Single microwave-photon detector using an artificial Λ-type three-level system

Single-photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photons extremely challenging. Here we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an impedance-matched artificial Λ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. Each signal photon deterministically induces a Raman transition in the Λ system and excites the qubit. The subsequent dispersive readout of the qubit produces a discrete ‘click'. We attain a high single-photon-detection efficiency of 0.66±0.06 with a low dark-count probability of 0.014±0.001 and a reset time of ∼400 ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing.

S ingle-photon detection is essential to many quantum-optics experiments, enabling photon counting and its statistical and correlational analyses 1 . It is also an indispensable tool in many protocols for quantum communication and quantum information processing [2][3][4][5] . In the optical domain, various kinds of single-photon detectors are commercially available and commonly used 1,6 . However, despite the latest developments in nearly-quantum-limited amplification 7,8 and homodyne measurement for extracting microwave photon statistics 9 , the detection of a single microwave photon in an itinerant mode remains a challenging task due to its correspondingly small energy. Meanwhile, the demand for such detectors is rapidly increasing, driven by applications involving both microwave and hybrid optical-microwave quantum systems. In this article we demonstrate an efficient and practical single microwave-photon detector based on the deterministic switching in an artificial L-type three-level system implemented using the dressed states of a driven superconducting quantum circuit. The detector operates in a time-gated mode and features a high quantum efficiency 0.66 ± 0.06, a low dark-count probability 0.014±0.001, a bandwidth B2p Â 16 MHz, and a fast reset time B400 ns. It can be readily integrated with other components for microwave quantum optics.
Our detection scheme carries several advantages compared with previous proposals. It uses coherent quantum dynamics, which minimizes energy dissipation on detection and allows for rapid resetting with a resonant drive, in contrast to schemes that involve switching from metastable states of a current-biased Josephson junction into the finite voltage state [10][11][12] . Moreover, our detection scheme does not require any temporal shaping of the input photons, nor precise time-dependent control of system parameters adapted to the temporal mode of the input photons, in contrast to the photon-capturing experiments [13][14][15] . Temporal mode mismatch of the photons also limits the maximum efficiency in the recently demonstrated single-photon detection using a transmon qubit in a three-dimensional (3D) cavity 16 . Finally, our scheme also achieves a high efficiency without cascading many devices 10,17 .
The operating principle of the detector fully employs the elegance of waveguide quantum electrodynamics, which has recently attracted significant attention in various contexts surrounding photonic quantum information processing [18][19][20][21] . When electromagnetic waves are confined and propagate in a one-dimensional (1D) mode, their interaction with a quantum emitter/scatterer is substantially simplified and enhanced compared with 3D cases. These advantages result from the natural spatial-mode matching of the emitter/scatterer with a 1D mode and its resulting enhancement of quantum interference effects. Remarkable examples are the perfect extinction of microwave transmission for an artificial atom coupled to a 1D transmission line 22,23 , the photon-mediated interaction between two remote atoms coupled to a 1D transmission line 24 , and the perfect absorption-and thus 'impedance matching'-of a L-type three-level system terminating a 1D transmission line 25,26 . In the latter system, the incident photon deterministically induces a Raman transition, which switches the state of the L system 25,27 . This effect has recently been demonstrated in both the microwave and optical domains 26,28 , indicating its potential for photon   (c) Energy-level diagram of the coupled system and the pulse sequence for single-photon detection. The system is first prepared in the ground state. During the detection stage, we concurrently apply the drive and signal pulses. The drive is parameterized to fulfil the impedance-matched condition such that a signal photon (blue arrow) induces a deterministic Raman transition. A downconverted photon (green arrow) is emitted in the process and discarded. In the readout stage, we detect the qubit excited state nondestructively by sending a qubit readout pulse. The qubit-state-dependent phase shift in the reflected pulse is discriminated by the PPLO. Detailed parameters of the pulse sequence are provided in Methods. detection 29 as well as for implementing deterministic entangling gates with photonic qubits 30 .

