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Cyclically Operated Microwave Single-Photon Counter with Sensitivity of $10^{- 22} W / \sqrt{Hz}$

L. Balembois, J. Travesedo, L. Pallegoix, A. May, E. Billaud, M. Villiers, D. Estève, D. Vion, P. Bertet, and E. Flurin

Phys. Rev. Applied 21, 014043 – Published 23 January 2024

Abstract

Single-photon detection played an important role in the development of quantum optics. Its implementation in the microwave domain is challenging because the photon energy is five orders of magnitude smaller. In recent years, significant progress has been made in developing single microwave photon detectors (SMPDs) based on superconducting quantum bits or bolometers. In this paper we present a practical SMPD based on the irreversible transfer of an incoming photon to the excited state of a transmon qubit by a four-wave mixing process. This device achieves a detection efficiency $η = 0.43$ and an operational dark count rate $α = 85 s^{- 1}$ , mainly due to the out-of-equilibrium microwave photons in the input line. The corresponding power sensitivity is $S = 10^{- 22} W / \sqrt{Hz}$ , one order of magnitude lower than the state of the art. The detector operates continuously over hour time-scales with a duty cycle $η_{D} = 0.84$ , and offers frequency tunability of at least 50 MHz around 7 GHz.

Received 7 July 2023
Revised 14 December 2023
Accepted 21 December 2023

DOI:https://doi.org/10.1103/PhysRevApplied.21.014043

Physics Subject Headings (PhySH)

Optoelectronics Quantum information with solid state qubits Quantum measurements Quantum sensing

Superconducting qubits

Cavity resonators Microwave techniques Single-photon detectors

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

L. Balembois ¹, J. Travesedo ¹, L. Pallegoix ¹, A. May ^1,2, E. Billaud¹, M. Villiers³, D. Estève ¹, D. Vion¹, P. Bertet¹, and E. Flurin^1,*

¹Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette Cedex, France
²Alice&Bob, 53 boulevard du Général Martial Valin, 75015 Paris
³Laboratoire de Physique de l’Ecole Normale Suprérieure, Paris, France

^*[email protected]

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Vol. 21, Iss. 1 — January 2024

