Non-canonical steady state of two coupled oscillators in the strong coupling regime

Felipe Recabal Universidad de Santiago de Chile

In a previous work, we describe the suppression of reaction rate inside a cavity where the electromagnetic vacuum is in strong coupling with an ensemble of molecule [1]. We model the system through a master equation where the local-Lindblad terms describe the relaxation processes of the cavity mode and the molecular vibrational modes. We show that local- Lindblad theory is necessary to obtain a non-canonical steady state for the system that describes the reaction rate suppression. Meanwhile, Redfield master equation in the system eigenbasis leads to canonical steady state that does not capture the resonant behavior. Based on the previous discussion, in the work we microscopically derive a master equation for two coupled harmonic oscillators in the strong coupling regime (see Fig.1(a)). The derivation considers weak coupling and Born-Markov approximation for the system-bath interaction. The master equation obtained contains local terms, that describes relaxation, and non-local terms, due to include the oscillator coupling in the derivation [2,3]. Results shows that the non-local terms are associate to production of coherences induced by the baths, leading the system to a canonical steady state. When the non-local terms are neglected, the system have a non-canonical steady state, with results that agree with the resonant behavior observed using local Lindblad master equation (see Fig.1(b)). Possible ways to neglect the non-local terms are discussed, including tuning temperature and energy detuning, and the inclusion of non-linear system bath interactions.

[1] W. Ahn, J. F. Triana, F. Recabal, F. Herrera & B. S. Simpkins, Science, 380(6650), 1165- 1168 (2023).

[2] C. Joshi, et al., Phys. Rev. A, 90(6), 063815 (2014).

[3] J. Sousa, et al., Phys. Rev. A, 106(3), 032401 (2022).