How much can we cool a quantum oscillator? A useful analogy to understand laser cooling as a thermodynamical process

We analyze the lowest achievable temperature for a mechanical oscillator (representing, for example, the motion of a single trapped ion) which is coupled with a driven quantum refrigerator. The refrigerator is composed of a parametrically driven system (which we also consider to be a single oscillator in the simplest case) which is coupled to a reservoir where the energy is dumped. We show that the cooling of the oscillator (that can be achieved due to the resonant transport of its phonon excitations into the environment) is always stopped by a fundamental heating process that is always dominant at sufficiently low temperatures. This process can be described as the non resonant 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). Interestingly, we relate our model to the usual ones used to describe laser cooling of a single trapped ion and reobtaining the correct limiting temperatures for the limits of resolved and non-resolved sidebands. Our findings (that also serve to estimate the lowest temperatures that can be achieved in a variety of other situations) indicate that the limit for laser cooling can also be associated with non resonant pair production. In fact, as we show, this is the case: 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.