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Frontiers in Optics

Heterodyne phase-shift-amplified interferometry with improved shot-noise-limited sensitivity

Egor Liokumovitch, Shmuel Sternklar

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Heterodyne phase-shift-amplified interferometry is demonstrated. A phase-shift-amplification factor of 30 is achieved. Theory predicts a shot-noise-limited sensitivity improvement of 2 compared to a standard heterodyne Mach-Zehnder interferometer.
DOI
10.1364/fio.2019.jtu4a.12

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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.
To enhance the phase sensitivity of Mach–Zehnder interferometers, we use a tunable phase shift before the light beams are injected into the interferometer. The analytical result of the optimal phase shift is obtained, which only depends on the initial input states. For a non-zero optimal phase shift, the phase sensitivity of the interferometers in the output ports is always enhanced. We can achieve this enhancement for most states, including entangled and mixed states. The optimal phase shift is exhibited in three examples. Compared to previous methods, this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.
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.