Letter pubs.acs.org/NanoLett
Bright Phonon-Tuned Single-Photon Source Simone Luca Portalupi,† Gaston Hornecker,‡ Valérian Giesz,† Thomas Grange,‡ Aristide Lemaître,† Justin Demory,† Isabelle Sagnes,† Norberto D. Lanzillotti-Kimura,† Loïc Lanco,†,§ Alexia Auffèves,*,‡ and Pascale Senellart*,†,∥ †
CNRS-LPN Laboratoire de Photonique et de Nanostructures, Route de Nozay, 91460 Marcoussis, France CEA/CNRS/UJF joint team “Nanophysics and Semiconductors”, Institut Néel-CNRS, BP 166, 25 rue des Martyrs, 38042 Grenoble Cedex 9, France § Département de Physique, Université Paris Diderot, 4 rue Elsa Morante, 75013 Paris, France ∥ Département de Physique, Ecole Polytechnique, F-91128 Palaiseau, France Downloaded by UNIV OF NEBRASKA-LINCOLN on September 7, 2015 | http://pubs.acs.org Publication Date (Web): September 4, 2015 | doi: 10.1021/acs.nanolett.5b00876
‡
S Supporting Information *
ABSTRACT: Bright single photon sources have recently been obtained by inserting solid-state emitters in microcavities. Accelerating the spontaneous emission via the Purcell effect allows both high brightness and increased operation frequency. However, achieving Purcell enhancement is technologically demanding because the emitter resonance must match the cavity resonance. Here, we show that this spectral matching requirement is strongly lifted by the phononic environment of the emitter. We study a single InGaAs quantum dot coupled to a micropillar cavity. The phonon assisted emission, which hardly represents a few percent of the dot emission at a given frequency in the absence of cavity, can become the main emission channel by use of the Purcell effect. A phonon-tuned single photon source with a brightness greater than 50% is demonstrated over a detuning range covering 10 cavity line widths (0.8 nm). The same concepts applied to defects in diamonds pave the way toward ultrabright single photon sources operating at room temperature. KEYWORDS: Purcell enhancement, photon, quantum dot, micropillar cavity, phonon, NV centers
T
source, by reducing the time interval between consecutive excitation pulses.12 Exploiting the Purcell effect requires that the optical transition of the emitter is spectrally matched to the resonance of the cavity mode. Such condition is difficult to obtain with solid-state emitters due to the large dispersions in their emission frequencies. However, solid-state emitters also strongly interact with their environment: in particular, phonon-assisted emission is observed in every system. The phonon side bands (PSB) cover a spectral range of few nanometers for QDs at cryogenic temperature13−15 to more than 100 nm for defects in diamond.16 Yet, at a given frequency, the phonon assisted emission represents at best few percents of the emission. Here, we evidence that a high quality factor cavity can greatly increase the phonon assisted emission and allow efficient extraction, and this for any spectral position of the cavity within the PSB. We experimentally demonstrate these concepts in a technologically very mature system, namely InGaAs QDs in pillar cavities, for which single photon source with a brightness exceeding 50% over 10 cavity line widths is
rue single photon sources, devices that emit only one photon at a time, are key components for quantum applications. Efficient single photon generation is at the heart of quantum cryptography and metrology, and indistinguishable single photons open the way to scalable linear optical quantum computing and long distance quantum communications. Atomic-like emitters such as semiconductor quantum dots (QDs), defects in diamond or colloidal nanocrystals are promising systems to build such single-photon sources in the solid state. Although the quantum statistics of the emitted light has long been established in each system,1−3 a major challenge for applications is to efficiently collect the photons. This emission is almost isotropic if no engineering of the electromagnetic field surrounding the emitter is used. Recently, two strategies have allowed reaching very high extraction efficiencies: inserting the emitter in a dielectric antenna like a photonic nanowires4−7 or in an optical microcavity.8,9 In the latter approach, coupling the emitter to the confined optical mode of a microcavity enhances its emission rate into the mode by the Purcell factor FP.10,11 For an unchanged emission rate in the other modes, the photon extraction into the cavity mode is β = FP/(FP + 1). This approach based on the acceleration of spontanenous emission offers the attractive possibility to increase the maximum operation rate of the single photon © XXXX American Chemical Society
