Abstract
Singlephoton detection is a requisite technique in quantumoptics 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 impedancematched 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 singlephotondetection efficiency of 0.66±0.06 with a low darkcount 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.
Introduction
Singlephoton detection is essential to many quantumoptics 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 singlephoton detectors are commercially available and commonly used^{1,6}. However, despite the latest developments in nearlyquantumlimited 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 opticalmicrowave quantum systems. In this article we demonstrate an efficient and practical single microwavephoton detector based on the deterministic switching in an artificial Λtype threelevel system implemented using the dressed states of a driven superconducting quantum circuit. The detector operates in a timegated mode and features a high quantum efficiency 0.66±0.06, a low darkcount 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 currentbiased 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 timedependent control of system parameters adapted to the temporal mode of the input photons, in contrast to the photoncapturing experiments^{13,14,15}. Temporal mode mismatch of the photons also limits the maximum efficiency in the recently demonstrated singlephoton detection using a transmon qubit in a threedimensional (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 onedimensional (1D) mode, their interaction with a quantum emitter/scatterer is substantially simplified and enhanced compared with 3D cases. These advantages result from the natural spatialmode 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 photonmediated interaction between two remote atoms coupled to a 1D transmission line^{24}, and the perfect absorption— and thus ‘impedance matching’— of a Λtype threelevel 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 Λ system^{25,27}. This effect has recently been demonstrated in both the microwave and optical domains^{26,28}, indicating its potential for photon detection^{29} as well as for implementing deterministic entangling gates with photonic qubits^{30}.
Results
Implementation of a single microwavephoton 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 ω_{d} and power P_{d}, the system functions as an impedancematched 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 phaselocked oscillator (PPLO), which enables fast and nondestructive qubit readout (ref. 32; also see Supplementary Notes 1 and 2, and Supplementary Fig. 2 for the details of the device and the experimental setup).
Figure 1c shows the level structure of the qubit–resonator system and the protocol for the singlephoton 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〉}=nω_{r} and ω_{e,n〉}=ω_{ge}+n(ω_{r}−2χ), where ω_{ge} and ω_{r} 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 ω_{d}, the level structure becomes nested, that is, ω_{g,0〉}<ω_{e,0〉}<ω_{e,1〉}<ω_{g,1〉}, for ω_{d} in the range ω_{ge}−2χ<ω_{d}<ω_{ge} (refs 25, 26). On the plateau of the drive pulse, the lowertwo levels g, 0〉 and e, 0〉 (highertwo levels g, 1〉 and e, 1〉) hybridize to form dressed states and ( and ). Under a proper choice of P_{d}, the two radiative decay rates from (or ) to the lowesttwo levels become identical. Thus, an impedancematched Λ system comprising , and (alternatively, , and ) 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 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 ω_{rd}=ω_{r}−2χ=ω_{e,1〉}−ω_{e,0〉} through the signal port, which, on reflection at the resonator, acquires a qubitstatedependent phase shift of 0 or π. This phase shift is detected by the PPLO with high fidelity: in the present setup, the readout fidelity of the qubit is ∼0.9, which is primarily limited by qubit relaxation before readout^{32}.
Demonstration of single microwavephoton detection
We first determine the operating point where the Λ system deterministically absorbs a signal photon. We simultaneously apply a drive pulse of length t_{d}=178 ns and a signal pulse of length t_{s}=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 ω_{s} (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 (P_{d}, ω_{s}/2π)=(−76 dBm, 10.268 GHz), in close agreement with theory (Fig. 2c). The dip indicates a nearperfect absorption condition, that is, impedance matching, where the reflection of the input microwave photon vanishes due to destructive selfinterference. Correspondingly, a deterministic Raman transition of is induced, and the qubit state is flipped.
To obtain a ‘click’ corresponding to singlephoton 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 10^{4} times and evaluate the singlephotondetection 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 P_{d} and ω_{s}. The darkcount 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 impedancematching 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 (P_{d}, ω_{s}/2π)=(−75.5 dBm, 10.268 GHz; Fig. 2e). The efficiency exceeds 0.5 over a signalfrequency 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 impedancematched Λ system). is maintained near 0.1 in the measurement, implying that ∼0.5% of the weakcoherent signal pulses contain multiple photons. Our detector also responds to multiphoton pulses, as do many photodetectors, but it cannot discriminate them from singlephoton pulses. The efficiency η includes those counts. We theoretically confirm that our detector also works for other signalpulse shapes such as rectangular and exponential decay^{29}.
