Article Cite This: J. Phys. Chem. A 2019, 123, 5918−5927
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State-Selective Polariton to Dark State Relaxation Dynamics Published as part of The Journal of Physical Chemistry virtual special issue “Pacific Conference on Spectroscopy and Dynamics”. Bo Xiang,‡ Raphael F. Ribeiro,† Liying Chen,† Jiaxi Wang,† Matthew Du,† Joel Yuen-Zhou,† and Wei Xiong*,†,‡ †
Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, United States Materials Science and Engineering Program, University of California, San Diego, La Jolla, California 92093, United States
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‡
S Supporting Information *
ABSTRACT: The modification of vibrational dynamics is essential for controlling chemical reactions and IR photonic applications. The hybridization between cavity modes and molecular vibrational modes provides a new way to control molecular dynamics. In this work, we study the dynamics of molecular vibrational polaritons in various solvent environments. We find the dynamics of the polariton system is strongly influenced by the nature of the solvents. While the relaxation from upper polariton (UP) to dark modes is always fast ( Γvib or Γcav,10 meaning the light−matter coupling strength, g, needs to be larger than the homogeneous full-width-at-half-maximum (fwhm) of both modes (Γvib and Γcav). When this condition is satisfied, two new bright hybrid eigenstates, known as polaritons, are formed with their own characteristic transition frequencies (Figure 1a). The mode with lower frequency is referred to as lower polariton (LP), and the one at higher frequency is called upper polariton (UP). Because of the mixing between the vibrational and cavityphoton wave functions, molecular vibrational polaritons simultaneously feature properties of both photons and molecules, which leads to fascinating emergent phenomena. Notable examples include manipulation of rate and selectivity of organic deprotection reactions inside cavities.11−14 In addition, the optical nonlinearity of molecular polaritons can © 2019 American Chemical Society
be controlled through macroscopic parameters such as cavity longitudinal length and molecular concentration,15 whereas such effects are absent from the weak coupling regime or pure molecular systems.16−22 Further developments of many of these new features hinge on a deep understanding of the polariton dynamics. However, molecular vibrational polariton dynamics are complicated by virtue of the dark states; for example, excited polariton states only last a short duration and then decay by either photonic leakage or relaxation to dark states. Having relaxed to the latter, the system loses it photonic character, and most novel polaritonic features disappear. Thus, a sufficiently long time scale for the relaxation of polaritons into the dark reservoir is essential for certain strategies of cavity chemistry4,12,14 and polariton photonic applications.23−29 To understand the microscopic basis of dark states, we will briefly go through the quantum mechanical description of polaritons. For more detailed theoretical descriptions, we refer to the works in several review papers.4,10,24 The Hamiltonian of the polariton system can be written as1,2,5 Received: May 14, 2019 Revised: June 18, 2019 Published: June 21, 2019 5918
DOI: 10.1021/acs.jpca.9b04601 J. Phys. Chem. A 2019, 123, 5918−5927
Article
The Journal of Physical Chemistry A
Figure 1. Vibrational polariton 2D IR spectroscopy. (a) Schematic diagram showing the formation of vibrational polaritons via strong coupling between molecular vibrations and the cavity modes. (b) Dispersive IR transmission curves of a microcavity filled with saturated W(CO)6 in hexane solution with various tilting angles θ. (c) Schematic illustration of vibrational polariton 2D IR spectroscopy setup (symmetric pump and probe IR incidence with same tilting angle θ). (d) Microscopic illustration of the physics of vibrational polariton formation, where the “pure gray modes” are the vibrational modes that are not strongly coupled to the cavity while the rest correspond to the strongly coupled modes with LP state (red part), UP state (blue part), and dark modes (gray). N
/̂ polariton = Ecava†̂ a ̂ +
†
N
†
∑ Evibbî bî + ∑ gi(a†̂ bî + bî a)̂ i=1
i=1
(1)