Received: March 4, 2015 Revised: July 23, 2015
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DOI: 10.1021/acs.nanolett.5b00876 Nano Lett. XXXX, XXX, XXX−XXX
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and wavelength. For each temperature, two emission lines are observed, corresponding to the QD excitonic ZPL (X) and the PSB enhanced by cavity mode (C). To account for these two emission peaks, the QD is modeled by a two-level system coupled to a longitudinal acoustic phonon bath and to the electromagnetic field (Figure 2). The density of states of the
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reported. We then theoretically extend our approach to the case of a NV center at room temperature. We study a single InGaAs quantum dot deterministically positioned at the maximum of a pillar cavity fundamental mode with 50 nm accuracy by means of the in-situ lithography technique.17 The vertical structure for the cavity presents an adiabatic design of mirror layers that allows minimizing sidewall losses18 (see Figure 1a and Supporting Information). As shown
Figure 2. Quantum dot is considered as a two-level system and the phonon bath and electromagnetic field are described as continua. The density of states of the electromagnetic field is modified by the cavity and is peaked around its resonance frequency ωc. The coupling to the phonons is treated nonperturbatively using the independent bosons model while the coupling to the electromagnetic field is treated in first order perturbation theory (see text and Supporting Information).
latter is modified by the cavity and peaked around its resonance wavelength λC, detuned from the ZPL by δX,C = λX − λC. The coupling to the phonons is described using the independent bosons model,26 whereas the photon emission is treated in first−order perturbation theory, in the weak coupling regime (see Supporting Information). The QD exciton state can radiatively recombine at its intrinsic frequency ωX with no associated phonon process giving rise to the ZPL or at a different energy by emitting or absorbing one or several phonons corresponding to the PSB. As shown in ref 25, the emission spectrum presented in Figure 1c is the product of the bare cavity spectrum SC(λ) (red line) and the QD emission PSB spectrum in the bulk SQD (λ) = SZPL QD + SQD (blue line) where the two terms correspond to the ZPL and the PSB. The total emission spectrum (black line) presents therefore two emission peaks. Because the PSB spreads over a few nanometers spectral range, largely overcoming the cavity width γC = 80 pm (measured in reflectivity and corresponding to a Q factor of Q = 12 000), the second term gives rise to an emission peak roughly centered at the cavity resonance. This emission line, corresponding to the PSB enhanced by the cavity, is usually called the cavity line (C). Note that emission within the cavity line can also arise from multiexcitonic states in the large detuning range.27,28 Here, we limit our discussion to detuning ranges corresponding to the PSB spectral range, typically a few millielectronvolts, for self-assembled InGaAs QDs. The enhancement of the phonon assisted emission gives also rise to an acceleration of spontaneous emission when the ZPL is spectrally detuned from the cavity mode as observed for QDs in photonic crystal cavities.19,22 The detuning δX,C between the cavity line and the ZPL is varied using the temperature. Figure 1d presents the measured enhancement of the excitonic decay
Figure 1. (a) Schematic of the system under study: a single quantum dot deterministically positioned in a micropillar cavity. The right plot presents the layer thickness W normalized to the nominal W0 = λ/4n thickness (see Supporting Information). The arrows indicate the radiative decay rate into the cavity mode Γ∥ and into the other modes Γ⊥. (b) Emission intensity of the device as a function of temperature and detuning δX,C. (c) Black: calculated emission spectrum S(λ) for a QD exciton line coupled to cavity line, with δX,C = −0.5 nm. The blue line is the QD spectrum SQD(λ) of the QD coupled to the phonon bath but not coupled to the cavity; the red line is the cavity spectrum SC(λ). (d) Measured radiative decay time normalized to the decay time in the planar cavity τ0X/τX − 1 as a function of temperature (top) and detuning δX,C (bottom). The dotted line is Purcell factor for an ideal two level system FP(δ X,C) = FP Feff P
γc2 2 γc2 + 4δ X,C
. The solid line is the modeled
including phonon mechanisms.
