Cooling a quantum circuit via coupling to a multiqubit system

The cooling effects of a quantum $\mathit{LC}$ circuit coupled inductively with an ensemble of artificial qubits are investigated. The particles may decay independently or collectively through their interaction with the environmental vacuum electromagnetic field reservoir. For appropriate bath temperatures and the resonator’s quality factors, we demonstrate an effective cooling well below the thermal background. In particular, we found that for larger samples the cooling efficiency is better for independent qubits. However, the cooling process can be faster for collectively interacting particles.

Figure 1

An ensemble of $N$ independent three-junction flux qubits coupled to a $\mathit{LC}$ quantum circuit by their mutual inductances. An ac magnetic flux $\Phi (t)$ drives the qubits.

Figure 2

The mean photon number $\langle n\rangle$ into the quantum circuit as function of $\delta \omega$ and different numbers of independent qubits. The solid line is for $N=1$, the long-dashed line stands for $N=10$, and the short-dashed curve corresponds to $N=30$. The dotted curve shows the saturation photon number $n_0$ for $N=30$ qubits. Here, $\mathrm{n̄}({\omega }_c)=4$, $\Delta /2\pi =3\times {10}^9\hspace{0.5em}\mathrm{Hz}$, $\epsilon =0.01\Delta$, $g/2\pi ={10}^6$ Hz, ${\omega }_c/2\pi ={10}^7$ Hz, $\gamma /2\pi ={10}^5$ Hz, $\kappa /2\pi ={10}^3$ Hz, and ${\mathrm{\Omega ̃}}_0=\sqrt{{\Omega }^2-(\delta \omega ){}^2}$.

Figure 3

The mean photon number $\langle a^{†}a\rangle$ of the quantum oscillator as the function of $\delta \omega$ and different numbers of collectively interacting qubits. The solid line is for $N=10$, while the long-dashed line stands for $N=15$. The short-dashed curve corresponds to $N=30$, while the dotted one corresponds to $N=30$, but $\kappa /2\pi ={10}^2$ Hz. Other parameters are the same as in Fig. 2.