Single microwave-photon detector using an artificial $\Lambda$-type three-level system

Our device is composed of a $\lambda /2$ superconducting coplanar waveguide (CPW) resonator and a superconducting flux qubit (Fig. 1A). The CPW resonator is made of a 50-nm-thick Nb film sputtered on a 300-$\mu$m-thick undoped silicon wafer with a 300-nm-thick thermal oxide on the surface. It is patterned by electron-beam (EB) lithography using the ZEP520A-7 resist and $C{F}_4$ reactive ion etching. The flux qubit with three Josephson junctions, where one is made smaller than the other two by a factor of $\alpha$, is fabricated by EB lithography and double-angle evaporation of Al using PMMA ($50$ nm)/Ge ($50$ nm)/MMA ($400$ nm) trilayer resist (Fig. 5B). The thicknesses of the bottom and the top Al layers separated by an $A{l}_2{O}_3$ layer are 20 and 30 nm, respectively. In order to realize a superconducting contact between Nb and Al, the surface of Nb is cleaned by Ar ion milling before the evaporation of Al. The qubit is located at one end of the resonator and is coupled to the resonator dispersively through a capacitance of 4 fF, while it is coupled to the drive port inductively (Fig. 5A).

The flux qubit is always biased with a half flux quantum where the transition frequency of the qubit ${\omega }_{ge}$ from the ground state $|g⟩$ to the excited state $|e⟩$ is $2\pi \times 5.508$ GHz ($T_1\sim 700$ ns during photon-detection experiments), while the resonator frequency ${\omega }_r$ is $2\pi \times 10.256$ GHz ($Q$ factor $\sim 630$) when the qubit is in the $|g⟩$ state. It is shifted by a dispersive interaction with the qubit of $-2\chi =-2\pi \times 69$ MHz, which is enhanced by the straddling effect and the capacitive coupling Inomata et al. (2012) when the qubit is in the $|e⟩$ state. Note that ${\omega }_{ge}$ and ${\omega }_r$ denote not their bare frequencies but the renormalized ones including the dispersive shifts Inomata et al. (2014).

A parametric phase-locked oscillator (PPLO) Lin et al. (2014), which is previously operated as a flux-driven Josephson parametric amplifier (JPA) Yamamoto et al. (2008) consists of a $\lambda /4$ superconducting CPW resonator terminated by a dc-SQUID (superconducting quantum interference device). A pump port is coupled to the SQUID loop inductively. The device was fabricated by the planarized Nb trilayer process at MIT Lincoln Laboratory. The resonator and the pump port are made out of a 150-nm-thick Nb film sputtered on a Si substrate covered by a 500-nm-thick SiO${}_2$ layer. A static resonant frequency of the PPLO is ${\omega }_r^{PO}=2\pi \times 10.948$ GHz. The PPLO chip is the same as the one used in Ref. Lin et al. (2014).

A schematic of the measurement setup including the wiring in a cryogen-free ${}^3$He/${}^4$He dilution refrigerator, circuit components, and instruments used in the experiment is shown in Fig. 6.

The qubit$+$resonator and the PPLO circuits are fabricated on separate chips and are separately mounted in microwave-tight packages equipped with an independent coil for the flux bias. They are protected independently by the Cryoperm magnetic shield from an external flux noise such as the geomagnetic field.

Microwave pulses for the drive, signal, and pump ports are generated by mixing the continuous microwaves with pulses which have independent IF frequencies generated by DACs (digital to analog converter) developed by Martinis group at UCSB DAC (). The pulses are applied through the input microwave semi-rigid cables, each with attenuators of $42$ dB in total, and DC-blocks for the drive and pump ports. For the signal port, the microwave pulses are further attenuated by 20 dB, and are input to the resonator through a circulator to separate the input and reflected waves. The reflected waves are routed to PPLO via three circulators ($9$-$11$ GHz) and are reflected there again, and are propagated through a low-pass ($f_c=12.4$ GHz) and band-pass filters ($9$-$11$ GHz), two isolators ($9$-$11$ GHz), and the circulator ($9$-$11$ GHz) with a $50\Omega$ termination. Finally, the signals are amplified by a cryogenic HEMT amplifier and a room-temperature amplifier with a total gain of $\sim 66$ dB, and mixed with a local oscillator at an I/Q mixer down to the IF frequency. The I component of the reflected signals are sampled at 1 GHz/s by an ADC (analog to digital converter).

