Cooling with fermionic thermal reservoirs

The quantum reservoirs commonly considered in open-quantum systems theory are those modeled by quantum harmonic oscillators, which are called bosonic reservoirs. Recently, quantum reservoirs modeled by two-level systems, the so-called fermionic reservoirs, have received attention due to their features. Given that the components of these reservoirs have a finite number of energy levels, unlike bosonic reservoirs, some studies are being carried out to explore the advantages of using this type of reservoir, especially in the operation of heat machines. In this paper, we carry out a case study of a quantum refrigerator operating in the presence of bosonic or fermionic thermal reservoirs, and we show that fermionic baths have advantages over bosonic ones.

Figure 1

Schematic of the SCQR refrigerator and its respective thermal reservoirs. The SCQR is composed of three interacting qubits having energy gaps $E_1$–$E_3$ in contact with their respective thermal reservoirs. Here, $T_h$ is the temperature of the hot thermal reservoir, $T_r$ is the temperature of the “room” thermal reservoir, $T_c$ is the temperature of the cold thermal reservoir, and $g$ is the coupling constant between the qubits.

Figure 2

Temperature difference $T_1-T_c$ versus $T_h$ for (a) three bosonic and (b) three fermionic thermal reservoirs, considering three different values of $T_c$: $T_c=1$ (dotted green line), $T_c=1.5$ (dashed red line), and $T_c=2$ (solid blue line). Refrigeration occurs for $T_1-T_c<0$. Note the difference in behavior in the two figures: whereas, in (a) temperature $T_1$ reaches a minimum and then starts to increase, approaching zero, in (b) $T_1$ decreases monotonically, practically stabilizing for sufficiently high $T_h$, thus, indicating that the lowest temperatures reached by qubit 1 occur for fermionic thermal reservoirs.