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arXiv:2407.05147 · Nature Communications

Correlation measurement of propagating microwave photons at millikelvin

Aarne Keränen, Qiming Chen, András Gunyhó, Priyank Singh, Jian Ma, Visa Vesterinen, Joonas Govenius, Mikko Möttönen

Published Apr 24, 2025• 5 citations
arXivHTMLPDF

Abstract

Abstract Microwave photons are essential carriers of quantum information in several promising platforms for quantum computing. However, measurement of the quantum statistical properties of microwave photons is demanding owing to their low energy relative to thermal fluctuations of any room-temperature detector, and phase-insensitive voltage amplification necessarily adds noise. Here, we overcome this trade-off with a nanobolometer that directly measures the photon statistics at millikelvin. Using a cryogenic temperature-controlled blackbody radiator, we demonstrate the detection of the mean photon number $$\langle \hat{n}\rangle$$ ⟨ n ̂ ⟩ and reveal the expected photon number variance $${(\Delta n)}^{2}=\langle \hat{n}\rangle \left(\langle \hat{n}\rangle+1\right)$$ ( Δ n ) 2 = ⟨ n ̂ ⟩ ⟨ n ̂ ⟩ + 1 , following the Bose–Einstein distribution. By engineering the coherent and incoherent proportions of the input field, we observe a transition between super-Poissonian and Poissonian statistics from the bolometric second-order correlation measurements. This technique is poised to serve in fundamental tests of quantum mechanics and function as a scalable readout solution for a quantum information processor.

DOI
10.1038/s41467-025-59230-2

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Abstract Microwave photons are essential carriers of quantum information in several promising platforms for quantum computing. However, measurement of the quantum statistical properties of microwave photons is demanding owing to their low energy relative to thermal fluctuations of any room-temperature detector, and phase-insensitive voltage amplification necessarily adds noise. Here, we overcome this trade-off with a nanobolometer that directly measures the photon statistics at millikelvin. Using a cryogenic temperature-controlled blackbody radiator, we demonstrate the detection of the mean photon number ⟨n^⟩\langle \hat{n}\rangle⟨n^⟩ ⟨ n ̂ ⟩ and reveal the expected photon number variance (Δn)2=⟨n^⟩(⟨n^⟩+1){(\Delta n)}^{2}=\langle \hat{n}\rangle \left(\langle \hat{n}\rangle+1\right)(Δn)2=⟨n^⟩(⟨n^⟩+1) ( Δ n ) 2 = ⟨ n ̂ ⟩ ⟨ n ̂ ⟩ + 1 , following the Bose–Einstein distribution. By engineering the coherent and incoherent proportions of the input field, we observe a transition between super-Poissonian and Poissonian statistics from the bolometric second-order correlation measurements. This technique is poised to serve in fundamental tests of quantum mechanics and function as a scalable readout solution for a quantum information processor.
In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n^{2}+n photon number variance of thermal microwave photons emitted from a blackbody radiator for mean photon numbers, 0.05≲n≲1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.
Propagating microwave photons have gained great interest due to their potential being used in the applications of the quantum technology, such as communication and sensing. The use of propagating microwave photons as information carriers requires methodology that is able to characterize the incoming photon signals. Since the signal could consist of only a few photons, the signal detection is truly a challenging task. Amplifying a weak microwave signal to room temperature would cause excessive noise and cover the signal. Previously, amplification-free signals have been measured with qubit-based photon detection, which relies on excitation of the qubit. This method is limited by a narrow bandwidth, since the qubit can absorb only a few discrete energies. However, a bolometer utilizing resistive absorption of the photons offers a broad bandwidth and enables the measurement without amplification. This thesis examines the use of bolometer as a phase and amplitude sensitive detector for propagating microwave signals. The phase sensitivity of the bolometer is enabled by homodyne detection, where the measurement signal is combined with a strong local oscillator signal. The combining of these signals is implemented with a beam splitter. Amplitude sensitivity is studied by repeating the measurement with multiple signal powers, and phase sensitivity is studied using a phase modulated measurement signal with different modulation amplitudes. The data is extracted from the bolometer by assuming a linear dependency between the average resonance frequency and the average photon number. Similarly, a linear dependency is assumed between the variances. This thesis demonstrates that the bolometer is able to detect changes in the measurement signal power and phase by measuring the average photon number and variance. The average photon number and variance oscillate, meaning that the phase modulation is detected. The oscillation amplitudes increase as a function of power indicating the amplitude sensitivity. A strong local oscillator signal allows the detection of weak signals without amplification, and thus the measurement can be conducted with minimal added noise. These results together show, that the bolometer is a versatile microwave detector and a promising candidate for quantum technology applications in the microwave region.
When measuring electromagnetic radiation of frequency f, the most sensitive detector counts single quanta of energy hf. Single photon detectors have been demonstrated from γ-rays to infrared wavelengths, with ongoing efforts to extend their range to microwaves. Here we show that an underdamped Josephson junction can detect 14 GHz thermal photons, with energy 10 yJ or 50 μeV, stochastically emitted by a microwave copper cavity at millikelvin temperatures. After characterizing the source and the detector, we vary the cavity temperature and measure the photon rate. The device achieves 45% efficiency and a dark count rate of 0.1 Hz over several GHz. Demonstrated super-Poissonian photon statistics is a signature of thermal light and a hallmark of quantum chaos. We discuss applications in dark matter axion searches and note its relevance to quantum information and fundamental physics. It is shown that 14 GHz photons, thermally emitted from a copper cavity, can be detected by a Josephson junction with 45% efficiency and 0.1 Hz dark count rate. Demonstrated super-Poissonian photon statistics is a signature of thermal light and a hallmark of quantum chaos.
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Propagating photons serve as essential links for distributing quantum information and entanglement across distant nodes. Knowledge of their Wigner functions not only enables their deployment as active information carriers but also provides error diagnostics when photons passively leak from a quantum processing unit. While well-established for standing waves, characterizing propagating microwave photons requires post-processing of room-temperature signals with excessive amplification noise. Here, we demonstrate amplification-free Wigner function tomography of propagating microwave photons using a superconductor--normal-metal--superconductor bolometer based on the resistive heating effect of absorbed radiation. By introducing two-field interference in power detection, the bolometer acts as a sensitive and broadband quadrature detector that samples the input field at selected angles at millikelvin with no added noise. Adapting the principles of computed tomography (CT) in medical imaging, we implement Wigner function CT by combining quadrature histograms across different projection angles and demonstrate it for Gaussian states at the single-photon level. Compressed sensing and neural networks further reduce the projections to three without compromising the reconstruction quality. These results address the long-standing challenge of characterizing propagating microwave photons in a superconducting quantum network and establish a new avenue for real-time quantum error diagnostics and correction.
We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury Brown and Twiss correlations. The super-Poissonian and Poissonian photon statistics of thermal and coherent sources, respectively, made of a resistor and a radio frequency generator, are measured down to the quantum regime at milli-Kelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductors.