Cooling a quantum oscillator: A useful analogy to understand laser cooling as a thermodynamical process

Abstract

We analyze the lowest achievable temperature for a mechanical oscillator coupled with a quantum refrigerator composed of a parametrically driven system that is in contact with a bosonic reservoir where the energy is dumped. We show that the cooling of the oscillator (achieved by the resonant transport of its phonon excitations into the environment) is always stopped by a fundamental heating process that is dominant at sufficiently low temperatures. This process can be described as the nonresonant production of excitation pairs. This result is in close analogy with the recent study that showed that pair production is responsible for enforcing the validity of the dynamical version of the third law of thermodynamics [Phys. Rev. E 95, 012146 (2017)]. Interestingly, we relate our model to the ones used to describe laser cooling of a single trapped ion reobtaining the correct limiting temperatures for the regimes of resolved and nonresolved sidebands. We show that the limiting temperature for laser cooling is achieved when the cooling transitions induced by the resonant transport of excitations from the motion into the electromagnetic environment is compensated by the heating transitions induced by the creation of phonon-photon pairs.