below, this allows reaching high extraction efficiencies with high Purcell factors. Electron−hole pairs in QDs couple to acoustic phonons: PSB are observed in photoluminescence (PL) spectroscopy,13−15 resulting from the emission of a photon together with the emission or absorption of one or more phonons. In InGaAs QDs, PSB represent typically 10% of the total emission at 10 K and they spread over a spectral range of a few nanometers, as opposed to the spectrally narrow zerophonon line (ZPL). PSB have led to interesting new features when the QD is inserted in a cavity.19−25 One feature is the observation of two emission lines when the QD and the cavity are detuned as shown in Figure 1b. The QD-pillar device is excited in the p-shell around 905 nm, using a picosecond TiSapphire laser with a repetition rate of 82 MHz. The emission intensity of the device is presented as a function of temperature B
DOI: 10.1021/acs.nanolett.5b00876 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters rate into the cavity mode as a function of δX,C. This experimentally measured Purcell factor is defined as τX0 − τX(δ X,C) 0 and τX = 1.3
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FPeff (δ X,C) =
1 with τX the measured decay time of
ns the X decay time in the planar cavity. the X line As shown in Figure 1d, a strong enhancement of the Feff P is observed, reaching 10 ± 2 at resonance (symbols). Away from resonance, the experimental Purcell factor Feff P does not follow the Lorentzian dependence one would expect for an ideal twolevel system, but evidence the imprint of phonon-assisted mechanisms, with a noticeable enhancement of spontaneous emission out of the ZPL-cavity resonance. This behavior is fully accounted for by the model, where both the zero phonon line and the phonon assisted emission channels experience Purcell effect with enhanced decay rates into the cavity mode Γ∥ZPL and Γ∥PSB (see Supporting Information). Phonon coupling thus leads to an enhanced total exciton decay rate Γtot = ΓZPL + ΓPSB + Γ⊥ on a large ∥ ∥ detuning range. Γ⊥ is the emission decay rate for both ZPL and PSB emission mechanisms into the other optical modes of the electromagnetic field and is close to the emission decay rate in bulk material.10 As shown in Figure 1c, the experimentally measured Purcell factor is well reproduced by an effective Purcell factor
FPeff (δ X,C)
=
Γ ZPL + Γ PSB Γ⊥
Figure 3. (a) Emission spectrum measured at 12 K at an excitation power close to the X saturation. (b) Photon correlation measurements: exciton autocorrelation (blue); cavity line autocorrelation (red); exciton-cavity cross correlation (black). Experimental curves have been vertically shifted for clarity. (c) Calculated total spectrum (dashed line) with the contributions from the X line (solid black) and XX line (dotted red) to the cavity emission. (d) Calculated values of g(2) C,C(0) for different cavity biexciton detunings. The X−C blue detuning is fixed to δX,C = −0.5 nm and the temperature is set to 12 K. The pillar under study shows a cavity-biexciton detuning δXX,C = 0.5 nm.
.