Results
Implementation of a single microwave-photon detector. Our device consists of a superconducting flux qubit capacitively and dispersively coupled to a microwave resonator ( Fig. 1b and ref. 31; also see Supplementary Note 1 and Supplementary Fig. 1 for the details of the device). With a proper choice of the qubit drive frequency o d and power P d , the system functions as an impedance-matched L system with identical radiative decay rates from its upper state to its two lower states ( Fig. 1a) 25,26 . The qubit-resonator coupled system is connected to a parametric 10 Figure 1c shows the level structure of the qubit-resonator system and the protocol for the single-photon detection. We label the energy levels |q, ni and their eigenfrequencies o |q,ni , where q ¼ {g, e} and n ¼ {0, 1, ?}, respectively, denote the qubit state and the photon number in the resonator. In the dispersive coupling regime, the qubit-resonator interaction renormalizes the eigenfrequencies to yield o |g,ni ¼ no r and o |e,ni ¼ o ge þ n(o r À 2w), where o ge and o r are the renormalized frequencies of the qubit and the resonator, respectively, and w is the dispersive frequency shift of the resonator due to its interaction with the qubit. Only the lowest four levels with n ¼ 0 or 1 are relevant here.
We prepare the system in its ground state |g, 0i (Fig. 1c, Initialization) and apply a drive pulse to the qubit (Fig. 1c,  Detection). In a frame rotating at o d , the level structure becomes nested, that is, o |g,0i oo |e,0i oo |e,1i oo |g,1i , for o d in the range o ge À 2woo d oo ge (refs 25, 26). On the plateau of the drive pulse, the lower-two levels |g, 0i and |e, 0i (higher-two levels |g, 1i and |e, 1i) hybridize to form dressed states j1i and j2i (j3i and j4i). Under a proper choice of P d , the two radiative decay rates from j4i (or j3i) to the lowest-two levels become identical. Thus, an impedance-matched L system comprising j1i, j2i and j4i (alternatively, j1i, j2i and j3i) is realized. An incident single microwave photon (Gaussian envelope, length t s ), synchronously applied with the drive pulse through the signal port and in resonance with the j1i ! j4i transition, deterministically induces a Raman transition, j1i ! j4i ! j2i, and is downconverted to a photon at the j4i ! j2i transition frequency. This process is necessarily accompanied by an excitation of the qubit.
Finally, we adiabatically switch off the qubit drive and dispersively read out the qubit state (Fig. 1c, Readout). We apply a readout pulse with the frequency o rd ¼ o r À 2w ¼ o |e,1i À o |e,0i through the signal port, which, on reflection at the resonator, acquires a qubit-state-dependent phase shift of 0 or p. This phase shift is detected by the PPLO with high fidelity: in the present setup, the readout fidelity of the qubit is B0.9, which is primarily limited by qubit relaxation before readout 32 .
Demonstration of single microwave-photon detection. We first determine the operating point where the L system deterministically absorbs a signal photon. We simultaneously apply a drive pulse of length t d ¼ 178 ns and a signal pulse of length t s ¼ 85 ns, and proceed to measure the reflection coefficient |r| of the signal pulse as a function of the drive power P d and the signal frequency o s (Fig. 2a). The signal pulse is in a weak coherent state with mean photon number n s $ 0:1. A pronounced dip with a depth of o À 25 dB is observed in |r| at (P d , o s /2p) ¼ ( À 76 dBm, 10.268 GHz), in close agreement with theory (Fig. 2c). The dip indicates a near-perfect absorption condition, that is, impedance matching, where the reflection of the input microwave photon vanishes due to destructive self-interference. Correspondingly, a deterministic Raman transition of j1i ! j4i ! j2i is induced, and the qubit state is flipped.
To obtain a 'click' corresponding to single-photon detection, we read out the qubit state by using the PPLO immediately after the Raman transition. Before initiating readout, the drive pulse is turned off to suppress unwanted Raman transitions induced by the readout pulse, for example, j2i ! j3i ! j1i. We repeatedly apply the pulse sequence in Fig. 1c 10 4 times and evaluate the single-photon-detection efficiency Z P(|ei)/[1 À P(0)], where P(|ei) and P(0) exp( À n s ) are the probabilities for the qubit being in the excited state and the signal pulse being in the vacuum state, respectively. We emphasize that the detection efficiency here is defined with respect to the mean photon number in the propagating signal pulses. Figure 2b depicts Z as a function of P d and o s . The dark-count probability of the detector-mainly caused by the nonadiabatic qubit excitation due to the drive pulse and the imperfect initialization-is subtracted when evaluating Z (see Supplementary Note 3 and Supplementary Fig. 3 for the details of the dark count in the detector). We observe that Z is maximized at the dip position in Fig. 2a in accordance with the impedance-matching condition. We also confirm that the result agrees with numerical calculations based on the parameters determined independently (Fig. 2d). The maximum value, Z ¼ 0.66±0.06, is obtained at (P d , o s /2p) ¼ ( À 75.5 dBm, 10.268 GHz; Fig. 2e). The efficiency exceeds 0.5 over a signalfrequency range of B20 MHz, which is comparable to the bandwidth of the detector, k/2pB16 MHz (see Supplementary Note 4 and Supplementary Fig. 4 for the details of the time constant of the impedance-matched L system). n s is maintained near 0.1 in the measurement, implying that B0.5% of the weak-coherent signal pulses contain multiple photons. Our detector also responds to multi-photon pulses, as do many photodetectors, but it cannot discriminate them from singlephoton pulses. The efficiency Z includes those counts. We theoretically confirm that our detector also works for other signal-pulse shapes such as rectangular and exponential decay 29 .
Optimization of detection efficiency. In Fig. 3a, we plot efficiency Z as a function of the signal pulse length t s . Here, we fix o s and P d at the values which maximize Z in Fig. 2e. The drive pulse duration t d is set to be t d ¼ 1.5t s þ 50 ns, which empirically maximizes Z at each t s . We observe that Z is a non-monotonic function of t s and attains a maximum at t s ¼ 85 ns. The initial increase of Z at short t s is due to the narrowing of the signal bandwidth resulting in an improved overlap with the detection bandwidth. The characteristic response time of the impedancematched L system is estimated to be 2/k ¼ 20 ns in terms of the voltage amplitude. The shortest signal pulse length 34 ns in Fig. 3a is comparable to this. For longer t s , the qubit relaxation limits Z (ref. 29). Next, we examine how the photon detector behaves when n s in the signal pulse is varied. Figure 3b shows P(|ei) as a function of n s for fixed signal pulse lengths at t s ¼ 34, 85, and 189 ns. P(|ei) increases linearly with n s as expected. Moreover, the observed P(|ei) agree very well with the theoretically predicted values (dashed lines) based on the independently calibrated qubit lifetime and input signal power (Supplementary Note 5). Figure 3c shows the photon detection efficiency Z calculated from P(|ei) and P(0) in Fig. 3b. The detection efficiencies stay constant for n s t1 regardless of the pulse lengths. This validates the determination of Z in our measurements using signal pulses in weak coherent states. For n s 41, Z slightly depends on n s because of the possibility to drive multiple Raman transitions.
