Introduction

Single-photon detection is essential to many quantum-optics experiments, enabling photon counting and its statistical and correlational analyses1. It is also an indispensable tool in many protocols for quantum communication and quantum information processing2,3,4,5. In the optical domain, various kinds of single-photon detectors are commercially available and commonly used1,6. However, despite the latest developments in nearly-quantum-limited amplification7,8 and homodyne measurement for extracting microwave photon statistics9, 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 Λ-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 ∼2π × 16 MHz, and a fast reset time ∼400 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 state10,11,12. 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 experiments13,14,15. 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) cavity16. Finally, our scheme also achieves a high efficiency without cascading many devices10,17.

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 processing18,19,20,21. 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 line22,23, the photon-mediated interaction between two remote atoms coupled to a 1D transmission line24, and the perfect absorption— and thus ‘impedance matching’— of a Λ-type three-level system terminating a 1D transmission line25,26. In the latter system, the incident photon deterministically induces a Raman transition, which switches the state of the Λ system25,27. This effect has recently been demonstrated in both the microwave and optical domains26,28, indicating its potential for photon detection29 as well as for implementing deterministic entangling gates with photonic qubits30.

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 ωd and power Pd, the system functions as an impedance-matched Λ 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 phase-locked oscillator (PPLO), which enables fast and non-destructive qubit readout (ref. 32; also see Supplementary Notes 1 and 2, and Supplementary Fig. 2 for the details of the device and the experimental set-up).

Figure 1: Experimental set-up and pulse sequence.
figure 1

(a) Image of the sample chip containing a flux qubit and a superconducting microwave resonator coupled capacitively and operated in the dispersive regime. For certain proper conditions of the qubit drive, the coupled system functions as an impedance-matched Λ-type three-level system. (b) Schematic of the itinerant microwave-photon detector consisting of the coupled system and connected to a parametric phase-locked oscillator (PPLO) via three circulators in series. The circuit has three input ports: signal, qubit drive, and pump for the PPLO. (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.

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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, n〉 and their eigenfrequencies ω|q,n〉, where q={g, e} and n={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 ω|g,n〉=nωr and ω|e,n〉=ωge+n(ωr−2χ), where ωge and ωr are the renormalized frequencies of the qubit and the resonator, respectively, and χ is the dispersive frequency shift of the resonator due to its interaction with the qubit. Only the lowest four levels with n=0 or 1 are relevant here.

We prepare the system in its ground state |g, 0〉 (Fig. 1c, Initialization) and apply a drive pulse to the qubit (Fig. 1c, Detection). In a frame rotating at ωd, the level structure becomes nested, that is, ω|g,0〉<ω|e,0〉<ω|e,1〉<ω|g,1〉, for ωd in the range ωge−2χ<ωd<ωge (refs 25, 26). On the plateau of the drive pulse, the lower-two levels |g, 0〉 and |e, 0〉 (higher-two levels |g, 1〉 and |e, 1〉) hybridize to form dressed states and ( and ). Under a proper choice of Pd, the two radiative decay rates from (or ) to the lowest-two levels become identical. Thus, an impedance-matched Λ system comprising , and (alternatively, , and ) is realized. An incident single microwave photon (Gaussian envelope, length ts), synchronously applied with the drive pulse through the signal port and in resonance with the transition, deterministically induces a Raman transition, , and is downconverted to a photon at the 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 ωrd=ωr−2χ=ω|e,1〉−ω|e,0〉 through the signal port, which, on reflection at the resonator, acquires a qubit-state-dependent phase shift of 0 or π. This phase shift is detected by the PPLO with high fidelity: in the present set-up, the readout fidelity of the qubit is ∼0.9, which is primarily limited by qubit relaxation before readout32.

Demonstration of single microwave-photon detection

We first determine the operating point where the Λ system deterministically absorbs a signal photon. We simultaneously apply a drive pulse of length td=178 ns and a signal pulse of length ts=85 ns, and proceed to measure the reflection coefficient |r| of the signal pulse as a function of the drive power Pd and the signal frequency ωs (Fig. 2a). The signal pulse is in a weak coherent state with mean photon number . A pronounced dip with a depth of <−25 dB is observed in |r| at (Pd, ωs/2π)=(−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 is induced, and the qubit state is flipped.

