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arXiv:2408.12903 · Nature Nanotechnology

Time-resolved sensing of electromagnetic fields with single-electron interferometry

Hugo Bartolomei, Elric Frigerio, M. Ruelle, Giacomo Rebora, Yuan Jin, U. Gennser, A. Cavanna, Emmanuel Baudin, Jean‐Marc Berroir, Inès Safi A, Pascal Degiovanni, Gerbold C. Ménard, Gwendal Fève

Published Mar 17, 2025• 14 citations
arXivHTMLPDF

Abstract

Characterizing quantum states of the electromagnetic field at microwave frequencies requires fast and sensitive detectors that can simultaneously probe the field's time-dependent amplitude and its quantum fluctuations. So far, this has been achieved by using either homodyne detection or fast digitizers. Both methods rely on the extraction of microwave radiation through an amplification chain towards the detector placed at room temperature, thereby limiting the time resolution to the ~10-GHz bandwidth of the measurement chain. Additionally, the coupling of high-impedance samples to the 50-Ω measurement chain is very weak, setting strong limitations on the detection sensitivity. In this work, we demonstrate an on-chip quantum sensor that exploits the phase of a single-electron wavefunction, measured in an electronic Fabry-Pérot interferometer, to detect the amplitude of a classical time-dependent electric field. The interferometer is implemented in a GaAs/AlGaAs quantum Hall conductor. The time resolution, limited by the temporal width of the electronic wavepacket, is ~35 ps. The interferometry technique provides a voltage resolution of ~50 μV, corresponding to a few microwave photons. Importantly, our detector measures both phase and contrast of the interference pattern. The latter opens the way to the detection of non-classical electromagnetic fields, such as squeezed or Fock states.

DOI
10.1038/s41565-025-01888-2

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Characterizing quantum states of the electromagnetic field at microwave frequencies requires fast and sensitive detectors that can simultaneously probe the field's time-dependent amplitude and its quantum fluctuations. So far, this has been achieved by using either homodyne detection or fast digitizers. Both methods rely on the extraction of microwave radiation through an amplification chain towards the detector placed at room temperature, thereby limiting the time resolution to the ~10-GHz bandwidth of the measurement chain. Additionally, the coupling of high-impedance samples to the 50-Ω measurement chain is very weak, setting strong limitations on the detection sensitivity. In this work, we demonstrate an on-chip quantum sensor that exploits the phase of a single-electron wavefunction, measured in an electronic Fabry-Pérot interferometer, to detect the amplitude of a classical time-dependent electric field. The interferometer is implemented in a GaAs/AlGaAs quantum Hall conductor. The time resolution, limited by the temporal width of the electronic wavepacket, is ~35 ps. The interferometry technique provides a voltage resolution of ~50 μV, corresponding to a few microwave photons. Importantly, our detector measures both phase and contrast of the interference pattern. The latter opens the way to the detection of non-classical electromagnetic fields, such as squeezed or Fock states.
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The use of quantum properties of light has allowed researchers to create technologies that can outperform classical setups. In quantum imaging and sensing, the cross-correlation of photon pairs enables precise time synchronization of photons reaching the photodetectors, effectively suppressing environmental noise, and improving measurement accuracy. Building on this concept, we theoretically introduce and experimentally explore phase-dependent Hong-Ou-Mandel (HOM) interferometry. This technique employs phase-shifted indistinguishable photon pairs in a modified HOM interferometer for detection of microwave signals. We demonstrate that applying a phase shift to photon pairs via electro-optic modulation in the modified HOM interferometer causes a change in the middle interference structure, which can be used to gain information about the microwave signal causing the phase shift. In this work, we explore the quantization of the electromagnetic field, as well as nonclassical states of light. Phase estimation and metrics in quantum metrology are explored to gain insight into the benefits of utilizing these nonclassical states. An understanding of optical interferometry is built by investigating different types of interferometers, before introducing the HOM interferometer. Theory for the modified HOM interferometer is introduced, followed by an exploration of the interference structure that arises from the different path lengths in the modified system. We gathered data experimentally, showing the addition of a phase through electro-optic modulators (EOMs) leads to a change in the height of the structure. From this data, we calculate the Fisher information (FI), and find a maximum sensitivity of 58 mradians for phase difference, and 25 mV for amplitude. Additionally, we theoretically explore the FI to find optimal parameters to increase the system's sensitivity.
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.
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