We study the phenomenon of absorption refrigeration, where refrigeration is achieved by heating instead of work, in two different setups: a minimal set up based on coupled qubits and two nonlinearly coupled resonators. Considering
ZZ interaction between the two qubits, we outline the basic ingredients required to achieve cooling. Using local as well as global master equations, we observe that inclusion of an
XX type term in the qubit-qubit coupling is detrimental to cooling. We compare the cooling effect obtained in the qubit case with that of nonlinearly coupled resonators (multilevel system) where the
ZZ interaction translates to a Kerr-type nonlinearity. For small to intermediate strengths of nonlinearity, we observe that multilevel quantum systems, for example qutrits, give better cooling effect compared to the qubits. Using Keldysh nonequilibrium Green's function formalism, we go beyond first order sequential tunneling processes and study the effect of higher order processes on refrigeration. We find a reduced cooling effect compared to the master equation calculations.
We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also operate in a parameter regime where no or negligible steady-state cooling is achieved, but there is considerable transient cooling. The steady-state temperature can be lowered significantly by an increase in the strength of the few-body interaction terms existing due to the use of the common bath in the refrigerator setup. The proposed refrigerator built with three qubits and two baths is shown to provide steady-state cooling for both Markovian qubit-bath interactions between the qubits and canonical bosonic thermal reservoirs, and a simpler reset model for the qubit-bath interactions.
A quantum absorption refrigerator driven by noise is studied with the purpose of determining the limitations of cooling to absolute zero. The model consists of a working medium coupled simultaneously to hot, cold, and noise baths. Explicit expressions for the cooling power are obtained for Gaussian and Poisson white noise. The quantum model is consistent with the first and second laws of thermodynamics. The third law is quantified; the cooling power J(c) vanishes as J(c) ∝ T(c)(α), when T(c)→0, where α=d+1 for dissipation by emission and absorption of quanta described by a linear coupling to a thermal bosonic field, where d is the dimension of the bath.