Demonstration of a fast reset protocol. After a single-photondetection event, the qubit remains in the excited state until it spontaneously relaxes to the ground state, which leads to a relatively long dead time of the detector. However, our coherent approach allows us to implement a fast reset protocol (Fig. 4a): in conjunction with the drive pulse that forms the L system, we apply a relatively strong reset pulse through the signal port, which induces an inverse Raman transition, j2i ! j3i ! j1i. We optimize the drive-pulse power P dr and the reset-pulse frequency o rst (see Methods section) such that the resulting qubit excitation probability P(|ei) is minimized (Fig. 4b). At the optimal reset point (P dr , o rst /2p) ¼ ( À 72.1 dBm, 10.162 GHz), P(|ei) attains a minimum value 0.017 ± 0.002, equivalent to the value 0.016 ± 0.001 obtained in the absence of the initial p-pulse used to mimic a photon absorption event. Without a reset pulse, we obtain P(|ei) ¼ 0.490±0.010. A comparison of the two results indicates that the reset pulse is highly efficient. However, the reset pulse results in a twice-larger occupation of the qubit excited state compared with the value 0.008 ± 0.001 obtained through equilibration. This indicates a small probability of unwanted nonadiabatic excitation due to the drive pulse during the reset protocol. Finally, we demonstrate microwave photon detection combined with the fast reset protocol. We apply the drive and the signal pulses (the same conditions as in the measurement in Fig. 2b) after the reset protocol and readout the qubit. We achieve Z ¼ 0.67±0.06, consistent with the maximum value of Z in Fig. 2e. This indicates that the reset protocol does not affect subsequent detection efficiency. The time-gated operation with the reset protocol can be repeated at a rate exceeding 1 MHz (see Methods section).

Discussion
For the moment, the detection efficiency of this detector is limited by the relatively short qubit relaxation time T 1 B0.7 ms. Nonetheless, our theoretical work indicates that efficiencies reaching B0.9 are readily achievable with only a modest improvement of the qubit lifetime 29 . An extension from time-gated-mode to continuous-mode operation is also possible 33 .

Methods
Protocol for the single-photon detection. The drive frequency is set at is the detuning from the qubit energy and is fixed through all the experiments. The drive pulse is synchronized with the signal pulse, which has a Gaussian envelope with a length t s corresponding to its full width at half maximum in its voltage amplitude (Fig. 1c). The duration t d of the drive pulse is optimized as t d ¼ 1.5t s þ 50 ns so that the signal pulse is completely covered by the drive pulse and is efficiently absorbed by the L system. To suppress unwanted nonadiabatic qubit excitations, the rising and falling edges of the drive-pulse envelope are smoothed by a Gaussian function with full width at half maximum of 2t rise ¼ 30 ns in its voltage amplitude. The readout pulse (with frequency o rd ¼ o r À 2w ¼ 2p Â 10.187 GHz, length t rd ¼ 60 ns, and mean photon number n rd $ 10) is applied after a delay of t delay1 ¼ t d /2 þ t rise from the centre of the drive and signal pulses. The reflected readout pulse works as a locking signal for the PPLO output phase, and the pump pulse (with frequency o pump ¼ 2o rd , length t pump ¼ 400 ns, and power P pump B À 60 dBm) is applied after t delay2 ¼ 40 ns. The parametric oscillation signal with either 0 or p phase is output from the PPLO during the application of the pump pulse, and a data acquisition time of B100 ns is required to extract the phase.
Optimization of the reset protocol. We first apply a p pulse of length 6 ns to directly excite the qubit from the |g, 0i to the |e, 0i state (Fig. 4a). Then, we apply the drive and reset pulses to induce the j2i ! j3i ! j1i transition. To find the operating point which maximizes the reset efficiency, we swept the frequency o rst of the reset pulse and the drive power P dr . After fixing o rst and P dr , we adjust the drive pulse length t dr , and the mean photon number in the reset pulse n rst to minimize P(|ei). Finally we measure P(|ei) as a function of o rst and P dr using the reset protocol with optimized parameters. Parameters for the readout and pump pulses are the same as the ones in Fig. 1c.
It takes 410 ns to reset the system and 208 ns to detect a single photon for t s ¼ 85 ns. Both of the durations are determined by the drive pulse widths including 2t rise ¼ 30 ns. The qubit readout is completed by accumulating data for 100 ns after t delay2 ¼ 40 ns. The period of the single-photon detection including the reset protocol is B760 ns, which allows a photon counting rate of B1.3 MHz.
Data availability. The data that support the findings of this study are available from the corresponding author upon request.