Two-quanta processes in coupled double-quantum-dot cavity systems

TL;DR

The paper addresses the dynamics of a semiconducting DQD qubit coupled to a leaking microwave resonator under two-photon resonance ($\Omega \approx 2\omega_r$), incorporating phonon and photon baths. It develops a theoretical framework by diagonalizing the DQD, deriving an interaction-picture Hamiltonian that includes two-photon processes, and obtaining a Born-Markov master equation with explicit dissipative channels; from this, it derives exact equations for photon-number–resolved variables and the current, enabling analysis of steady-state photon numbers and photon statistics. The results reveal a critical coupling where the cavity photon population jumps and the current tracks this change, with photon statistics transitioning from thermal-like to Poissonian, i.e., lasing-like, at microwave frequencies; phonons dampen these effects to a modest extent. This work provides a rigorous method to quantify current–photon interconversion and photon-statistics engineering in DQD-cavity and circuit-QED-like devices under two-photon resonances, with potential applications in microwave quantum light sources and quantum information processing.

Abstract

The quantum dynamics of a compound sample consisting from a semiconductor double quantum dot (DQD) system non-linearly coupled with a leaking single-mode micro-resonator is theoretically investigated. The focus is on the resonance condition when the transition frequency of the double quantum dot equals to the doubled resonator frequency, respectively, and the resulting interplay among the involved phonon or photon channels. As a result, the steady-state quantum dynamics of this complex non-linear system exhibits a variety of possible effects that have been demonstrated here. Particularly, we have found the relationship among the electrical current through the double quantum dot and the microwave field inside the resonator that is nonlinearly coupled to it, with a corresponding emphasizing on their critical behaviors. Additionally, the quantum correlations of the photon flux generated into the resonator mode vary from super-Poissonian to Poissonian photon statistics, leading to single-qubit lasing phenomena at microwave frequencies.

Figures (3)

• Figure 1: The steady-state behaviour of the cavity mean photon number $\langle n\rangle=\langle a^{\dagger}a\rangle$ as a function of the ratio of the qubit-resonator coupling strength $g$ over the cavity frequency $\omega_{r}$. Here $\tau/\epsilon=0.1$, $\epsilon/\omega_{r}=1.96$, $\hbar\omega_{r}/(k_{B}T)=5$, $\Gamma_{L}/\omega_{r}=\Gamma_{R}/\omega_{r}=0.03$, $\gamma_{d}/\omega_{r}=10^{-3}$, $\kappa/\omega_{r}=7\cdot 10^{-4}$ and $\kappa(\Omega)/\omega_{r}=10^{-4}$. The solid line corresponds to $\Gamma(\Omega)/\omega_{r}=0.02$, $\Gamma(\Omega_{\pm})/\omega_{r}=0.01$, and $\Gamma(\omega_{r})/\omega_{r}=0.01$, whereas the dashed one to $\Gamma(\Omega)$=$\Gamma(\Omega_{\pm})$= $\Gamma(\omega_{r})=0$, i.e., no phonons involved.
• Figure 2: The steady-state dependence of the current $I_{q}$ through the DQD system as a function of $g/\omega_{r}$. All other involved parameters are the same as in Fig. (\ref{['fig-1']}).
• Figure 3: The normalized steady-state second-order photon-photon correlation function $g^{(2)}(0)$ versus the ratio $g/\omega_{r}$. Other parameters are as in Fig. (\ref{['fig-1']}).