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arXiv:1604.08637 · Physical Review A

Molecular spectra in collective Dicke states

Eran Sela, V. Fleurov, Vladimir Yurovsky

Published Sep 26, 2016• 11 citations
arXivHTMLPDF

Abstract

We introduce a model describing the competition of interactions between $N$ two-level systems (TLSs) against decoherence. We apply it to analyze dye molecules in an optical microcavity, where molecular vibrations provide a local source for decoherence. The most interesting case is when decoherence strongly affects each individual TLS, e.g., via broadening of emission lines as well as vibrational satellites; however, its influence is strongly suppressed for large $N$ due to the interactions between TLSs. In this interaction-dominated regime we find unique signatures in the emission spectrum, including strong $O(\sqrt{N})$ level shifts, as well as $1/N$ suppression of both the decoherence width and the vibrational satellites. These effects are most pronounced in the unexplored regime near $50%$ polarization of the TLSs.

DOI
10.1103/physreva.94.033848

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We introduce a model describing the competition of interactions between NNN two-level systems (TLSs) against decoherence. We apply it to analyze dye molecules in an optical microcavity, where molecular vibrations provide a local source for decoherence. The most interesting case is when decoherence strongly affects each individual TLS, e.g., via broadening of emission lines as well as vibrational satellites; however, its influence is strongly suppressed for large NNN due to the interactions between TLSs. In this interaction-dominated regime we find unique signatures in the emission spectrum, including strong O(N)O(\sqrt{N})O(N​) level shifts, as well as 1/N1/N1/N suppression of both the decoherence width and the vibrational satellites. These effects are most pronounced in the unexplored regime near 5050%50 polarization of the TLSs.
Motivated by recent experiments reporting Bose-Einstein condensation of light coupled to incoherent dye molecules in a microcavity, we show that due to a dimensionality mismatch between the two-dimensional cavity photons and the three-dimensional arrangement of molecules, the system permits superfluid regimes where the relevant molecular degrees of freedom are collective Dicke states rather than individual excitations. For sufficiently high dye concentration, Dicke states become robust against local decoherence. In the limit when all dye molecules become excited, this system also shows Mott-Hubbard physics, despite the absence of an underlying lattice.
We employed the Tavis-Cummings model to study the pump-probe spectra of molecular polaritons. To describe the dissipative effects caused by the environment, the population decays of the photon mode and the two level states (TLSs), as well as the fast component of the dephasing of TLSs, are described by using the Lindblad equation. The effect of static disorder in the TLS transition frequency is incorporated into the equation of motion of the density matrix. The pump-probe spectra of the model system are calculated using the optical response function approach. Pronounced Rabi oscillations are observed in the pump-probe spectra, which are signatures of the strong light-matter coupling between the cavity mode and the collective bright state of the TLSs. To help understand the pump-probe spectra, we also simulate the laser pulse induced dynamics of the bright state of the molecular polaritons. The results show that the bright state lifetime is primarily determined by the dephasing time of the TLSs, consistent with the fast decay of the Rabi oscillations observed in the pump-probe spectra. Once the coherence decays, the long-time pump-probe response is dominated by the excited state population of the dark state manifold.
Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of NNN anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting ${\mathrm{\ensuremath{\Omega}}}_{R}$ is approximately equal to the molecular anharmonic shift $2\mathrm{\ensuremath{\Delta}}$. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible ${S}_{0}\ensuremath{\rightarrow}{S}_{1}\ensuremath{\rightarrow}{S}_{2}$ transitions) and strongly interact with a UV-visible cavity.
We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the system are studied using a renormalized master equation, both with multipolar and minimal-coupling interaction schemes. We show that both models lead to the same result and, in contrast to nonrenormalized models, predict that the relative orientation of the (coaligned) dipoles is unimportant in the Dicke limit. Our master equation is of relevance to any system of dipole-coupled two-level atoms, and gives bounds on the strength of the dipole-dipole interaction for closely spaced atoms. Exact calculations for small atom systems in the near-Dicke limit show the increased emission times resulting from the evolution generated by the strong dipole-dipole interaction. However, for large numbers of atoms in the near-Dicke limit, it is shown that as the number of atoms increases, the effect of the dipole-dipole interaction on collective emission is reduced.
We present a consistent analysis of linear spectroscopy for arrays of nearest-neighbor dipole-coupled two-level molecules that reveals distinct signatures of weak- and strong-coupling regimes separated for infinite-size arrays by a quantum critical point. In the weak-coupling regime, the ground state of the molecular array is disordered, but in the strong-coupling regime, it has (anti)ferroelectric ordering. We show that multiple molecular excitations [odd (even) in the weak- (strong-) coupling regime] can be accessed directly from the ground state. We analyze the scaling of absorption and emission with system size and find that the oscillator strengths show enhanced superradiant behavior in both ordered and disordered phases. As the coupling increases, the single-excitation oscillator strength rapidly exceeds the well-known Heitler-London value. In the strong-coupling regime we show the existence of a unique spectral transition with excitation energy that can be tuned by varying the system size and that asymptotically approaches zero for large systems. The oscillator strength for this transition scales quadratically with system size, showing an anomalous one-photon superradiance. For systems of infinite size, we find a novel singular spectroscopic signature of the quantum phase transition between disordered and ordered ground states. We outline how arrays of ultracold dipolar molecules trapped in an optical lattice can be used to access the strong-coupling regime and observe the anomalous superradiant effects associated with this regime.
The field of Polaritonic Chemistry studies molecules strongly coupled to the light field of optical cavities. The resulting modification of the potential energy landscape has been demonstrated to enable control over the chemical and physical properties of materials and molecular ensembles. This thesis extends the Tavis–Cummings model to describe molecules under strong light–matter coupling, incorporating static dipole moments and dipole self-energy contributions derived from the Pauli–Fierz Hamiltonian. These additional terms are shown to be essential for reproducing cavity-modified molecular dynamics and spectra. Simulations on the nuclear wavefunction propagation of MgH+ molecules demonstrate the impact of these terms, while an effective two-level system model accurately captures the behavior of large ensembles. Beyond single excitations, the thesis also explores the higher excitation manifolds of the Tavis-Cummings model, which reveals that allowing for more than a single excitation makes the reaction of the involved polaritons entropically more favorable. Open-system simulations highlight how the coherence of the system's initial state governs decay pathways and enables long-lived energy storage. Finally, a multilevel vibrational model coupled to a two-mode cavity is introduced, where a Raman scheme enables selective mixing of vibrational states. The simulation results show that continuous pumping can drive molecules into specific vibrational states while suppressing electronic excitation, both for single molecules and small ensembles. Together, these results provide new theoretical insights into the mechanisms by which optical cavities reshape molecular energy landscapes. The results suggest approaches for controlling photonic, electronic, and vibrational dynamics in strongly coupled systems, contributing to the theoretical foundation of polariton chemistry.