Quantum Nondemolition Detection of a Propagating Microwave Photon

The ability to nondestructively detect the presence of a single, traveling photon has been a long-standing goal in optics, with applications in quantum information and measurement. Realizing such a detector is complicated by the fact that photon-photon interactions are typically very weak. At microwave frequencies, very strong effective photon-photon interactions in a waveguide have recently been demonstrated. Here we show how this type of interaction can be used to realize a quantum nondemolition measurement of a single propagating microwave photon. The scheme we propose uses a chain of solid-state three-level systems (transmons) cascaded through circulators which suppress photon backscattering. Our theoretical analysis shows that microwave-photon detection with fidelity around 90% can be realized with existing technologies.

Figure 1

A chain of $N$ transmons cascaded from microwave circulators interacts with control and probe fields, which are close to resonance with the 0-1 and 1-2 transition, respectively. In the absence of a control photon, the chain is transparent to the probe. A control photon with temporal profile $\xi (t)$ drives each transmon consecutively, which then displaces the probe field, which is detected by homodyne measurement.

Figure 2

Signal-to-noise ratio (SNR) and detector dynamics. (a) SNR calculated using the master equation (ME) with Fock state input (Supplemental Material [25]) (red circles), stochastic master equation (SME) with a Fock state input (green squares), and stochastic master equation with a tunable cavity as photon source (blue triangles). The dashed line shows a $\sqrt{N}$ fit assuming that each transmon contributes equally and independently to the signal. Inset: Detection fidelity $F$ of correctly inferring the control photon number, Eq. (4). The crosses are results of Monte Carlo sampling from the stochastic master equation; the dashed line is inferred from the SNR, assuming a normal distribution. (b) Histogram of signal with 0 (blue) and 1 (red) control photons. For $N=1$ transmon, the distributions overlap significantly ($\mathrm{SNR}=0.7$); for $N=8$, the distributions are well resolved ($\mathrm{SNR}=1.85$). (c) Transmon excitation $P_{\text{exc}}$ and average homodyne current $⟨j(t)⟩$ over time for $N=3$. (d) Integrated output photon flux for $N=1$, 4, and 8, showing unity transmission. Transmon parameter values are listed in Table 1, the homodyne local oscillator phase is $\varphi =\pi /2$ and probe integration window $4<t<8+1.5(N-1)$, a value which is found by numerical optimization to limit the amount of added noise to the signal. All quantities are in units of ${\mathrm{\Gamma }}_c^{(1)}={\mathrm{\Gamma }}_{01}^{(1)}$.

Figure 3

(a) SNR with different input photon shapes. The parameters of the transmons and the probe field are optimized for each of the pulse shapes (see Table 1). The dashed lines are fitted using $\chi \sqrt{N}$; the best-fit values of $\chi$ are in Table 1 Effect of losses in circulators on the SNR for a Gaussian input photon for two realistic choices of power loss $P_{\text{loss}}$ in each circulator. (c) Number of transmons that would be required to achieve $\mathrm{SNR}\ge 1$ for a Gaussian input photon for detector efficiency $\eta$.