Optimization of detection efficiency
In Fig. 3a, we plot efficiency η as a function of the signal pulse length t_{s}. Here, we fix ω_{s} and P_{d} at the values which maximize η in Fig. 2e. The drive pulse duration t_{d} is set to be t_{d}=1.5t_{s}+50 ns, which empirically maximizes η at each t_{s}. We observe that η is a nonmonotonic function of t_{s} and attains a maximum at t_{s}=85 ns. The initial increase of η 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 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 t_{s}, 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 t_{s}=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.
Demonstration of a fast reset protocol
After a singlephotondetection 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 drivepulse power P_{dr} and the resetpulse frequency ω_{rst} (see Methods section) such that the resulting qubit excitation probability P(e〉) is minimized (Fig. 4b). At the optimal reset point (P_{dr}, ω_{rst}/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 πpulse 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 twicelarger 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 timegated 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}∼0.7 μs. Nonetheless, our theoretical work indicates that efficiencies reaching ∼0.9 are readily achievable with only a modest improvement of the qubit lifetime^{29}. An extension from timegatedmode to continuousmode operation is also possible^{33}.
Methods
Protocol for the singlephoton detection
The drive frequency is set at ω_{d}=ω_{ge}−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 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}=1.5t_{s}+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 drivepulse envelope are smoothed by a Gaussian function with full width at half maximum of 2t_{rise}=30 ns in its voltage amplitude.
The readout pulse (with frequency ω_{rd}=ω_{r}−2χ=2π × 10.187 GHz, length t_{rd}=60 ns, and mean photon number ) is applied after a delay of t_{delay1}=t_{d}/2+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 ω_{pump}=2ω_{rd}, length t_{pump}=400 ns, and power P_{pump}∼−60 dBm) is applied after t_{delay2}=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 ω_{rst} of the reset pulse and the drive power P_{dr}. After fixing ω_{rst} and P_{dr}, we adjust the drive pulse length t_{dr}, and the mean photon number in the reset pulse to minimize P(e〉). Finally we measure P(e〉) as a function of ω_{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}=85 ns. Both of the durations are determined by the drive pulse widths including 2t_{rise}=30 ns. The qubit readout is completed by accumulating data for 100 ns after t_{delay2}=40 ns. The period of the singlephoton 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 microwavephoton detector using an artificial Λtype threelevel system. Nat. Commun. 7:12303 doi: 10.1038/ncomms12303 (2016).
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Acknowledgements
This work was partially supported by JSPS KAKENHI (Grant Number 25400417, 26220601, 15K17731), ImPACT Program of Council for Science and the NICT Commissioned Research.
Author information
Author notes
 Kunihiro Inomata
 & Zhirong Lin
These authors contributed equally to this work.
Affiliations
RIKEN Center for Emergent Matter Science (CEMS), Wako 3510198, Saitama, Japan
 Kunihiro Inomata
 , Zhirong Lin
 , JawShen Tsai
 & Yasunobu Nakamura
College of Liberal Arts and Sciences, Tokyo Medical and Dental University, Ichikawa 2720827, Chiba, Japan
 Kazuki Koshino
MIT Lincoln Laboratory, Lexington, Massachusetts 02420, USA
 William D. Oliver
Departent of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
 William D. Oliver
Department of Physics, Tokyo University of Science, Shinjukuku, Tokyo 1628601, Japan
 JawShen Tsai
NEC IoT Device Research Laboratories, Tsukuba 3058501, Ibaraki, Japan
 Tsuyoshi Yamamoto
Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Meguroku, Tokyo 1538904, Japan
 Yasunobu Nakamura
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Contributions
K.K., T.Y., Y.N., K.I. and Z.R.L. conceived the experiment. K.I. designed and fabricated the qubit device. T.Y. designed PPLO, which was fabricated at the group of W.D.O. Z.R.L characterized the PPLO. K.I. and Z.R.L performed the measurement and data analysis. K.K. developed the theory and performed the numerical simulations. K.I. prepared the manuscript. All authors contributed to the discussion of the results and helped in editing the manuscript.
Competing interests
The authors declare no competing financial interests.
Corresponding author
Correspondence to Kunihiro Inomata.
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