Enabling the self-contained refrigerator to work beyond its limits by filtering the reservoirs

In this paper, we study the quantum self-contained refrigerator [Linden et al., Phys. Rev. Lett. 105, 130401 (2010)] in the strong internal coupling regime with engineered reservoirs. We find that if some modes of the three thermal reservoirs can be properly filtered out, the efficiency and the working domain of the refrigerator can be improved in contrast to the those in the weak internal coupling regime, which indicates one advantage of the strong internal coupling. In addition, we find that the background natural vacuum reservoir could cause the filtered refrigerator to stop working and the background natural thermal reservoir could greatly reduce the cooling efficiency.

Figure 1

Three coupled qubits interact separately with their reservoirs denoted by $H$, $R$, and $C$ of different temperatures labeled by $T_H$, $T_R$, and $T_C$. Between each qubit and its reservoir is a (maybe conceptual) filter which allows only some modes with certain frequencies in the reservoir to interact with the qubit and filters other modes out. The arrows represent the channels by which the three qubits interact with their reservoirs. Experimentally, the filtered thermal reservoir in some cases might be realized by a gas noise lamp and the filter by a wave guide cutting off the certain frequencies [9].

Figure 2

The heat currents ${\dot{Q}}_{\mu }/{\omega }_C$ [J/s] versus $T_H\left[\mathrm{K}\right]$. The solid yellow line, the dashed red line, and the dash-dotted blue line correspond to ${\dot{Q}}_R$, ${\dot{Q}}_H$, and ${\dot{Q}}_C$, respectively. The horizontal solid line shows the zero values. The vertical dotted lines are used to distinguish the four different stages defined in Eq. (41). With $T_H$ increasing, the four regions from left to right sequentially correspond to the four stages from stage 1 to stage 4. Here ${\omega }_C=2\pi \times 210\text{GHz}$, ${\omega }_H=3{\omega }_C$, $T_C=10\text{K}$, $T_R=40\text{K}$, $T_0=12\text{K}$, $\gamma =0.6{\omega }_C$.

Figure 3

The heat currents ${\dot{Q}}_{\mu }^B/{\omega }_C$ [J/s] versus $T_H$ [K]. The solid yellow line, the dashed red line, and the dash-dotted blue line correspond to ${\dot{Q}}_R^B$, ${\dot{Q}}_H^B$, and ${\dot{Q}}_C^B$, respectively. The vertical dotted lines and all the parameters are used the same as Fig. 2.

Figure 4

The efficiency versus $T_H$ [K]. The negative efficiency means the different directions of heat currents ${\dot{Q}}_C$ and ${\dot{Q}}_H$. The horizontal solid line shows the value zero.

Figure 5

The entropy production rate $\sigma /{\omega }_C$ [J/Ks] versus $T_H$ [K], where $\sigma$ is defined by $\sigma =-\sum \frac{{\dot{Q}}_{\alpha }}{T_{\alpha }}-\sum \frac{{\dot{Q}}_{\alpha }^B}{T_0}$. All the parameters are the same as Fig. 1.