Irreversible Qubit-Photon Coupling for the Detection of Itinerant Microwave Photons

Single photon detection is a key resource for sensing at the quantum limit and the enabling technology for measurement-based quantum computing. Photon detection at optical frequencies relies on irreversible photoassisted ionization of various natural materials. However, microwave photons have energies 5 orders of magnitude lower than optical photons, and are therefore ineffective at triggering measurable phenomena at macroscopic scales. Here, we report the observation of a new type of interaction between a single two-level system (qubit) and a microwave resonator. These two quantum systems do not interact coherently; instead, they share a common dissipative mechanism to a cold bath: the qubit irreversibly switches to its excited state if and only if a photon enters the resonator. We have used this highly correlated dissipation mechanism to detect itinerant photons impinging on the resonator. This scheme does not require any prior knowledge of the photon waveform nor its arrival time, and dominant decoherence mechanisms do not trigger spurious detection events (dark counts). We demonstrate a detection efficiency of 58% and a record low dark count rate of 1.4 per millisecond. This work establishes engineered nonlinear dissipation as a key enabling resource for a new class of low-noise nonlinear microwave detectors.

Popular Summary

The detection of single photons is a key resource for sensing at the quantum limit and an enabling technology for certain types of quantum computing. While photon detection at optical frequencies relies on ionization of various natural materials, microwave photons are far less energetic and therefore much less likely to trigger measurable macroscopic phenomena. And yet the detection of single microwave photons is increasingly sought after in applications ranging from dark matter detection to quantum-enhanced imaging. To that end, we observe a new type of interaction between a microwave resonator and a single qubit that could provide the foundation for such detectors.

In our experimental setup, the resonator and qubit do not directly interact but instead dissipate energy to a common cold bath. If a microwave photon enters the resonator, the qubit irreversibly switches to its excited state. We use this highly correlated dissipation mechanism to detect itinerant photons impinging on the resonator. This scheme does not require any prior knowledge of the photon waveform nor its arrival time, and dominant decoherence mechanisms do not trigger spurious detection events (dark counts). We find that this scheme performs as well as state-of-the-art microwave photon counters with a dark count that is at least an order of magnitude better.

This work establishes engineered nonlinear dissipation as a key-enabling resource for a new class of low-noise nonlinear microwave detectors.

Figure 1

Principle of the itinerant photon detector. (a) The circuit consists of two microwave modes: a buffer (orange) and a waste (green) coupled to a transmon qubit (blue). Each mode is well coupled to its own transmission line so that a photon can enter the device on the left and leave on the right into the dissipative $50\mathrm{\Omega }$ environment. A pump (purple) is applied on the Josephson junction to make the three-wave mixing interaction resonant [Eq. (2)]. (b) When a photon enters the buffer, the pump converts it via the Josephson nonlinearity (black cross) into one excitation of the qubit and one photon in the waste. The waste excitation is irreversibly radiated away in the transmission line, so that the reverse three-wave process cannot occur. The quantum state of the qubit is measured with a standard dispersive readout via the waste to detect whether or not a photon arrived while the pump was on. (c) When a coherent tone drives the waste, the qubit excitation can combine with waste photons and be released via the Josephson nonlinearity in the buffer, enabling a fast reset of the detector.

