Continuous-Wave Single-Photon Transistor Based on a Superconducting Circuit

We propose a microwave frequency single-photon transistor which can operate under continuous wave probing and represents an efficient single microwave photon detector. It can be realized using an impedance matched system of a three level artificial ladder-type atom coupled to two microwave cavities connected to input-output waveguides. Using a classical drive on the upper transition, we find parameter space where a single photon control pulse incident on one of the cavities can be fully absorbed into hybridized excited states. This subsequently leads to series of quantum jumps in the upper manifold and the appearance of a photon flux leaving the second cavity through a separate input-output port. The proposal does not require time variation of the probe signals, thus corresponding to a passive version of a single-photon transistor. The resulting device is robust to qubit dephasing processes, possesses low dark count rate for large anharmonicity, and can be readily implemented using current technology.

Figure 1

(a) Sketch of the system, showing a driven qutrit coupled to two superconducting cavities, each connected to a separate input-output line. (b) Energy diagram of three lowest artificial atom levels with associated cavity and drive couplings. (c) Relevant manifold of SPT operational levels with dressed excited states.

Figure 2

(a) Reflection coefficient for the first cavity as a function of input coupling rate ${\kappa }_1$ (log scale). The dotted line is a full numerical calculation, and the solid line represents Eq. (4) with ${\mathrm{\Gamma }}_{\text{set}}$ given by Eq. (3). Here $\mathrm{\Omega }/g_2=2$, $g_1/g_2=0.05$, and ${\kappa }_2/g_2=2$. (b) Tunability of the effective setting rate as a function of drive strength $\mathrm{\Omega }$ and varying ${\kappa }_2$ with $g_1/g_2=0.05$. The full lines are the result of a numerical simulation which agree with the analytical prediction of Eq. (4) for ${\kappa }_2\gtrsim 1$. The dashed horizontal line represents the impedance matching condition which can always be obtained by varying $\mathrm{\Omega }$.

Figure 3

(a) Time dependence of second cavity output calculated for Gaussian single photon pulse incident on the first cavity; $g_1/g_2=0.05$, $\mathrm{\Omega }/g_2=2$, ${\kappa }_2/g_2=1$. (b) SPT gain and bandwidth plotted as function of the first cavity coupling $g_1$ for various drive strengths; ${\kappa }_1={\mathrm{\Gamma }}_{\text{set}}$, ${\kappa }_2/g_2=1$. (c) SPT gain and bandwidth for varying output coupling ${\kappa }_2$; $g_1/g_2=0.05$.

Figure 4

(a) Gain of SPT as a function of decay (solid curves) and pure dephasing rates (dashed lines); $\mathrm{\Omega }/g_2=2$, $g_1/g_2=0.05$, ${\kappa }_1={\mathrm{\Gamma }}_{\text{set}}$. (b) The SPT enhanced ${\mathrm{\Gamma }}_{\text{dark}}^{(\mathrm{m})}$ (lower two curves) and single ${\mathrm{\Gamma }}_{\text{dark}}^{(\mathrm{s})}$ (upper two curves) dark count rates as a function of the qutrit anharmonicity $A$. Here, $\mathrm{\Omega }/g_2=2$, $g_1/g_2=0.05$. Numerical results were obtained using the wave function Monte Carlo approach and studying no-jump evolution of the system [37]. We show analytical results for a single dark count rate derived using effective operator formalism [Eq. (6), black solid curves]. For ${\mathrm{\Gamma }}_{\text{dark}}^{(\mathrm{m})}$ we also show a fit $\eta {\mathrm{\Gamma }}_{\text{dark},\text{ss}}^{(\mathrm{m})}$ with $\eta \approx 4$.