Quantum Theory of Collective Strong Coupling of Molecular Vibrations with a Microcavity Mode

Francisco Javier Del Pino Department of Theoretical Condensed Matter Physics and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Madrid, Spain Johannes Feist Department of Theoretical Condensed Matter Physics and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Madrid, Spain Francisco García-Vidal Department of Theoretical Condensed Matter Physics and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Madrid, Spain

The field of cavity optomechanics explores the interaction between electromagnetic radiation and the quantized mechanical motion of nano- or microoscillators. Recent developments promise a variety of applications such as precision mechanical measurements and coherent control of quantum states. When the interaction becomes sufficiently large, coherent energy exchange between the optical and mechanical degrees of freedom becomes possible and the system reaches the strong coupling regime. A novel approach consists in coupling a cavity mode to a molecular bond vibration, which is in the ground state already at room temperature, without requiring any cooling. In order to achieve strong coupling, this has to be done using an ensemble of molecules. In this case, the cavity mode couples to a global superposition of the molecular vibrations, the so-called bright state, forming polaritons with an energy splitting given by the Vacuum Rabi Splitting ΩR. All other superpositions (the dark states) remain uncoupled. Within this setting, a thermal bath of low-frequency rovibrational excitations, which normally only introduces dephasing, may affect the dynamics and population of the system. We describe the system using a quantum-mechanical model of a single photon mode coupled to an ensemble of oscillators.

We consider two possible schemes of coupling to a low-frequency thermal bath through a dephasing-type interaction. The former corresponds to coupling of each oscillator to a separate bath. We show that these baths can lead to a population transfer between polaritons and dark states, with the strength of the effect strongly depending on the spectral density of the background vibrations at the Rabi splitting ΩR. A different situation arises when the ensemble of oscillators is collectively coupled to a bath. In this case only the bright mode plays a role in the dynamics and the dominant process is population transfer between both polaritons.

The experimental results reported in ref [1] seem to be compatible with the latter situation.

[1] A. Shalabney, J. George, J. A. Hutchison, G. Pupillo, C. Genet, and T. W. Ebbesen, arXiv:1403.1050 (2014)

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