Figure 2

Calibration and diagnosis of the detector. (a)–(d) A pump tone (purple pulse) of duration $t_p$ powers the device through the qubit port, and an incoming coherent wave packet (orange pulse) of duration $t_b$ and amplitude $b_{\mathrm{in}}$ is applied on the buffer. The qubit excited state population $p_e$ is detected after a delay $t_d$ through the waste (green pulse). (a) We plot the pump frequency $f_p$ which maximizes $p_e$ for various pump powers ($x$ axis). The first 10 data points (purple open circles) are fitted using a linear regression (purple line), leading to a $y$ intercept within 0.04% of the expected value $f_{p0}=({\omega }_q+{\omega }_w^e-{\omega }_b^g)/2\pi$. The slope of this line provides a calibration of the pump power in units of photon number $|{\xi }_p{|}^2$ [see Eq. (c5)]. For each pump power, we plot the induced nonlinear dissipation rate ${\kappa }_{\mathrm{nl}}$ (blue open circles), which is extracted from a full model simulation [see Eq. (e4)], to best match all measured values of $p_e$ for small values of $b_{\mathrm{in}}$, taking into account the readout fidelity (0.94). For pump powers $|{\xi }_p{|}^2<0.11$, these extracted values follow a linear trend within 10% of the expected one ${\kappa }_{\mathrm{nl}}=4|{\xi }_p{|}^2{\chi }_{qb}{\chi }_{wq}/{\kappa }_w$ (blue line). For all subsequent experiments, $|{\xi }_p{|}^2=0.11$ (gray arrow). The saturation of ${\kappa }_{\mathrm{nl}}$ is mainly due to the fact that, as $g_3$ increases with the pump power, we are leaving the adiabatic elimination regime. (b) Measured $p_e$ (open circles) as a function of $1-{\mathbb{P}}_0$, where ${\mathbb{P}}_0$ is the probability of the incoming wave packet being in the vacuum; see Eq. (e13). This quantity is varied by increasing $b_{\mathrm{in}}$ for a fixed $t_b=2\mu \mathrm{s}$. The slope at the origin is the detection efficiency $\eta$, and the $y$ intercept is the dark count. The theory (solid line) is obtained by simulating the full model Eq. (e4). (c) For each $t_b$ ($x$ axis), $\eta$ is measured (open circles) as in (b). The theory curves (solid lines) are obtained by simulating the full model Eq. (e4) with readout infidelity (brown) in four regimes: $T_1$, ${\kappa }_b=\infty$ (red), ${\kappa }_b=\infty$ (orange), $T_1=\infty$ (green), and the measured $T_1$, ${\kappa }_b$ (blue). Note that the discrepancy between orange and red at small time is due to the finite switching time of the pump pulse $t_d=500\mathrm{ns}$. (d) Measured $p_e$ (open circles) as a function of $t_p$ with $b_{\mathrm{in}}=0$, at a repetition rate of 2 ms. An exponential fit (solid line) rises from the residual excited population after the reset $p_e(t_p=0)=0.003$ to the thermal equilibrium $n_{q,\mathrm{th}}=0.015$ at a rate ${\mathrm{\Gamma }}_{\mathrm{dc}}^{\min }=1.4{\mathrm{ms}}^{-1}=n_{q,\mathrm{th}}/T_1$ at early time.

Figure 3

Reset protocol and cyclic operation. (a) The qubit is initialized in its excited state (blue pulse) and the pump is activated. The decay of $p_e$ is measured (open circles) in the presence (green) or absence (blue) of a reset tone of duration $t_r$ applied to the waste mode (green pulse). The exponential fits (solid lines) yield a qubit $T_1$ reduced from $7.7\mu \mathrm{s}$ to 370 ns. Note that the residual qubit population is reduced in the presence of the reset tone from 3.5% (see Fig. 2) to 0.7%, demonstrating that the reset is in fact cooling the qubit below its effective bath occupation. (b) Cyclic operation of the pulse sequence in between the two vertical dashed lines, in the presence of a continuous input tone of variable amplitude (orange pulse). First, the qubit is reset for $2\mu \mathrm{s}$ (first green and purple pulses), followed by a heralding measurement to confirm the preparation in the ground state (second green pulse). The detector is then activated during a time $t_p=3\mu \mathrm{s}$ by switching on the pump (second purple pulse), and finally, the qubit state is read out (third green pulse). The measured $p_e$ (open circles) is plotted as a function of the photon number in the input pulse integrated over the cycle time $7\mu \mathrm{s}$. A linear regression (solid line) yields an overall efficiency of 20% (which accounts for the 43% duty cycle) and a dark count of 2% per cycle. (c) Real-time trajectories of 1000 successive detection cycles, with $\overline{n}=0$ (top) and $\overline{n}=0.38$ (bottom), as marked by the full dot in (b).

Figure 4

Quantum nondemolition characterization by tomography of the quantum state released in the waste line. (a) The three-wave-mixing interaction is activated by a pump tone (purple pulse) during which the detector is first initialized by a reset pulse on the waste port (first green pulse) preceding the injection of a small coherent field (mean occupation $\overline{n}=0.35$) on the buffer port. The qubit excitation, detected at the end of the sequence by a readout pulse (second green pulse), is correlated with the creation of a single photon by the waste. During the detection process, a near quantum-limited phase-preserving amplifier is used to monitor the field emitted by the waste (gray shaded rectangle). (b) The signal, demodulated at the frequency $({\omega }_w^g+{\omega }_w^e)/2$, is dominated by quantum and amplifier noise, as exemplified with 20 overlayed single-quadrature time traces (2 time traces have been colored in black for readability). (c) The waveform of the emitted wave packet can be deconvoluted from the uncorrelated detection noise by statistical analysis of the traces [38]. The real, imaginary part, and envelope of the waveform retrieved experimentally are represented in full line, dashed line, and green shaded area, respectively. (d) The quantum state of the field in the temporal mode plotted in (c) is reconstructed by analyzing the moments of the measured amplitude distribution [39] as described in Appendix pp8. The Wigner function of the state conditioned on the detection of the qubit in state $|g⟩$ ($|e⟩$) is represented on the left (right).