For the impedance-matching measurement (Fig. 2A), the PPLO is kept off. Namely, pump pulse is off (the output from the DAC in the pump port is turned off) and ${\omega }_r^{PO}$ is far detuned from ${\omega }_r$ so that the PPLO acts as a perfect mirror. In other measurements, the PPLO is kept on.

To estimate the photon detection efficiency precisely, calibration of the signal microwave power level on the sample chip is required. For the calibration, we measure the reflection coefficient as a function of the signal microwave frequency ${\omega }_s$ and the drive power $P_d$ and determine the impedance-matching points (Fig. 7). Here, we use continuous microwaves for both the signal and the qubit drive, and set the drive frequency at ${\omega }_d={\omega }_{ge}-2\pi \times 46$ MHz. We observe two dips representing the impedance matching, similarly to the inset of Fig. 2A. In the limit of weak signal power and no intrinsic loss of the resonator, these dips are expected to appear at the same $P_d$, where the two radiative decay rates of the $\Lambda$ system are balanced, ${\tilde{\kappa }}_{31}={\tilde{\kappa }}_{32}$ and ${\tilde{\kappa }}_{41}={\tilde{\kappa }}_{42}$ Koshino et al. (2013), where ${\tilde{\kappa }}_{ij}$ is the radiative decay rate for the $|\tilde{i}⟩\to |\tilde{j}⟩$ transition in the impedance-matched $\Lambda$ system. In the actual system, however, the finite population in the level $|\tilde{2}⟩$ as well as the intrinsic loss of the resonator weakens the elastic photon scattering from the $\Lambda$ system, and the impedance matching occurs when the radiative decay rates are not balanced, ${\tilde{\kappa }}_{31}>{\tilde{\kappa }}_{32}$ and ${\tilde{\kappa }}_{41}>{\tilde{\kappa }}_{42}$ Inomata et al. (2014). This yields a difference in the drive power, $P_{diff}$, between the two dips. $P_{diff}$ is sensitive to the input signal power: As we increase the signal power, the level $|\tilde{2}⟩$ is more populated and $P_{diff}$ gets larger. Note that the small $P_{diff}$ observed in the inset of Fig. 2A is attributed to the intrinsic loss of the resonator, since the pulsed signal field is sufficiently weak in this measurement.

We use $P_{diff}$ to calibrate the signal power level. We determine the signal power level which reproduces $P_{diff}=6.0$ dB (Fig. 7B) by the numerical simulation, following Ref. Koshino et al. (2013). In the numerical simulation, we employ the following parameters which are estimated by independent measurements: the qubit decay rate $\Gamma /2\pi =0.174\pm 0.012$ MHz (during this measurement $T_1$ shows ${\Gamma }^{-1}=919\pm 62$ ns) and the ratio of the external and total decay rates of the resonator photon ${\kappa }_{ext}/\kappa =0.964\pm 0.003$ (for other parameters, see “Device” section of this supplementary material). As a result, the signal power is estimated to be $P_s=-145.28$ dBm at

maximum ($\Gamma /2\pi =0.186$ MHz and ${\kappa }_{ext}/\kappa =0.967$) and $P_s=-146.02$ dBm at minimum ($\Gamma /2\pi =0.162$ MHz and ${\kappa }_{ext}/\kappa =0.961$). Therefore, $P_s=-145.65\pm 0.37$ dBm. This agrees well with an independent estimation of $P_s=-146.0$ dBm by taking into account the total losses in the input port.

In the main text (Fig. 1C), we show the protocol for single photon detection. Here, we present the detailed parameters of the pulses in the protocol.

The drive frequency is set at ${\omega }_d={\omega }_{ge}-\delta \omega$, where $\delta \omega =2\pi \times 49$ MHz ($<2\chi$) is the detuning from the qubit energy, and is fixed through all the experiments described in the main text. The drive pulse is synchronized with the signal pulse with a Gaussian envelope with a length $t_s$ corresponding to its full width at half maximum (FWHM) in the voltage amplitude. 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 $\Lambda$ system. In order to suppress unwanted nonadiabatic qubit excitations, the rising and falling edges of the drive-pulse envelope are smoothed by Gaussian function with FWHM of $2t_{rise}=30$ ns in the voltage amplitude.

