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Optics Letters

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

Egor Liokumovitch, Shmuel Sternklar

Published Feb 20, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1364/ol.387359

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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.
We present a new technique for improving the sensitivity of an interferometer, phase-shift-amplified interferometry (PAI), which is based on two embedded interferometers. The internal interferometer, which is biased in anti-phase, amplifies the phase shift; the external interferometer converts this into an amplified intensity shift. PAI can improve the sensitivity of standard interferometers by an order of magnitude or more. The theory of PAI, including its enhanced immunity to relative intensity noise, phase noise, and other post-detection noise and distortion components, is presented. We experimentally demonstrate a phase-shift amplification factor of 11.
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.
Phase-shifting interferometry (PSI) promises excellent performance for quantitative phase measurement. However, the PSI is commonly realized by utilizing the Mach-Zehnder interferometer (MZI) fed with classical resources, and hence its phase sensitivity is hindered by the photon shot noise. In this paper, we propose to introduce specific phase-shifting algorithms into the well-established quantum-enhanced MZI, seeded by coherent and squeezed vacuum states and followed by single-mode intensity detection and difference intensity detection, to achieve quantitative phase measurement with sensitivity beyond that achieved by the corresponding Mach-Zehnder-type PSI with classical input. We show that when the average photon number of the coherent state is dominant, the optimal phase sensitivity of the Mach-Zehnder-type PSI with coherent plus squeezed vacuum input is better than the phase sensitivity of the Mach-Zehnder-type PSI with single coherent input under the same phase-sensing intensity condition in both of detection setups. We also show that for the typical MZI seeded with a high-power coherent state and a finitely squeezed vacuum state, the combination of intensity detection and phase-shifting algorithm can still improve the sensitivity of quantitative phase measurement. Furthermore, we derive the phase sensitivity of the fixed MZI as well as the quantum Cramér-Rao bound for two detection schemes. Finally, we explore the impacts of photon losses on the phase sensitivity enhancements of the Mach-Zehnder-type PSI and the fixed MZI in the high-intensity regime for each detection setup. The robustness to losses is compared between the Mach-Zehnder-type PSI and the fixed MZI. Our results may be helpful to promote the exploration of quantum-enhanced quantitative phase sensing.
In this paper, we investigate the angular displacement measurements using the homodyne detection method in a modified-SU(2) Mach-Zehnder interferometer (MZI). Three parametric amplifiers (PAs) are used. PA’s role is to increase the number of photons and to reduce the shot-noise. We also consider quantum Fisher information (QFI) and derive expressions for single- and twoparameter cases and corresponding quantum Cramer-Rao bounds (QCRB). We find that angular displacement sensitivity exceeds the standard quantum limit (SQL) or shot-noise limit (SNL) and approaches single- and two-parameter QCRB. Finally, we investigate the impact of photon losses on the sensitivity of interferometer