Figure 2: Impedance matching and itinerant microwave-photon detection.
figure 2

(a) Amplitude of the reflection coefficient |r| of the input signal pulse with mean photon number as a function of the qubit drive power Pd and the signal frequency ωs. The PPLO is not activated during this measurement. The impedance-matched region is resolved (dark-blue point), where the input microwave photon is absorbed almost completely. In the inset, we also observe another dip in |r|, corresponding to the Raman transition of . Microwave power levels stated in this article are referred to the value at the corresponding ports on the sample chip. (b) Detection efficiency η of an itinerant microwave photon. The efficiency reaches its maximum at the impedance-matched point, where the Raman transition of takes place. (c,d) Theoretical predictions corresponding to a and b. (e) Cross-sections of (b) (blue dots) and (d) (red dashed line) at ωs/2π=10.268 GHz. The error bars are due to the uncertainty in the input power calibration (see Supplementary Note 5 and Supplementary Fig. 5 for the details of the input power calibration).

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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, . We repeatedly apply the pulse sequence in Fig. 1c 104 times and evaluate the single-photon-detection efficiency η≡P(|e〉)/[1−P(0)], where P(|e〉) and P(0)≡exp(−) 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 η as a function of Pd and ωs. 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 η (see Supplementary Note 3 and Supplementary Fig. 3 for the details of the dark count in the detector). We observe that η 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, η=0.66±0.06, is obtained at (Pd, ωs/2π)=(−75.5 dBm, 10.268 GHz; Fig. 2e). The efficiency exceeds 0.5 over a signal-frequency range of ∼20 MHz, which is comparable to the bandwidth of the detector, κ/2π∼16 MHz (see Supplementary Note 4 and Supplementary Fig. 4 for the details of the time constant of the impedance-matched Λ system). is maintained near 0.1 in the measurement, implying that ∼0.5% 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 single-photon pulses. The efficiency η includes those counts. We theoretically confirm that our detector also works for other signal-pulse shapes such as rectangular and exponential decay29.

Optimization of detection efficiency

In Fig. 3a, we plot efficiency η as a function of the signal pulse length ts. Here, we fix ωs and Pd at the values which maximize η in Fig. 2e. The drive pulse duration td is set to be td=1.5ts+50 ns, which empirically maximizes η at each ts. We observe that η is a non-monotonic function of ts and attains a maximum at ts=85 ns. The initial increase of η at short ts is due to the narrowing of the signal bandwidth resulting in an improved overlap with the detection bandwidth. The characteristic response time of the impedance-matched Λ system is estimated to be 2/κ=20 ns in terms of the voltage amplitude. The shortest signal pulse length 34 ns in Fig. 3a is comparable to this. For longer ts, the qubit relaxation limits η (ref. 29). Next, we examine how the photon detector behaves when in the signal pulse is varied. Figure 3b shows P(|e〉) as a function of for fixed signal pulse lengths at ts=34, 85, and 189 ns. P(|e〉) increases linearly with as expected. Moreover, the observed P(|e〉) 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 η calculated from P(|e〉) and P(0) in Fig. 3b. The detection efficiencies stay constant for regardless of the pulse lengths. This validates the determination of η in our measurements using signal pulses in weak coherent states. For >1, η slightly depends on because of the possibility to drive multiple Raman transitions.

Figure 3: Optimization of the efficiency.
figure 3

(a) Single-photon-detection efficiency η as a function of the signal pulse length ts. The mean photon number for the weak-coherent signal pulse is ∼0.1. (b) Probability of the qubit excitation by single microwave photons, P(|e〉), as a function of . Dashed lines represent theoretical predictions and the solid line indicates probability for the signal pulse being in the vacuum state, P(0)=exp(−). The statistical error in P(|e〉) is smaller than the dot size. (c) η calculated from P(|e〉) and P(0) in b as a function of . Dashed lines indicate theoretical predictions. In all the plots, the error bars both in and η are due to the uncertainty in the input power calibration.