where Ecav (Evib) is the energy of the cavity-photon (vibrational dipole) modes, ↠(â) is the creation (annihilation) operator of the photon, the creation (annihilation) operator of the ith vibrational dipole is b̂†i (b̂i), and gi is the strength of interaction between the electromagnetic resonance and the vibrational dipole of the ith molecule. Without loss of generality, we take the light−matter interaction to be equal across the molecular ensemble, i.e., gi = g0.10 Molecular inhomogeneous broadening is also neglected as its effect on polariton states is suppressed, especially in the resonant regime of our interest (when Ecav ≈ Evib).10 The eigenstates and eigenvalues of this Hamiltonian can be found by diagonalizing the (N + 1) × (N + 1) matrix which represents N vibrational modes, each equally coupled to the single cavity-mode; the corresponding secular determinant reads
At zero detuning, Ecav = Evib = E0, and the eigenvalues of the Hamiltonian are ELP = E0 −
N g0 = E0 − gc
EUP = E0 +
N g0 = E0 + gc
(E Dark )i = 1,2,◦...,◦(N − 1) = E0
(3)
where gc = N g0is the collective coupling strength of an Nmolecule system in the cavity electromagnetic volume. Notably, aside from the two optically bright states (LP and UP), there are N − 1 dark states, which are nontotally symmetric superpositions of vibrational states, composed of products of N − 1 molecular wave functions in the groundstate, a single molecular excited-state, and the cavity field in its vacuum state (Figure 1d). Recent theoretical discussions1,2,4,30 indicate thatbecause of the larger density of dark states compared to polariton statesthe dark reservoir must play an 5919
DOI: 10.1021/acs.jpca.9b04601 J. Phys. Chem. A 2019, 123, 5918−5927
Article
The Journal of Physical Chemistry A
Figure 2. Pump probe, 2D IR spectra of molecular polaritons. (a) Pump-on and pump-off spectra of strongly coupled W(CO)6/hexane system in transient pump−probe experiment at t2 = 25 ps;( b) UP branch zoom-in; (c) pump−probe spectrum at t2 = 25 ps; d) LP branch zoom-in; (e) 2D IR spectrum of strongly coupled W(CO)6/hexane system at t2 = 5 ps; (f) Schematic illustration of the population transfer process when the polariton system is in equilibrium (t2 > 3 ps).
probe specific transitions, a feature which is critical to discerning the nonlinear optical response mediated by polariton or dark state excitations. We quantify relevant time scales for relaxation of LP and UP into the dark reservoir and propose a mechanism. We find that these relaxation times can be different depending on whether the initial state is LP or UP. This effect can be attributed to the stronger interactions between highly excited molecular states and the LP. More importantly, we have discovered that the relaxation from LP to the (single-excitation) dark states is highly dependent on the microscopic solvent environment and that energy harvested by the polariton states can be channeled into highly excited vibrational modes with lifetimes longer than the polaritons, a feature which is likely relevant for the manipulation of cavity chemistry.40,41
essential role in polariton dynamics and novel polariton chemistry. Both polariton and dark modes have been studied, and their spectroscopic signatures have been reported by us and others.1,2,6 In this work, building on our previous study, we describe the first state-resolved dynamics of molecular vibrational polaritons, using time-resolved pump−probe and two-dimensional infrared (2D IR) spectroscopy31,32 (experimental setup illustrated in Figure 1c). Both spectroscopies are critical to characterize molecular vibrational polariton ultrafast physics, because unlike exciton-polaritons, vibrational-polaritons feature many more intramolecular vibrational relaxation pathways that can suppress their fluorescence, making techniques10,26,27,33−39 developed for characterization of exciton-polaritons inapplicable here. 2D IR measures the third-order nonlinear optical response function of a material, providing detailed spectral and dynamical features hidden from pump−probe spectra.1,2,30 2D IR can selectively excite and 5920
DOI: 10.1021/acs.jpca.9b04601 J. Phys. Chem. A 2019, 123, 5918−5927
Article
The Journal of Physical Chemistry A
Figure 3. Dynamics of molecular polaritons in acetone. (a) 1948 cm−1 near the LP state for strongly coupled W(CO)6 in acetone, showing that the pump−probe signals decay monotonically after early time polariton coherence response (within 5 ps), indicating relaxation dynamics of the dark states. (b) 2D-IR spectra of W(CO)6/acetone in the strong coupling regime at t2 = 5 ps. (c) 2D IR dynamic traces at ωpump = ωUP and ωprobe = ωLP area (black box in b), showing the pure decay trend after 5 ps; (d) 2D IR dynamic traces at ωpump = ωLP and ωprobe = ωLP area (red box in b), showing the pure decay trend after 5 ps.