Figure 5

(a) Schematic of microwave cabling of the dilution refrigerator. (b) Superconducting coplanar-waveguide layout; note that this vector layout is the exact mask used for the circuit fabrication.

Figure 6

Complete spectroscopic data. (a),(b) The excited state population of the qubit $p_e$ (color coded) is represented as a function of the pump amplitude ($x$ axis) and pump frequency ($y$ axis). (a) When there is no incoming photon on the buffer port, we find one spectroscopic line (red diamonds) for which the qubit is sent into its excited state. This corresponds to a higher-order amplification process of the form. We also observe that the background $p_e$ is rising approximately linearly with the pump power at all the frequencies, which is consistent with the heating of the qubit bath by the pump. (b) When we add a pulse on the buffer port at frequency ${\omega }_b$, another line (purple circles) appears. This line corresponds the process $\widehat{b}{\widehat{\sigma }}^{†}{\widehat{w}}^{†}$ and the white dashed line indicates the chosen pump power which maximize the ratio $\eta /{\mathrm{\Gamma }}_{\mathrm{dc}}$. We can also observe a spectroscopic line which goes upward which seems to cool the qubit and thus decreases the efficiency [see dip in ${\kappa }_{\mathrm{nl}}$ in Fig. 1]. This was the main reason for limiting the pump power to the chosen value. Also, past this line, the dark count rate increases too much compared to the gain in the efficiency.

Figure 7

Tomography of the itinerant field states. Measurement of the field emitted during a detection sequence (left) and calibration experiment (right). (a),(g) Pulse sequences for the state-reconstruction experiment (a) and amplification calibration (g). The field emitted by the waste is monitored by a phase-preserving amplifier (gray rectangle). (b),(h) Experimental traces demodulated at $({\omega }_w^g+{\omega }_w^e)/2$ (only one quadrature is represented): the first part of the trace (duration $t_m$) is used for the itinerant field state reconstruction while the second part (duration $t_r$) is used for qubit state discrimination. (c),(i) Mode shape determined experimentally for the single photon (c) and coherent fields (i) used for calibration. (d),(j) Measured phase space distribution of the propagating field before amplification $\widehat{S}/\sqrt{G}$; it corresponds to the Husimi-$Q$ representation of the quantum state broadened by the equivalent input noise of the amplifier expressed in units of square root of photons. The distribution is conditioned on the detection of the qubit in $|g⟩$ or $|e⟩$ (d) and for the various coherent state amplitudes used for calibration (j). (e),(k) Experimental reconstruction of the moments of the distribution $⟨({\widehat{a}}^{†}{)}^n{\widehat{a}}^m{⟩}_{\rho }$ obtained by inverting Eq. (h5). (f) Diagonal of the reconstructed density matrix. The error bars are estimated assuming a $\pm 0.5\mathrm{dB}$ miscalibration of the amplification chain gain.

Figure 8

Probability tree for modeling imperfection of the detector and quantum nondemolition character of the device. The input of the tree denotes the joint state of the qubit, the buffer, and the waste, respectively. Starting from the qubit in the ground state and the input field in a coherent state $\alpha$, a spurious thermal excitation can flip the qubit with a probability $p_{\mathrm{th}}$, the coherent state gets projected to the vacuum state with a probability $p_0$, the photon gets detected with a probability ${\eta }_{\det }$, and the qubit gets read out correctly with a probability $p_{\mathrm{c}}^e$ when in its excited state or $p_{\mathrm{nc}}^g$ when in its ground state.

Figure 9

Spectroscopy of the waste mode. (a),(b) Relative reflected phase (a) and power (b) ($y$ axis) of a small spectroscopic tone on the waste port for varying frequencies ($x$ axis). (a) The sharp $2\pi$ phase roll corresponds to the waste mode, whereas the wide one corresponds to the Purcell filter. (b) Because of the presence of a lossy Purcell filter (large interdigitated capacitor; see Fig. 5), the relative reflected power is not flat around the waste frequency (solid line). The detected photon comes out of the detector with ${\chi }_{qw}$ frequency shift (dashed line).