Theoretical Investigation of non-Markovian Dynamics of an Optomechanical System Acting as an Autonomous Quantum Heat Engine*

While new quantum technologies are being developed at an accelerating pace, the field of quantum thermodynamics [1] is attracting a lot of attention, as researchers are discovering a plethora of phenomena in quantum systems subjected to thermal fluctuations. The key example of such a quantum device is the quantum heat engine (QHE) [2] --- a device operating at the quantum level, designed to interact with heat reservoirs and extract work from heat flow. We propose utilizing a well-known quantum device, the optomechanical system, in a novel manner to realize an autonomous QHE.

In this work, we show that when the optical cavity of an optomechanical system is coupled to non-Markovian heat baths, it is possible to reach excitation generation in the mechanical mode. We study the classical analogue of the equations of motion of the optomechanical system with the key difference that instead of coherent drive, we subject the optical cavity only to thermal fluctuations from two baths with different temperatures. Further, we shall not resort to Markovian approximation, but rather study the full non-Markovian dynamics with coloured quantum noise. We derive quasiclassical Langevin equations describing the intricate non-linear dynamics of the system and study their solutions. 

[1] S. Deffner and S. Campbell. Morgan and Claypool, 2019.

[2] H. Goswami and U. Harbola. Phys. Rev. A, 88:013842, Jul 2013

[3] A. Schmid, Jour. of Low Temp. Phys, vol. 49, no. 5-6, Dec. 1982