We analyze the lowest achievable temperature for a mechanical oscillator(representing, for example, the motion of a single trapped ion) which iscoupled with a driven quantum refrigerator. The refrigerator is composed of aparametrically driven system (which we also consider to be a single oscillatorin the simplest case) which is coupled to a reservoir where the energy isdumped. We show that the cooling of the oscillator (that can be achieved due tothe resonant transport of its phonon excitations into the environment) isalways stopped by a fundamental heating process that is always dominant atsufficiently low temperatures. This process can be described as the nonresonant production of excitation pairs. This result is in close analogy withthe recent study that showed that pair production is responsible for enforcingthe 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 usedto describe laser cooling of a single trapped ion and reobtaining the correctlimiting temperatures for the limits of resolved and non-resolved sidebands.Our findings (that also serve to estimate the lowest temperatures that can beachieved in a variety of other situations) indicate that the limit for lasercooling can also be associated with non resonant pair production. In fact, aswe show, this is the case: The limiting temperature for laser cooling isachieved when the cooling transitions induced by the resonant transport ofexcitations from the motion into the electromagnetic environment is compensatedby the heating transitions induced by the creation of phonon-photon pairs.
展开▼