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Demonstration of a fast reset protocol

After a single-photon-detection 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 Λ system, we apply a relatively strong reset pulse through the signal port, which induces an inverse Raman transition, . We optimize the drive-pulse power Pdr and the reset-pulse frequency ωrst (see Methods section) such that the resulting qubit excitation probability P(|e〉) is minimized (Fig. 4b). At the optimal reset point (Pdr, ωrst/2π)=(−72.1 dBm, 10.162 GHz), P(|e〉) attains a minimum value 0.017±0.002, equivalent to the value 0.016±0.001 obtained in the absence of the initial π-pulse used to mimic a photon absorption event. Without a reset pulse, we obtain P(|e〉)=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 η=0.67±0.06, consistent with the maximum value of η 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).

Figure 4: Demonstration of the fast reset protocol.
figure 4

(a) Pulse sequence used to evaluate the reset efficiency. The initial π-pulse mimics a single-photon detection and excites the qubit. During the reset stage, a drive pulse and a reset pulse with the mean photon number of are concurrently applied, inducing an inverse Raman transition: . The remaining population in the |e〉 state is then detected. (b) Population of the qubit excited state after the reset operation P(|e〉), as a function of the reset-pulse frequency ωrst and the drive-pulse power Pdr. (c) Theoretical prediction for (b) with no free parameters. (d) Cross sections of (b) (blue dots) and (c) (red dashed line) at ωrst/2π=10.162 GHz.

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Discussion

For the moment, the detection efficiency of this detector is limited by the relatively short qubit relaxation time T1∼0.7 μs. Nonetheless, our theoretical work indicates that efficiencies reaching ∼0.9 are readily achievable with only a modest improvement of the qubit lifetime29. An extension from time-gated-mode to continuous-mode operation is also possible33.

Methods

Protocol for the single-photon detection

The drive frequency is set at ωd=ωge−δω, where δω=2π × 49 MHz (<2χ) 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 ts corresponding to its full width at half maximum in its voltage amplitude (Fig. 1c). The duration td of the drive pulse is optimized as td=1.5ts+50 ns so that the signal pulse is completely covered by the drive pulse and is efficiently absorbed by the Λ 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 2trise=30 ns in its voltage amplitude.

The readout pulse (with frequency ωrd=ωr−2χ=2π × 10.187 GHz, length trd=60 ns, and mean photon number ) is applied after a delay of tdelay1=td/2+trise 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 ωpump=2ωrd, length tpump=400 ns, and power Ppump∼−60 dBm) is applied after tdelay2=40 ns. The parametric oscillation signal with either 0 or π phase is output from the PPLO during the application of the pump pulse, and a data acquisition time of ∼100 ns is required to extract the phase.

Optimization of the reset protocol

We first apply a π pulse of length 6 ns to directly excite the qubit from the |g, 0〉 to the |e, 0〉 state (Fig. 4a). Then, we apply the drive and reset pulses to induce the transition. To find the operating point which maximizes the reset efficiency, we swept the frequency ωrst of the reset pulse and the drive power Pdr. After fixing ωrst and Pdr, we adjust the drive pulse length tdr, and the mean photon number in the reset pulse to minimize P(|e〉). Finally we measure P(|e〉) as a function of ωrst and Pdr 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 ts=85 ns. Both of the durations are determined by the drive pulse widths including 2trise=30 ns. The qubit readout is completed by accumulating data for 100 ns after tdelay2=40 ns. The period of the single-photon detection including the reset protocol is ∼760 ns, which allows a photon counting rate of ∼1.3 MHz.

Data availability

The data that support the findings of this study are available from the corresponding author upon request.

Additional information

How to cite this article: Inomata, K. et al. Single microwave-photon detector using an artificial Λ-type three-level system. Nat. Commun. 7:12303 doi: 10.1038/ncomms12303 (2016).