Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot

We investigate the nonclassical states of light that emerge in a microwave resonator coupled to a periodically driven electron in a nanowire double quantum dot (DQD). Under certain drive configurations, we find that the resonator approaches a thermal state at the temperature of the surrounding substrate with a chemical potential given by a harmonic of the drive frequency. Away from these thermal regions we find regions of gain and loss, where the system can lase, or regions where the DQD acts as a single-photon source. These effects are observable in current devices and have broad utility for quantum optics with microwave photons.

Figure 1

(a) A microwave resonator is coupled to charge states in a DQD. The DQD is subject to periodic driving and strongly coupled to acoustic phonons, which are held at a fixed temperature. (b) Energy level diagram of the DQD with $t_c=20\mu \mathrm{eV}$. For $A\ll \hslash \omega$ with $\omega \approx 2t_c/\hslash$, resonance fluorescence of the DQD dominates, leading to antibunched light. When $A\gg \hslash \omega$, the phonon sideband dominates, leading to thermalization.

Figure 2

(a) $g^{(2)}(0)$ as a function of $A$ and $\omega$. We took ${\omega }_c/2\pi =16\mathrm{GHz}$, $t_c=20\mu \mathrm{eV}$, ${\epsilon }_0=0$, $g_c/2\pi =70\mathrm{MHz}$, $\kappa /2\pi =1.3\mathrm{MHz}$, $\eta =0.5{\mathrm{ns}}^{-1}$, and $T=200\mathrm{mK}$. Vertical lines correspond to zeros of $J_0(A/\hslash \omega )$. (b) Effective temperature of the photons in the thermal regions [defined by $g^{(2)}(0)>1.9$], with cavity decay neglected. Inset: Raman scattering processes leading to thermalization of photons when $\delta ={\omega }_c-n_c\omega$ is near zero. The red line is a photon, the solid line is the drive, and the curved black line is a phonon.

Figure 3

Mean photon number $⟨a^{†}a⟩$ in the resonator for varying $A$ and $\omega$ for ${\omega }_c/2\pi =7.5\mathrm{GHz}$, $\eta =5{\mathrm{ns}}^{-1}$, and the other parameters from Fig. 2. Contours indicate $g^{(2)}(0)=(1.5/1/0.5)$ (red/white/blue), asterisks denote single-photon source operating points with $⟨a^{†}a⟩\approx 1$ and $g^{(2)}(0)<0.5$, and RF marks the point of conventional resonance fluorescence $\omega =2t_c$.