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EXPERIMENTAL METHOD Polariton Preparation. The collective coupling strength satisfies gc ∝ μ c , where μ is the transition dipole moment for a single molecular absorber and c is the molecular concentration. Thus, theoretically, the light−matter coupling can be enhanced by increasing the number of molecules in the cavity-mode volume or by reducing the cavity-mode volume itself. For practical purposes, the simplest option is the first one, and in fact, molecular infrared strong coupling is most easily achieved by placing a large number of vibrational absorbers in a Fabry−Perot cavity. In this way, the ensemble of molecular vibrations (collective vibrational polarization) can reversibly exchange energy with the mesoscopic cavity modes and reach the strong coupling regime. The W(CO)6/cavity system is prepared in an IR spectral cell (Harrick) containing two Distributed Bragg Reflector (DBR) mirrors separated by a 12-μm Teflon spacer and filled with W(CO)6 (Sigma-Aldrich) solution in the various solvents (acetone, hexane, pentane, and toluene). The DBR mirror has a ∼96% reflectivity. Because the Rabi splitting (43−48 cm−1) is larger than the fwhm of both cavity (∼11 cm−1) and W(CO)6 vibrational modes (varying from 4.5 to 20.5 cm−1), the strong coupling criterion is satisfied. Dispersion Curve Measurement. The polariton transmission spectra are highly dispersive with respect to the incidence angle or wave vector. To obtain their dispersion curve, FT IR transmission spectra were collected while varying the tilting angle of the sample cell on a rotational stage. Figure 1b shows the FT IR spectral intensity map as a function of tilting angle of the cavity filled with the hexane-W(CO)6 solution. Although this measurement was taken for the
polaritons in hexane environment, the dispersion curves are similar when other solvents are employed. Pump Probe and 2D IR Spectroscopy. The spectrometer follows the pulse shaper enabled 2D IR31,32,42 setup, and a rotational stage is added to control beam incidence angle. In the 2D IR spectrometer, two pump-IR pulses and one probeIR pulse interact with a sample sequentially to create two vibrational coherences. The first coherence is characterized by scanning the time delay between two pump-IR pulses (t1). The second coherence introduces a macroscopic polarization which subsequently emits a third order 2D IR signal. The 2D IR signal is self-heterodyned and can be detected in frequency domain. The transient pump−probe signal can be obtained by simply setting t1 = 0 fs, while to display 2D IR spectra, the free induction decay (FID) in t1 is numerically Fourier transformed. More details are shown in the SI (S3 Pump−Probe and 2D IR Spectroscopy).
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RESULTS AND DISCUSSION Transient Pump−Probe and 2D IR Spectra of Molecular Vibrational Polariton Systems. Figure 2 shows representative transient pump−probe spectra under strong coupling conditions, along with 1D transmission polariton spectra (strongly coupled W(CO)6 in hexane) under pump-on and pump-off conditions, at t2 = 25 ps (Figure 2a).1,2,6 When the pump is turned on, the UP resonance undergoes a shift toward a lower frequency (Figure 2b). Under the same condition, the LP line shape acquires a small positive shoulder appearing at higher frequency, which corresponds to a blue shift (Figure 2d). These shifts are small but consistent and result in a derivative line shape in the transient pump−probe spectrum (Figure 2c). The peak-shift is 5921
DOI: 10.1021/acs.jpca.9b04601 J. Phys. Chem. A 2019, 123, 5918−5927
Article
The Journal of Physical Chemistry A
Figure 4. Polariton to dark states relaxation dynamics in hexane. (a) Pump−probe dynamic traces with broadband pump and probe frequency around 1963 cm−1 near the LP state for strongly coupled W(CO)6 in hexane, showing that the signal slowly rises and decays after early time polariton coherence responses (within 5 ps). (b) 2D-IR spectra of W(CO)6/hexane in the strong coupling regime at t2 = 5 ps. (c) 2D IR dynamic traces at ωpump = ωUP and ωprobe = ωLP area (black box in b), showing the pure decay trend after 5 ps. (d) 2D IR dynamic traces at ωpump = ωLP and ωprobe = ωLP area (red box in b), showing the slow rise and decay of the signal after 5 ps. (e) Upon pumping of UP, population transfer (within t2 ∼ 5 ps) ensues to localized dark modes (first excited molecular state), which can be probed by excited state absorption into the second excited molecular state. Pumping of LP attains the same effect but occurs via an intermediate state.
