Small quantum absorption refrigerator with reversed couplings

Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by “reversing” the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fridge, in particular the heat current extracted from the cold bath. We show that our model performs comparably to the standard three-level quantum fridge and thus appears appealing for possible implementations of nanoscale thermal machines.

Figure 1

(a) The two-qubit fridge viewed as a four-level system, with the couplings to the hot, cold, and sink reservoirs. (b) The four strokes of the cooling cycle. In each panel the balls represent the state each qubit can initially be found in, and the arrows depict the transitions that occur, driven by the respective baths. By making the four transitions shown (i.e., the four strokes) in sequence, the system undergoes a cyclic evolution and completes one cooling cycle.

Figure 2

Construction of equivalent qutrit fridge to compare performance.

Figure 3

Performance of the fridge (solid blue lines), and comparison with the three-level fridge (dashed red lines); see main text. (a) Heat current $Q_c$ drawn from the cold bath as a function of the temperature of the hot bath, $T_h$. (b) $Q_c$ as function of the energy of the second qubit, $E_2$, for fixed $T_h=20$. Clearly, the heat current is maximized at a finite value $E_2^{\text{opt}}$. (c) Dependency of $E_2^{\text{opt}}$ as a function of $T_h$. Finally, we note that in both (a) and (b), our model outperforms the standard three-level fridge.