Dispersive detection of single microwave photons with quantum dots

TL;DR

This work addresses the challenge of detecting a single itinerant microwave photon without absorbing it. It develops a dispersive readout scheme in a circuit QED setting where a cavity mode dispersively couples to a DQD tunnel-coupled to a lead, enabling photon detection through real-time monitoring of the QD charge state. A quantum cascade master equation provides a time-resolved description of a single-photon wavepacket impinging on the cavity, and a Lindblad-formulation captures photon–emitter–lead dynamics, including measurement backaction. The study finds that, under favorable conditions ($oldsymbol{ u}_{ m c} eq 0$, $|oldsymbol{ extlambda}| vert > oldsymbol{ u}_{ m c}$, and low temperature), the DQD charge readout can reveal photon entry with non-negligible efficiency, while backaction on the cavity becomes a critical design consideration. Experimental realization hinges on achieving ultra-low electron temperatures and fast, high-fidelity rf charge sensing to resolve transient charge depletion correlating with single-photon events.

Abstract

Within a circuit quantum electrodynamics architecture, we theoretically investigate the detection of a single propagating microwave photon traveling through a resonant microwave cavity dispersively interacting with a double quantum dot tunnel-coupled to a lead. Under suitable conditions, a single photon in the cavity can induce a measurable change in the electronic occupation of the charge states. We develop a quantum cascade approach that enables a time-resolved description of a single-photon wave packet impinging on the cavity. We make use of a simple model of charge detector to assess the efficiency of our photo-detection configuration as functions of key parameters such as coupling strength, tunneling rate, temperature, and photon resonance linewidth. We finally highlight a measurement-induced backaction effect on the cavity mode associated with the dispersive, non-absorptive detection process.

Figures (5)

• Figure 1: (a) The system consists of an incoming microwave photon pulse with frequency $\omega_\textrm{in}$, which is temporarily stored in a cavity (detection mode with frequency $\omega_c$). The cavity is dispersively coupled (coupling strength $\lambda$) to a single electron state, from which an electron can tunnel to and from a single lead at temperature $T$ and chemical potential $\mu$ with rate $\Gamma_\textrm{QD}$. (b) Concept of the dispersive measurement by monitoring the electron occupation. Initially, the energy of the electronic state is $\epsilon < \mu$, so this is almost fully occupied (in the low-temperature limit, see main text). When a photon enters the cavity, the energy of the electronic state shifts $\epsilon \to \epsilon + |\lambda|$, and the electron can tunnel out into the lead. The system charge occupation is monitored through a charge detector (not shown in the figure). Here we assumed the dispersive coupling $\lambda<0$ (see main text). The single electron level corresponds to the bonding level of the DQD whereas the antibonding level (not shown) always remains empty, see \ref{['fig:app_DQD_levels']} in Appendix \ref{['app:DispersiveRegime']}.
• Figure 2: Example of time evolution of the QD occupation $p^{(1)}$ (purple), the source mode $\langle\hat{n}_\textrm{in}\rangle$ (gray), and the detection mode $\langle\hat{n}_c\rangle$ (solid orange line) for $\omega_\textrm{in} = \omega_c +\lvert \lambda \rvert$, $\Gamma_\textrm{QD} = 4\gamma_c$, $\epsilon = -\lvert \lambda \rvert/2$, $\gamma_\textrm{in} = \gamma_c = 0.01 \omega_c$, $\gamma_c = 0.1 \, \lvert \lambda \rvert$, and $T = 0.01 \, \lvert \lambda \rvert$. To show the effect of the backaction due to the dispersive interaction, which always leads to a decrease of $\langle\hat{n}_c\rangle$, the detection mode occupation for $\lambda = 0$, $\langle\hat{n}_c\rangle_{( \lambda = 0)}$, is plotted for comparison (orange dashed line).
• Figure 3: (a) $n_\textrm{max}$ as function of $\lvert \lambda \rvert$ and system parameters $\Delta \omega$ (left), $\Gamma_\textrm{QD}$ (middle), and $\gamma_\textrm{in}$ (right). (b) $\Delta p_\textrm{max}$ as a function of the same parameters as in (a). (c) $T$ dependence of $n_\textrm{max}$ and (d) $\Delta p_\textrm{max}$ along cuts of constant $\lvert \lambda \rvert$. Constant parameters in all subfigures are set to $T = 0.1 \gamma_c$, $\epsilon = -\lvert \lambda \rvert/2$ and $\gamma_c = \gamma_\textrm{in} = 0.01 \omega_c$, $\Gamma_\textrm{QD} = 4\gamma_c$, $\Delta \omega = \lvert \lambda \rvert$.
• Figure 4: Full time evolution of $\Delta n_\textrm{det}(t)$ for different temperatures, for (a) $\gamma_\textrm{det} = 0.01 \Gamma_\textrm{QD}$ (solid lines) and (b) $\gamma_\textrm{det} = 100 \Gamma_\textrm{QD}$ (solid lines). The evolution of $p^{(0)}(t)$ is also shown for comparison (filled areas) for the corresponding choice of $T$. In (a) the dotted lines correspond to $\eta^*$ (see text). (c) Full time evolution $\langle \hat{n}_\textrm{det} \rangle$ (solid lines) and $\langle \hat{n}_\textrm{det}^{( \lvert \lambda \rvert =0)} \rangle$ (dashed lines) for different temperatures and for $\gamma_{\textrm{det}}=100 \Gamma_\textrm{QD}$. Notice that the curve $\langle \hat{n}_\textrm{det}^{( \lvert \lambda \rvert =0)} \rangle$ for $T = 0.01\,\lvert \lambda \rvert$ is so low that it is not visible. Parameters are set to $\lvert \lambda \rvert=0.1 \, \omega_c$, $\Gamma_\textrm{QD} = 4\gamma_c$, $\gamma_c = \gamma_\textrm{in} = 0.01\omega_c$, $\epsilon=- \lvert \lambda \rvert/2$ and with initial QD state $p^{(1)}(t~=~0)~=~1$ in all panels.
• Figure 5: Energy levels of the DQD without photon (black) and in presence of a photon (orange). The splitting between the bonding state with energy $\epsilon$ and antibonding state with energy $\epsilon'$ is given by $\Omega$. In the presence of a photon $\Omega~\to~\Omega + 2\lambda$. As explained in the text of Appendix \ref{['app:subsec-singlelevel']} the antibonding state always remains empty for our choice of parameters whereas the bonding state is tuned such that (a) $\epsilon < \mu$ if $\lambda <0$ (i.e., the initial state is occupied) or (b) $\epsilon > \mu$ if $\lambda >0$ (i.e. the initial state is empty).