transfer from the UP state to the dark mode while the LP-LP peak (Figure 2e, left-bottom) is mainly due to the LP to dark mode population transfer. As summarized in Figure 2f, it is believed that the UP/LP population transfer to dark modes is in a fast time scale, which subsequently makes the dark mode ν12 appear in the pump probe or 2D spectra. However, the time scale and mechanisms of LP/UP transferring to dark modes remain largely unexplored and are the interests of this work. We learn the polariton dynamics by measuring the dynamics of the LP peak in pump probe spectra (integrating over the transient pump probe peak near the LP position, e.g. shaded area in Figure 2c) and the dynamics of UP-LP and LPLP peaks from 2D IR spectra (integrating 2D spectral peaks at UP-LP and LP-LP area, e.g, blue boxes in Figure 2e). We note that the exact integrated areas depend on the peak positions of various polariton systems.
induced by the Rabi splitting contraction which arises due to the pump-induced reduction of molecular ground-state population. The substantially reduced LP transmission upon pumping, and consequently the absorptive line shape in the pump probe spectra (gray shadow in Figure 2c) results from the fact that the dark mode overtone ν12 transition (from first excited to second excited states, purple arrow in Figure 2f) is near resonance with the LP transition. As a result, ν12 become visible through the LP transmission window. Thus, when LP and ν12 are near resonance, the appearance of a strong absorptive transient signal at ωLP is a signature of populating the first excited state of dark modes. While pump probe spectroscopy allows following polariton to dark state dynamics, the state-selective 2D IR spectrum (Figure 2e) enables disentangling the dynamics: The UP-LP peak labeled in Figure 2e (left-top) represents the population 5922
DOI: 10.1021/acs.jpca.9b04601 J. Phys. Chem. A 2019, 123, 5918−5927
Article
The Journal of Physical Chemistry A Polariton Dynamics in Acetone. The transmission spectrum of the strongly coupled W(CO)6/acetone system exhibits LP and UP peaks with separation of ∼48 cm−1, with ωLP = 1948 cm−1 and ωUP = 1996 cm−1 (Figure S4a). When the probe is close to resonance with the LP (near 1948 cm−1, see Figure S4c, gray area), the pump−probe spectral dynamics of the LP peak reveals the relaxation dynamics of the dark molecular system (Figure 3a). The early time spike is attributed to the polariton bleach effect, which results from the interactions between polariton states created by pump and probe pulses.15 Within the cavity lifetime (∼5 ps), the signal reflects rapid polariton decay by photon leakage or population transfer to the first excited-state of dark modes. After this time scale, the polariton to dark state population transfer has equilibrated, and the evolution of the signal reflects the relaxation dynamics of dark modes, which exhibit a lifetime of 78 ± 4 ps (Figure 3a). As discussed in the previous section, these dynamics are detected by the probe pulse inducing excited-state absorption via the dark mode ν12 (1947 cm−1) transitions.42 The ensuing relaxation phenomena exhibit an exponential decay kinetics which is similar to that of the fundamental peak of uncoupled W(CO)6 in acetone (84 ± 4 ps, Figure.S2b). The similarity of the measured lifetimes is unsurprising, since the rate of change of the nonlinear signal in both cases is linearly proportional to the population of molecules in the first excited-state. Because both LP and UP are bright but could have different dynamics, we need to track the relaxation dynamics of each type of polariton to gain the full picture. We applied 2D IR spectroscopy to follow state-resolved dynamics. The 2D IR spectra at t2 = 5 ps are shown in Figure 3b. The relaxation dynamics is studied by plotting the integrated spectral region (indicated as black and red boxes in Figure 3b) as a function of t2. As discussed in the previous section, the black and red boxed regions in Figure 3b represent the population transfer from UP and LP to dark modes, respectively. The time traces indicate LP and UP both relax into the dark modes in a fast time scale (
