective strong coupling of QEs with the dipole mode can arise even at short distances to the nanoparticle surface. Finally, one of the major challenges in the field of strong coupling is presented by reaching stable Rabi splitting in nanostructures with single emitters. Although few observations of strong coupling with single quantum dots or molecules coupled to plasmonic antennas have been claimed,103,104,106 the value of Rabi splitting varied a lot between samples in these reports (see Table 1), what was mainly the result of a degree of randomness in their assembly. This is also a tangible issue for TMDCs where even isolation of a single exciton can be a problem, as noted above. Creating a robust single-emitter design with a stable and reproducible value of Rabi splitting would be a major milestone in the field. We envision that such a demonstration would be an essential step toward quantum optical experiments such as photon blockade, Figure 9e, and various ultrafast pump−probe experiments.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Tomasz J. Antosiewicz: 0000-0003-2535-4174 Timur Shegai: 0000-0002-4266-3721 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Authors acknowledge fruitful discussions with Alexander E. Krasnok and Oleg V. Kotov. D.G.B., M.W., J.C., and T.S. acknowledge support from Knut and Alice Wallenberg Foundation. D.G.B. acknowledges support from the Russian Foundation for Basic Research (Project No 16-32-00444). T.S. acknowledges financial support from the Swedish Research Council (Vetenskapsområdet, Grant No. 2012-0414). T.J.A. thanks the Polish Ministry of Science and Higher Education for support via the Iuventus Plus Project IP2014 000473 as well as the Swedish Foundation for Strategic Research via the project SSF RMA 11.

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