Nonabsorbing high-efficiency counter for itinerant microwave photons

Detecting an itinerant microwave photon with high efficiency is an outstanding problem in microwave photonics and its applications. We present a scheme to detect an itinerant microwave photon in a transmission line via the nonlinearity provided by a transmon in a driven microwave resonator. With a single transmon we achieve 84% distinguishability between zero and one microwave photons and 90% distinguishability with two cascaded transmons by performing continuous measurements on the output field of the resonator. We also show how the measurement diminishes coherence in the photon number basis thereby illustrating a fundamental principle of quantum measurement: The decoherence rate increases as the detector is made more effective.

Figure 1

Schematic of microwave photon counting. (a) A transmon qubit coupled to a microwave cavity provides the nonlinearity to detect the presence or absence of microwave photons propagating in the waveguide. If the waveguide is in the vacuum state, the transmon is transparent to the cavity field, so the probe field experiences no displacement; for a single signal photon, coherences in the transmon are produced, leading to a displacement of the probe field. A second transmon-cavity unit can be cascaded through a circulator to improve performance. (b) The energy level structure of the transmon. (c) The response of the cavity field to the incident single photon.

Figure 2

The histograms of filtered homodyne signal for the presence/absence of the signal photon and the corresponding distinguishability. The black curve plots the distinguishability versus threshold values. The signal photon pulse is an exponentially-decayed pulse from a source cavity, and the linear filter function is presented is Eq. (5). The parameters are: ${\gamma }_{01}=1,{\gamma }_{12}=0.1,g=2.45,{\delta }_1=-0.8,{\delta }_2=-18,{\gamma }_c=0.1,E=0.032,\kappa =0.037,\varphi =\pi /2,t_0=0$, and $T=80$.

Figure 3

(a) The scatter plot of the filtered homodyne signals from two probe cavities with the presence/absence of the signal photon. (b) The histogram of the sum homodyne signal $S_{AB}$ and the corresponding distinguishability in the two cascaded transmons case. The parameters are: ${\gamma }_{01}^A={\gamma }_{01}^B=1,{\gamma }_{12}^A={\gamma }_{12}^B=0.1,g_A=g_B=2.45,{\delta }_{1A}={\delta }_{1B}=-0.8,{\delta }_{2A}={\delta }_{2B}=-18,{\gamma }_c=0.1,E_A=E_B=0.032,{\kappa }_A={\kappa }_B=0.037,{\varphi }_A={\varphi }_B=\pi /2,t_0=0$, and $T=80$.

Figure 4

(a) Pulse envelope distortion. (b) Measurement induced decoherence of the signal microwave photon state. The gray dash curves denote the input signal field and the solid curves denote the output signal field at different distinguishability. The blue $\left({\delta }_2=-6\right)$ and orange $\left({\delta }_2=-18\right)$ curves represent the output signal field after interacting with one transmon and the green $\left({\delta }_{2A}={\delta }_{2B}=-18\right)$ curves represent the output signal field after interacting with two transmons. The other parameters are: ${\gamma }_{01}^A={\gamma }_{01}^B=1,{\gamma }_{12}^A={\gamma }_{12}^B=0.1,g_A=g_B=2.45,{\delta }_{1A}={\delta }_{1B}=-0.8,{\gamma }_c=0.1,E_A=E_B=0.032$ and ${\kappa }_A={\kappa }_B=0.037$.