Itinerant Microwave Photon Detector

The realization of a high-efficiency microwave single photon detector is a long-standing problem in the field of microwave quantum optics. Here, we propose a quantum nondemolition, high-efficiency photon detector that can readily be implemented in present state-of-the-art circuit quantum electrodynamics. This scheme works in a continuous fashion, gaining information about the photon arrival time as well as about its presence. The key insight that allows us to circumvent the usual limitations imposed by measurement backaction is the use of long-lived dark states in a small ensemble of inhomogeneous artificial atoms to increase the interaction time between the photon and the measurement device. Using realistic system parameters, we show that large detection fidelities are possible.

Figure 1

(a) Sketch of a single absorber model for photon detection. A signal photon (red) is absorbed in a mode $B$ and induces a coherent state displacement in a harmonic mode $A$ which is measured using homodyne measurement. (b) Coupling between $A$ and $B$ induces fluctuations in the absorption spectrum of mode $B$, preventing the absorption of incoming photons. (c) Illustration of phase space for mode $A$ as a photon is absorbed in $B$.

Figure 2

(a) Absorber $B$ is replaced by an ensemble of inhomogeneous modes coupled at the same point of the input waveguide. (b) Redrawing of (a) in the bright and dark states basis for $N=3$. (c) Possible circuit-QED implementation for $N=3$. Tunable transmon qubits acting as absorbers are coupled capacitively on one side to an input transmission line and on the other side to a measurement resonator.

Figure 3

(a) Fidelity as a function of the number of absorbers. The circles are calculated using the ideal model with ${\kappa }_A/{\kappa }_B=0.2$, $g_z^{(1)}/{\kappa }_B=1$, $g_z^{(2)}/{\kappa }_B=0.6$, $g_z^{(3)}/{\kappa }_B=0.5$, and $g_z^{(4)}/{\kappa }_B=0.4$ with the detunings ${\overrightarrow{\mathrm{\Delta }}}^{(2)}/{\kappa }_B=(0.55,-0.55)$, ${\overrightarrow{\mathrm{\Delta }}}^{(3)}/{\kappa }_B=(0.7,-0.7,0)$, and ${\overrightarrow{\mathrm{\Delta }}}^{(4)}/{\kappa }_B=(0.7,-0.7,0.23,-0.23)$. The diamonds are calculated using realistic parameters for a transmon ensemble dispersively coupled to a resonator with ${\kappa }_B/2\pi =10\mathrm{MHz}$, $g_z/\chi =10$, and $T_1$, $T_2=30\mu \mathrm{s}$. (b) Detector efficiency as a function of the dark count rate. Solid lines correspond to statistics extracted from trajectories, while for the dashed lines ${\mathrm{\Gamma }}_{\mathrm{dark}}$ was estimated using an analytical formula. The lines were calculated for the ideal model, and the points indicate where the fidelity is maximized. The black dashed line in (a) and (b) correspond the upper bound ${\eta }_{\max }$ imposed by the photon shape used here.

Figure 4

(a) Normalized number of detection events as a function of time for (a) different number of absorbers in the ideal model Eq. (3) and for (b) different thresholds for $N=4$. In both (a) and (b), the input photon shape (red) is shown for comparison and an arbitrary time offset has been substracted from the homodyne signal.