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Figure 1
(a) Principle of the photon detector. Two cavities, buffer (orange) and waste (green), are coupled to a transmon qubit whose nonlinearity allows the modes to be mixed. A pump tone (purple) triggers a four-wave mixing process, converting an incoming buffer photon into a long-lived qubit excitation and a waste photon quickly dissipated into the environment, making the reversal process impossible. (b) Schematic of the SMPD chip. The transmon qubit (blue) at frequency $ω_{q} / 2 π = 6.184$ GHz is capacitively coupled to two coplanar waveguide resonators: the buffer [see (c)] and the waste ( $ω_{w} / 2 π = 7.704$ GHz, $κ_{w} / 2 π = 1.8$ MHz). Two Purcell filters are added to protect the qubit from radiative relaxation. The tunability of the detector is ensured by inserting a superconducting quantum interference device (SQUID), driven by a flux line (red), in the buffer resonator. (c) Evolution of the buffer frequency with the respect to the magnetic flux through the SQUID. Orange points are data, the solid red line is a fit, and the dashed black line represents the buffer Purcell filter frequency. Due to the frequency detuning between the buffer and its filter, the buffer bandwidth $κ_{b}$ varies with its frequency. The red square represents the operating point. (d) Cyclic operation of the SMPD consisting of three steps repeated continuously. The detection window (D) involves switching on the pump tone (purple) for $T_{d} = 10 μ s$ to allow the conversion of the incoming photon (orange). The measurement window (M) involves applying a readout pulse (green) on the waste resonator to measure the qubit state. The reset window (R) is a conditional loop to reinitialize the qubit in its ground state. The excited population of the qubit during the pulse sequence is represented below. The average detector blind time is $T_{m} + T_{r} = 1.9 μ s$ .
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Figure 2
(a) Qubit-excited population as a function of the pump amplitude $| ξ |$ applied to the qubit when a coherent tone of 360 zW (77 850 photons per second) is applied on the buffer resonator. The pump frequency is adapted for each amplitude to follow the Stark shift. Orange points are data, the dark red solid line represents a fit using (3), and the black solid line represents the chosen amplitude. (b) Qubit-excited population as a function of the pump frequency $ω_{p} / 2 π$ when no signal is sent to the buffer (dark blue) and when a coherent tone (360 zW) is applied (orange). Solid red lines represent Lorentzian fit, and the dashed black line is the center of the resonance. (c) Qubit readout when no pulses are applied to the qubit (red), giving a qubit equilibrium population $p_{eq} = 2 \times 10^{- 4}$ , and qubit readout just after a reset sequence (green), giving a reset population $p_{reset} = 10^{- 5}$ . Solid lines represent Gaussian fit. The dashed black line represents the qubit readout after a $π$ -pulse, and the vertical solid line corresponds to the chosen readout threshold. (d) Qubit relaxation curve from the excited state (blue) and from the ground state (green). Solid lines represent exponential fits. The yellow window corresponds to the detection time $T_{d} = 10 μ s$ .
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Figure 3
(a) Time traces of the SMPD operated in cyclic mode; each vertical line represents one photon detection. The power of the coherent tone sent to the buffer resonator is progressively increased from 0 W (dark blue) to 54 zW (12 000 photons per second) (orange). (b) Detected count rate as a function of incoming photon rate. The efficiency $η$ is extracted with a linear fit (solid line). The deviation from the linear behavior is due to the detector saturation. (c) Dark count rate as the function of time. Each point is the average rate over approximately $12 s$ , which corresponds to $10^{6}$ cycles. The dashed line represents the dark count saturation $α = 85 s^{- 1}$ . (d) Inferred efficiency of the SMPD as a function of the frequency of the coherent tone applied to the buffer resonator. The power of the tone is still 360 zW. Solid lines represent a Lorentzian fit. The detector bandwidth defined as the full width at half maximum is $κ_{d} / 2 π = 0.57$ MHz.
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Figure 4
Johnson-Nyquist law demonstrated with the SMPD. Qubit relaxation time $T_{1}$ (a) and qubit equilibrium population $p_{eq}$ (b) taken every minute. These values are used to determine the value of $α_{qubit}$ . The fridge temperature is shown in dashed gray lines. (c) Thermal dark count rate $α_{th} = α - α_{qubit}$ for different refrigerator temperatures shown in dashed gray lines. Each point corresponds to the average dark count rate over $10^{5}$ cycles; the light blue areas correspond to the data selected to extract the averages by avoiding the transient regime. (d) Relation between the mode population ${\bar{n}}_{b}$ , calculated from the refrigerator temperature, and the thermal dark count rate $α_{th}$ . Each point (purple) corresponds to the average of the colored areas of (c); an example of distribution is given in the inset for the green zone. The solid line correspond to the Johnson-Nyquist relation where $η$ is the SMPD efficiency and $κ_{d}$ the SMPD bandwidth.
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Figure 5
(a) Pulse sequence used to measure efficiency. A pump tone (purple pulse) of duration $10 μ s$ is sent to the qubit mode, and an incoming coherent wave packet (orange pulse) of duration $t_{b}$ and amplitude $b_{in}$ is applied to the buffer. The qubit-excited state population $p_{e}$ is detected by the waste (green pulse). (b) Cycle similar to the main text repeated $n = 12 500$ times per experiment. (c) Efficiency $η / η_{D}$ as a function of wave-packet duration $t_{b}$ , measured with sequence (a). Each point is averaged $N$ times. (d) Dark count measured over $n = 12 500$ cycles of $t_{cycle} = 11.8 μ s$ . Each point corresponds to the average of $k = 500$ cycles. The experiment is repeated $N$ times and averaged.
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Figure 6
Schematic of the setup. Wiring and all the components used in this experiment at room temperature and cryogenic temperature are shown.
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Physical Review Applied

Cyclically Operated Microwave Single-Photon Counter with Sensitivity of 10−22W/Hz

L. Balembois, J. Travesedo, L. Pallegoix, A. May, E. Billaud, M. Villiers, D. Estève, D. Vion, P. Bertet, and E. Flurin

Phys. Rev. Applied 21, 014043 – Published 23 January 2024

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Cyclically Operated Microwave Single-Photon Counter with Sensitivity of $10^{- 22} W / \sqrt{Hz}$