The readout pulse (the frequency ${\omega }_{rd}={\omega }_r-2\chi =2\pi \times 10.187$ GHz, the length $t_{rd}=60$ ns, and the mean photon number ${\overline{n}}_{rd}\sim 10$) is applied after the delay of $t_{delay1}=t_d/2+t_{rise}$ from the center of the drive and signal pulses. The reflected readout pulse works as a locking signal for the PPLO output phase, and the pump pulse (the frequency ${\omega }_{pump}=2{\omega }_{rd}$, the length $t_{pump}=400$ ns, and the power $P_{pump}\sim -60$ dBm) is applied after $t_{delay2}=40$ ns. The parametric oscillation signal with either $0$ or $\pi$ phase is output from the PPLO during the application of the pump pulse, and the data acquisition time of $\sim 100$ ns is required to extract the phase.

In Figs. 2B, 2E, and 3A, a mean photon number in a signal pulse ${\overline{n}}_s$ is kept to be $\sim 0.1$, which implies that $\sim 5\%$ of the weak-coherent signal pulses contain multiple photons. Our detector responds to the multi-photon pulses but cannot discriminate them from single-photon pulses. The efficiency $\eta$ includes those counts.

Figure 8 shows the dark count probability in the detector, which is the click probability without applying the signal pulse in the pulse sequence of Fig. 1C. The dark count is mainly caused by the nonadiabatic qubit excitation due to the drive pulse and the imperfect initialization. The probability induced by the latter factor is constant and is measured to be $0.008\pm 0.001$, while the probability induced by the former factor depends on the power and the length of the drive pulse and remains finite even with the Gaussian envelope. We determine the dark count probability before and after each measurement of Figs. 2B, 2E, and Fig. 3 and subtracted the averaged value from the measurement result.

We denote the overall decay rate of the resonator by $\kappa$ and the radiative decay rate for the $|\tilde{i}⟩\to |\tilde{j}⟩$ transition in the $\Lambda$ system by ${\tilde{\kappa }}_{ij}$. Figure 9 shows ${\tilde{\kappa }}_{ij}/\kappa$ as a function of the drive power $P_d$, calculated based on the experimental parameters. In the experiment, we choose $P_d=-75.5$ dBm where the photon detection efficiency $\eta$ reaches the maximum. At this point, ${\tilde{\kappa }}_{41}/\kappa =0.49$. The time constant of the impedance-matched $\Lambda$ system for the voltage amplitude decay, ${\tau }_{\Lambda }$, is estimated to be $2/\kappa \sim 20$ ns, where $\kappa ={\tilde{\kappa }}_{41}+{\tilde{\kappa }}_{42}\sim 2\pi \times 16$ MHz. The shortest signal pulse length is $34$ ns in Fig. 3B, which is comparable with ${\tau }_{\Lambda }$.

In the main text (Fig. 4A), we show the reset protocol for the single photon detection. Here, we describe how to optimize the parameters of pulses in the protocol.

We first apply a $\pi$ pulse with the length of $6$ ns to directly excite the qubit from the $|g,0⟩$ to the $|e,0⟩$ state. Then, we apply the drive and reset pulses to induce the $|\tilde{2}⟩\to |\tilde{3}⟩\to |\tilde{1}⟩$ transition. To find the operating point to maximize the resetting efficiency, we swept the frequency ${\omega }_{rst}$ of the reset pulse and the drive power $P_{dr}$. After fixing ${\omega }_{rst}$ and $P_{dr}$, we optimize the drive pulse length $t_{dr}$, and the mean photon number in the reset pulse ${\overline{n}}_{rst}$ to minimize $P(|e⟩)$. Finally, we measure $P(|e⟩)$ as a function of ${\omega }_{rst}$ 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.

At the optimal reset point, $P(|e⟩)$ shows the minimum value of $0.017\pm 0.002$, which results in twice larger occupation of the qubit excited state compared to $0.008\pm 0.001$ obtained in the initialization in the equilibrium condition. This indicates the small probability of unwanted nonadiabatic excitations by the drive pulse in the reset protocol.

We demonstrate the 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 accomplish $\eta$ of $0.67\pm 0.06$ which is consistent with the maximum $\eta$ obtained in Fig. 2E. This indicates that the photon detection efficiency is unaffected by the reset protocol.

It takes $410$ ns to reset the system and $208$ ns to detect the single photon for $t_s=85$ ns. Both of the durations are determined by the drive pulse widths including $t_{rise}=15$ ns. The qubit readout is completed by accumulating data for $100$ ns after $t_{delay2}=40$ ns. The period of the single photon detection including the reset protocol is $\sim 760$ ns, which allows the photon counting rate of $\sim 1.3$ MHz.