Dressed-state engineering for continuous detection of itinerant microwave photons

We propose a scheme for continuous detection of itinerant microwave photons in circuit quantum electrodynamics. In the proposed device, a superconducting qubit is coupled dispersively to two resonators: one is used to form an impedance-matched $\mathrm{\Lambda }$ system that deterministically captures incoming photons, and the other is used for continuous monitoring of the event. The present scheme enables efficient photon detection: for realistic system parameters, the detection efficiency reaches 0.9 with a bandwidth of about 10 MHz.

Figure 1

Schematic of the single-photon detector. A qubit is coupled dispersively to two resonators. Resonators A and B and the qubit are respectively coupled to waveguides A, B, and C. We input a signal photon through waveguide A, a probe field through waveguide B, and a drive field through waveguide C.

Figure 2

Dressed-state engineering of the qubit-resonators system. (a) Level structure of the bare states $\left({\mathrm{\Omega }}_d=0\right)$ in the rotating frame. (b) Level structure of the dressed states at the operation point $\left({\mathrm{\Omega }}_d={\mathrm{\Omega }}_d^{\mathrm{imp}}\right)$. (c) Dependences of the decay rates on the drive power. The drive frequency is set at ${\omega }_d/2\pi =4.905$ GHz. An impedance-matched $\mathrm{\Lambda }$ system is formed at ${\mathrm{\Omega }}_d^{\mathrm{imp}}/2\pi =10.897\mathrm{MHz}$. ${\tilde{\kappa }}_{ji}^a \left({\tilde{\kappa }}_{ji}^b\right)$ is normalized by ${\kappa }_a \left({\kappa }_b\right)$. (d) Amplitude of the reflection coefficient $|r_s|$ of a continuous signal field applied through waveguide A, as a function of the signal frequency ${\omega }_s$ and the drive power ${\mathrm{\Omega }}_d$. The upper (lower) curve represents ${\tilde{\omega }}_{41} \left({\tilde{\omega }}_{31}\right)$.

Figure 3

Microwave response to a signal photon. The signal photon has a carrier frequency of ${\omega }_s/2\pi =10.00$ GHz and a Gaussian pulse shape with the length of $l=100\mathrm{ns}$. (a) Time evolution of the qubit excitation probability $p_e\left(t\right)$. The probe power $\langle n_b\rangle$ is indicated. The signal-photon profile $|f_s{\left(t\right)|}^2$ is also shown in units of ${(8ln2/\pi l^2)}^{1/2}$. (b) Time-averaged qubit excitation probability ${\overline{p}}_e\left(t\right)$ for $\langle n_b\rangle =0.05$. The integration time $\mathrm{\Delta }t$ is indicated.

Figure 4

Single-photon detection efficiency. The probe power is fixed at $\langle n_b\rangle =0.05$. (a) Dependence of the detection efficiency on the pulse length $l$ for various integration times $\mathrm{\Delta }t$. Values of the corresponding readout fidelity $\mathcal{F}$ are also indicated. The input photon is tuned at ${\omega }_s/2\pi =10.0\mathrm{GHz}$. (b) Detection efficiency as a function of ${\mathrm{\Omega }}_d$ and ${\omega }_s$ for $l=100\mathrm{ns}$ and $\mathrm{\Delta }t=660\mathrm{ns}$. The dashed lines indicate ${\tilde{\omega }}_{41},{\tilde{\omega }}_{31}$, and ${\mathrm{\Omega }}_d^{\mathrm{imp}}$. (c) Cross section of (b) at ${\mathrm{\Omega }}_d^{\mathrm{imp}}/2\pi =10.90\mathrm{MHz}$ (red solid). The results for different drive conditions are also shown: ${\omega }_d/2\pi =4.913$ GHz and ${\mathrm{\Omega }}_d^{\mathrm{imp}}/2\pi =16.82\mathrm{MHz}$ (green dashed) and ${\omega }_d/2\pi =4.921$ GHz and ${\mathrm{\Omega }}_d^{\mathrm{imp}}/2\pi =20.37\mathrm{MHz}$ (blue dotted).

Figure 5

(a) The probability $q\left(\tau \right)$ to detect the qubit excitation as a function of the excitation duration time $\tau$ (red solid) and its step-function approximation (blue dashed). (b) Comparison of ${\eta }_1$ (dotted) and ${\eta }_2$ (solid). The qubit lifetime ${\mathrm{\Gamma }}^{-1}$ is assumed to be $3\mu \mathrm{s}$ (blue), $6\mu \mathrm{s}$ (red), and $16\mu \mathrm{s}$ (green).