© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

IEEE Journal of Quantum Electronics

Reaching the True Shot-Noise-Limited Phase Sensitivity in Self-Heterodyne Interferometry

Vincent Michaud-Belleau, Jean-Daniel Deschênes, Jérôme Genest

Published Jan 7, 2022• 4 citations

Abstract

The use of an acousto-optic modulator in an interferometer enables heterodyne detection and can alleviate technical issues such as laser intensity noise and photodetector flicker noise. However, it also introduces at least a 3 dB penalty to the shot-noise limited phase sensitivity when compared to that attainable through homodyne detection. In this paper, we show theoretically that this penalty can be lifted by implementing detection and demodulation schemes that exploit the cyclostationary nature of shot noise observed at the outputs of the self-heterodyne interferometer. We also discuss how expected departures from ideality, namely imperfect interferometric visibility, non-zero stationary noise, and finite detection bandwidth, affect the performance of these schemes and propose a simplified procedure relaxing the requirement for a rigorous instrument characterization. While two independent detectors are required to reach the true (classical-light) shot-noise limit for phase, single-detector instruments can also benefit from the introduced ideas to achieve up to 3 dB improvement in phase sensitivity.

DOI: 10.1109/jqe.2022.3141056

Related papers

Audio-frequency interferometry at the shot noise limit using an EOIM-based frequency-synthesized light

Peng Yang, Chaoran Tu, Zhichao Shi +1 more

The shot-noise-limited sensitivity for detecting audio-frequency phase signals has garnered significant interest in both research and practical applications. This work presents a novel experimental setup that generates frequency-synthesized light with suppressed carrier and enhanced sidebands using an electro-optic intensity modulator (EOIM). When injected into a Mach-Zehnder interferometer (MZI), the EOIM-generated light not only enables phase-sensitive heterodyne locking to stabilize the relative phase of the MZI but also functions as a balanced heterodyne detector for audio-frequency phase measurements. By integrating these three key techniques into the MZI, phase detection sensitivity reaches the shot-noise limit across the audio-frequency band. This advancement holds promise for applications in gravitational wave detection, vacuum magnetic birefringence studies, spin-orbital interactions, material characterization, polarization microscopy, atomic magnetometry, and biomedical optics.

Optics Express•Feb 19, 2026•2 citations

Input spectrum for heterodyne detection in advanced gravitational wave detectors without non-stationary shot-noise

P. T. Beyersdorf

Future interferometric gravitational wave detectors will make use of the coupling between shot noise and radiation pressure noise that produces a squeezed output for the quantum noise at the dark-port of the interferometer allowing these interferometers to operate with a sensitivity that exceeds the standard quantum limit at certain frequencies. The ability of the detector to take advantage of this squeezed output state depends in part on the readout system used. With the phase modulated laser input planned for these interferometers the quantum-noise limited sensitivity is slightly better when homodyne (rather than heterodyne) detection is used. We show that by modifying the laser input spectrum for these interferometers, readout with heterodyne detection can be made to have the same quantum-noise limited sensitivity as readout with homodyne detection.

arXiv:gr-qc/0609113•Sep 25, 2006•0 citations

Subhertz interferometry at the quantum noise limit

Peng Yang, Boya Xie, Sheng Feng

Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1 Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.

Optics Letters•Apr 29, 2019•12 citations

Heterodyne phase-shift-amplified interferometry with improved shot-noise-limited sensitivity and immunity to RIN

Egor Liokumovitch, Shmuel Sternklar

Phase-shift-amplified interferometry (PAI) is demonstrated using a heterodyne detection scheme. We demonstrate a sensitivity amplification factor of 35, giving 7.9 ⋅ 10 − 4 rad, or 40 pm displacement, resolution. This was achieved due to the improved immunity of PAI to the total relative intensity noise (RIN) of the system. In addition, we predict a factor of 2 fundamental improvement to shot-noise-limited phase-shift sensitivity as compared to a regular heterodyne Mach–Zehnder interferometer.

Optics Letters•Feb 20, 2020•1 citation

Quantum-enhanced optical phase-insensitive heterodyne detection beyond 3-dB noise penalty of image band

Keitaro Anai, Yutaro Enomoto, H. Omura +4 more

Optical phase-insensitive heterodyne (beat-note) detection, which measures the relative phase of two beams at different frequencies through their interference, is a key sensing technology for various spatial/temporal measurements, such as frequency measurements in optical frequency combs. However, its sensitivity is limited not only by shot noise from the signal frequency band but also by the extra shot noise from an image band, known as the 3-dB noise penalty. Here, we propose a method to remove shot noise from all these bands using squeezed light. We also demonstrate beyond-3-dB noise reduction experimentally, confirming that our method actually reduces shot noise from both the signal and extra bands simultaneously. Our work should boost the sensitivity of various spatial/temporal measurements beyond the current limitations.