As seen in Figure 1b, a strong signal is observed at the cavity energy out of the ZPL resonance, in a regime where the spontaneous emission is significantly accelerated. In the following, we evaluate the performances of a single photon source based on such Purcell enhanced phonon assisted emission. First, we study the purity of the source. Figure 3a presents the measured emission spectrum at 12 K for an excitation power close to saturation of the X line. Three emission lines are observed: the exciton X, the biexciton XX, and an intense cavity line C. To confirm the nature of each emission line, photon correlation measurements are performed (Figure 3b). The top curve shows the exciton autocorrelation function g(2) X,X(τ) and evidence a good single photon purity with g(2) X,X(0) = 0.03 ± 0.02. Cross correlation of the X and C lines (bottom curve) also shows a strong antibunching g(2) C,X(0) = 0.12 ± 0.03, showing that the emission in the cavity mostly arises from the X phonon sideband. Finally, the middle curve shows the autocorrelation curve for the cavity line: a strong antibunching with g(2) C,C(0) = 0.20 ± 0.05 is observed: the cavity enhanced phonon assisted emission is a good single photon source. The brightness of this single photon source is now precisely measured. To do so, the experimental setup has been carefully calibrated under a pulsed excitation at 82 MHz (see Supporting Information). The brightness B, defined as the number of photons collected per pulse in the collection lens is derived from the number of counts on the detector I, using
emission at 12 K, when the X line is blue detuned from the cavity line by δX,C = −0.5 nm. At saturation, a brightness as high as BC(δX,C = −0.5 nm) = 35 ± 3% is obtained. Such high value shows that the cavity does not act only as a spectral filter. Indeed at 12 K, the PSB represents 15% of the overall QD emission and spreads over a few nanometer spectral range. We can estimate that a cavity filtered phonon assisted emission would be bounded by SQD(ωcav)κ/Γ ≈ 2%. Cavity quantum electrodynamics allows a very large fraction of the QD emission to be emitted through phonon assisted mechanisms. For applications where indistinguishable photons are not required, like short distance quantum communications, quantum cryptography, or quantum metrology, one can extract and use indifferently the photons emitted by the ZPL and by the PSB. The brightness of the detuned ZPL line reaches BX(δX,C = −0.5 nm) = 5% at saturation (red triangles) so that a total brightness BX(δX,C = −0.5 nm) + BC(δX,C = −0.5 nm) of 40 ± 4% (red crosses) is obtained for a detuning representing six cavity line widths. We now study the brightness of the source as a function of the detuning. The total brightness B(δX,C) = BX(δX,C) + BC(δX,C) is plotted on Figure 4b; a brightness exceeding 50% is demonstrated over a [−0.4 nm, 0.4 nm] detuning range. As explained in ref 8, the source brightness is given by B = βeff(Q/ Q0)qX where βeff is the fraction of emission into the mode, the Q/Q0 term accounts for the sidewall losses (Q0 being the planar cavity quality factor), and qX is the QD X state occupation factor at saturation. In the presence of phonon coupling
B = Iη 1 − g(2)(0) where η = 1.44 ± 0.1% is the overall setup detection efficiency and the last term is the correction from multiphoton events. Figure 4a presents the brightness of various lines as a function of power (top panel), with the corresponding g(2)(0) (bottom panel) for two detunings. The black symbols present the case where the X line is resonant to the cavity mode (δX,C = 0). At saturation, the corrected brightness amounts to BX(δX,C = 0) = 74 ± 7% collected photon per pulse. The red squares present the brightness and g(2) C,C(0) for the cavity enhanced phonon assisted
β eff = C
Γ ZPL + Γ PSB Γtot
results from accelerated emission into the DOI: 10.1021/acs.nanolett.5b00876 Nano Lett. XXXX, XXX, XXX−XXX
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coupled to pillar cavities, as shown in Supporting Information for different Purcell factors. For the device under study, the purity of the single-photon source g(2) C,C(τ) ≈ 0.2 at 12 K is limited by the small X−XX binding energy. Indeed, careful analysis of the zero delay peak in g(2) C,X(τ) in Figure 3b shows a strong temporal asymmetry, with the main signal for positive delays. Moreover, the area of the central peak is roughly half that of the cavity autocorrelation curve g(2) C,C(τ). This observation is the signature of the radiative cascade between the XX and X lines. Both the X and XX phonon sidebands feed the cavity line. At 12 K, because the XX line is on the low energy side of the cavity mode, the phonon processes resonant with the cavity arise from the absorption of a phonon, a process less efficient than phonon emission. Figure 3c shows the calculated contributions of various phonon sidebands to the total spectrum. From these spectra, the calculated g(2) C,C(0) is 0.27 (Figure 3d), close to the experimental value measured here for a X−XX binding energy below 1 nm. As a result, the purity of the source would be greatly enhanced for QDs presenting higher XX binding energy,29 as shown in Figure 3d presenting the calculated g(2) C,C of the cavity emission line at 12K for a large biexciton-cavity detuning range. A higher degree of purity could also be reached by removing any biexciton contribution, for instance using resonant pumping scheme such as the one used in ref 30, where exciting the neutral exciton leads to an efficient transfer to the charged exciton state and subsequent photon emission. Most importantly, the scheme proposed here is very well suited for the fabrication of single photon sources operating at room temperature using NV centers in diamonds or colloidal QDs. In these systems, no emission arises from multiexcitonic states such that one could obtain both bright and pure photon source using Purcell enhanced phonon assisted emission. To illustrate this possibility, we apply the same concepts to NV centers, turning their spectrally broad phonon sideband into a resource.31 A room temperature emission spectrum can be computed using the fit parameters given in ref 32 (see insert of Figure 5): the PSB spreads over 100 nm and represents more
Figure 4. (a) Top: collected photons per pulse for different lines. Black squares: X line for δX,C = 0. Red symbols are measured for nonzero detuning (δX,C = −0.5 nm). Red squares: cavity line. Red triangles: X line. Red crosses: total brightness, sum of C and X lines. Bottom: corresponding measured g(2)(0) for X at δX,C = 0 (black squares) and C at δX,C = −0.5 nm (red circles). (b) Total brightness B = BX + BC (black squares, left scale) compared with calculated mode coupling βeff (right scale) as a function of the detuning normalized to the cavity line width (δX,C/γC) for different values of FP. The corresponding effective Purcell factors at resonance (32 K) are also indicated.
cavity mode from the ZPL and PSB. βeff is plotted on the right scale of Figure 4b for various nominal Purcell factors FP. These calculations underline the importance of the Purcell effect in the efficient funneling of the phonon assisted emission. For very low nominal Purcell factors, the brightness of the source out of the ZPL-cavity resonance is calculated to be very low, approaching the limit case of a spectral filtering effect. On the contrary, for large Purcell factors, very high brightnesses can be obtained from the phonon assisted emission. To compare the measured brightness to the model, we deduce (Q/Q0)qX close to zero detuning. The experimental observations are well reproduced considering an effective Purcell factor around 12, a figure consistent with the effective Purcell factor measured at resonance. Using a nominal (effective) Purcell factor of 103 (37) would allow obtaining a brightness exceeding 60% in a detuning range covering 15 times the cavity line width. We note that an increased bandwidth for bright source operation is observed in a reproducible way for single QDs deterministically
Figure 5. Case of a NV center coupled to a cavity at 685 nm with a quality factor Q = 250. Calculated fraction of emission into the mode βeff as a function of nominal Purcell factor FP. Insert: Spectrum of a NV center at room temperature computed using the fit parameters given in ref 32.
than 90% of the total emission.16 We consider a cavity mode at 685 nm with a Q factor of 250 and various mode volumes, corresponding to various nominal Purcell factors. Figure 5 presents the fraction of emission into the mode βeff as a function of the nominal Purcell factor. The fraction of emission into the mode is shown to reach very high values (typically D
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above 40%) for a nominal Purcell factor FP above 20, a value fully compatible with the current state-of-the-art for photonic crystal or open access cavities.33−35 This experimental and theoretical study clearly shows that cavity quantum electrodynamics is a very promising strategy to optimize solid-state single photon sources, even at high temperature where emitters are spectrally broad. We finally note that such cavity funneling approach can also be extended to the generation of indistinguishable photons, with an efficiency greatly surpassing spectral filtering techniques, as recently theoretically proposed.36
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ASSOCIATED CONTENT
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S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b00876. Sample fabrication, setup description, calibration and brightness, spontaneous emission of a quantum dot coupled to a continuum of phonons in a cavity, photon correlations in the cavity mode at high power, and other examples of phonon tuned sources. (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail: alexia.auff
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was partially supported by the French ANR QDOM, ANR P3N CAFE, the Fondation Nanosciences de Grenoble, the ERC starting grant 277885 QD-CQED, the CHISTERA project SSQN, the RENATECH French network, the Laboratoire d’Excellence NanoSaclay, the EU-project WASPS. The authors aknowledge D. Valente for help in the theoretical modeling.
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REFERENCES
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DOI: 10.1021/acs.nanolett.5b00876 Nano Lett. XXXX, XXX, XXX−XXX