Molecule-photon interactions in phononic environments

Abstract

Molecules constitute compact hybrid quantum optical systems that can interface photons, electronic degrees of freedom, localized mechanical vibrations, and phonons. In particular, the strong vibronic interaction between electrons and nuclear motion in a molecule resembles the optomechanical radiation pressure Hamiltonian. While molecular vibrations are often in the ground state even at elevated temperatures, one still needs to get a handle on decoherence channels associated with phonons before an efficient quantum optical network based on optovibrational interactions in solid-state molecular systems could be realized. As a step towards a better understanding of decoherence in phononic environments, we take here an open quantum system approach to the nonequilibrium dynamics of guest molecules embedded in a crystal, identifying regimes of Markovian versus non-Markovian vibrational relaxation. A stochastic treatment, based on quantum Langevin equations, predicts collective vibron-vibron dynamics that resembles processes of sub-and super-radiance for radiative transitions. This in turn leads to the possibility of decoupling intramolecular vibrations from the phononic bath, allowing for enhanced coherence times of collective vibrations. For molecular polaritonics in strongly confined geometries, we also show that the imprint of optovibrational couplings onto the emerging output field results in effective polariton cross-talk rates for finite bath occupancies.

Engineering long-lived vibrational states for an organic molecule

“…/ω 2 b of a phonon mode14 .Interestingly, this molecular interaction mirrors the form of common cavity optomechanical Hamiltonians2,4,12,13,22,23 with the optomechanical constant g 0 = Ds ω b /2 EV12 , where D denotes the deformation potential induced in the impurity by the local strain s, E is the Young modulus of the host, and V is the phonon mode volume. Considering the deformation potential estimated in recent DBT:AC experiments 18 (D/2π ∼ 1300 THz), the small volumes of the nanocrystals (V ∼ 2.5 × 10 −4 µm 3 ), s ≈ 0.04 − 0.12, and E ≈ 10 10 Pa 23 (see SI), one arrives at g 0 /2π ∼ 50 − 150 MHz, comparable with or larger than the electronic decay rates of typical quantum emitters6,24,25 .…”

“…However, scientists have been increasingly turning their attention to molecules for their naturally rich and compact quantum mechanical settings, where a wide range of electronic, mechanical and magnetic degrees of freedom could be efficiently accessed and manipulated 2,[7][8][9][10] . A particularly intriguing promise of molecules is their use as quantum optomechanical platforms [2][3][4][5][11][12][13][14] , but this idea confronts the challenge that the various molecular degrees of freedom quickly lose their "quantumness" when coupled to the phononic bath of the environment in the condensed phase. In this theoretical work, we show how to create long-lived phononic states by tailoring the vibrational modes of organic crystals that embed impurity guest molecules.…”

“…1(b)). Vibrons can be long-lived in the gaseous state, but if the molecule is embedded in a solid matrix, the molecular levels also couple to the phonons (|b ) in the host 14,18 . The large phononic density of states in macroscopic solids then result in fast decays of vibrons in the range of picoseconds 6 .…”

“…We then solve the resulting master equation numerically via the QuTiP 35 to explore the main dynamical and steady-state properties of the system. To gain further insight into the simulations for the parameters considered in this work, we have also developed two analytical models based on the Quantum Langevin approach 14,36 . For the steady state averages, we noticed a fair approximation based on the decorrelated evolution between the electronic population and phononic displacement operator σ † σD(t)D † (t ) ≈ σ † σ(t) D(t)D † (t ) , which together with the dominance of the terms σb , σ † b † enable us to extend previous formulas 14,36 to driving conditions near saturation.…”

Collective Effects of Organic Molecules based on Holstein-Tavis-Cummings Model

“…Furthermore, an approach based on the quantum Langevin equation to solve the HTC model has been developed recently [17]. It provides an alternative path to understand the Stokes and anti-Stokes processes [17], Purcell effect under the influence of the phononic environments [21], and the Floquent engineering [22] at the level of operators rather than states. However, the previous works [17,21,22] mainly focus on a single molecule.…”