arXiv:2305.06579•Optics Express•May 2, 2024•8 citations

Optimal Detection Scheme for Shot-Noise-Limited Phase Estimation in Passive Classical-Light Interferometry

Vincent Michaud-Belleau, Jérôme Genest, Jean-Daniel Deschênes

Phase estimation is a central goal of optical interferometry, with applications ranging from gravitational-wave detection to fiber-optic sensing. Recent progress has focused on the use of nonclassical light to improve performance, but that approach is often unreasonably complicated. The authors reexamine the simple, passive Mach-Zehnder interferometer by linearizing the phase-estimation problem, for straightforward computation of an efficient estimator, which is then used to compare several detection schemes for two- and four-output interferometers. Independent monitoring of all available output ports leads to the best overall sensitivity, and allows cancellation of amplitude noise.

Physical Review Applied•Aug 17, 2018•11 citations

The use of an acousto-optic modulator in an interferometer enables heterodyne detection and can alleviate technical issues such as laser intensity noise and photodetector flicker noise. However, it also introduces at least a 3 dB penalty to the shot-noise limited phase sensitivity when compared to that attainable through homodyne detection. In this paper, we show theoretically that this penalty can be lifted by implementing detection and demodulation schemes that exploit the cyclostationary nature of shot noise observed at the outputs of the self-heterodyne interferometer. We also discuss how expected departures from ideality, namely imperfect interferometric visibility, non-zero stationary noise, and finite detection bandwidth, affect the performance of these schemes and propose a simplified procedure relaxing the requirement for a rigorous instrument characterization. While two independent detectors are required to reach the true (classical-light) shot-noise limit for phase, single-detector instruments can also benefit from the introduced ideas to achieve up to 3 dB improvement in phase sensitivity.

The shot-noise-limited sensitivity for detecting audio-frequency phase signals has garnered significant interest in both research and practical applications. This work presents a novel experimental setup that generates frequency-synthesized light with suppressed carrier and enhanced sidebands using an electro-optic intensity modulator (EOIM). When injected into a Mach-Zehnder interferometer (MZI), the EOIM-generated light not only enables phase-sensitive heterodyne locking to stabilize the relative phase of the MZI but also functions as a balanced heterodyne detector for audio-frequency phase measurements. By integrating these three key techniques into the MZI, phase detection sensitivity reaches the shot-noise limit across the audio-frequency band. This advancement holds promise for applications in gravitational wave detection, vacuum magnetic birefringence studies, spin-orbital interactions, material characterization, polarization microscopy, atomic magnetometry, and biomedical optics.

Future interferometric gravitational wave detectors will make use of the coupling between shot noise and radiation pressure noise that produces a squeezed output for the quantum noise at the dark-port of the interferometer allowing these interferometers to operate with a sensitivity that exceeds the standard quantum limit at certain frequencies. The ability of the detector to take advantage of this squeezed output state depends in part on the readout system used. With the phase modulated laser input planned for these interferometers the quantum-noise limited sensitivity is slightly better when homodyne (rather than heterodyne) detection is used. We show that by modifying the laser input spectrum for these interferometers, readout with heterodyne detection can be made to have the same quantum-noise limited sensitivity as readout with homodyne detection.

Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1 Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.

Phase-shift-amplified interferometry (PAI) is demonstrated using a heterodyne detection scheme. We demonstrate a sensitivity amplification factor of 35, giving 7.9 ⋅ 10 − 4 rad, or 40 pm displacement, resolution. This was achieved due to the improved immunity of PAI to the total relative intensity noise (RIN) of the system. In addition, we predict a factor of 2 fundamental improvement to shot-noise-limited phase-shift sensitivity as compared to a regular heterodyne Mach–Zehnder interferometer.

Optical phase-insensitive heterodyne (beat-note) detection, which measures the relative phase of two beams at different frequencies through their interference, is a key sensing technology for various spatial/temporal measurements, such as frequency measurements in optical frequency combs. However, its sensitivity is limited not only by shot noise from the signal frequency band but also by the extra shot noise from an image band, known as the 3-dB noise penalty. Here, we propose a method to remove shot noise from all these bands using squeezed light. We also demonstrate beyond-3-dB noise reduction experimentally, confirming that our method actually reduces shot noise from both the signal and extra bands simultaneously. Our work should boost the sensitivity of various spatial/temporal measurements beyond the current limitations.

Phase estimation is a central goal of optical interferometry, with applications ranging from gravitational-wave detection to fiber-optic sensing. Recent progress has focused on the use of nonclassical light to improve performance, but that approach is often unreasonably complicated. The authors reexamine the simple, passive Mach-Zehnder interferometer by linearizing the phase-estimation problem, for straightforward computation of an efficient estimator, which is then used to compare several detection schemes for two- and four-output interferometers. Independent monitoring of all available output ports leads to the best overall sensitivity, and allows cancellation of amplitude noise.