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arXiv:2209.06749

Enhanced nonlinear interferometry via seeding

Jefferson Flórez, Pearce, Emma, Nathan R. Gemmell, Yue Ma, Gabriele Bressanini, Chris C. Phillips, Rupert F. Oulton, Alex S. Clark

Published Sep 14, 2022• 5 citations

Abstract

We analyse a nonlinear interferometer, also known as an SU(1,1) interferometer, in the presence of internal losses and inefficient detectors. To overcome these limitations, we consider the effect of seeding one of the interferometer input modes with either a number state or a coherent state. We derive analytical expressions for the interference visibility, contrast, phase sensitivity, and signal-to-noise ratio, and show a significant enhancement in all these quantities as a function of the seeding photon number. For example, we predict that, even in the presence of substantial losses and highly inefficient detectors, we can achieve the same quantum-limited phase sensitivity of an unseeded nonlinear interferometer by seeding with a few tens of photons. Furthermore, we observe no difference between a number or a coherent seeding state when the interferometer operates in the low-gain regime, which enables seeding with an attenuated laser. Our results expand the nonlinear interferometry capabilities in the field of quantum imaging, metrology, and spectroscopy under realistic experimental conditions.

DOI: 10.48550/arxiv.2209.06749

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We analyse a nonlinear interferometer, also known as an SU(1,1) interferometer, in the presence of internal losses and inefficient detectors. To overcome these limitations, we consider the effect of seeding one of the interferometer input modes with either a number state or a coherent state. We derive analytical expressions for the interference visibility, contrast, phase sensitivity, and signal-to-noise ratio, and show a significant enhancement in all these quantities as a function of the seeding photon number. For example, we predict that, even in the presence of substantial losses and highly inefficient detectors, we can achieve the same quantum-limited phase sensitivity of an unseeded nonlinear interferometer by seeding with a few tens of photons. Furthermore, we observe no difference between a number or a coherent seeding state when the interferometer operates in the low-gain regime, which enables seeding with an attenuated laser. Our results expand the nonlinear interferometry capabilities in the field of quantum imaging, metrology, and spectroscopy under realistic experimental conditions.

The quantum Fisher information (QFI) bounds the sensitivity of a quantum measurement, heralding the conditions for quantum advantages when compared with classical strategies. Here, we calculate analytical expressions for the QFI of nonlinear interferometers under lossy conditions and with coherent-state seeding. We normalize the results based on the number of photons going through the sample that induces a phase shift on the incident quantum state, which eliminates some of the previously declared metrological advantages. We analyze the performance of nonlinear interferometers in a variety of geometries and robustness of the quantum advantage with respect to internal and external loss through direct comparison with a linear interferometer. We find the threshold on the internal loss at which the quantum advantage vanishes, specify when and how much coherent-state seeding optimally counters internal loss, and show that a sufficient amount of squeezing confers to the quantum advantages robustness against external loss and inefficient detection.

We analyze theoretically and experimentally cases of asymmetric detection, stimulation, and loss within a quantum nonlinear interferometer of entangled pairs. We show that the visibility of the SU(1,1) interference directly discerns between loss on the measured mode (signal) and the conjugated mode (idler). This asymmetry also affects the phase sensitivity of the interferometer, where coherent seeding is shown to mitigate losses that are suffered by the conjugated mode; therefore increasing the maximum threshold of loss that permits sub-shot-noise phase detection. Our findings can improve the performance of setups that rely on direct detection of entangled pairs, such as quantum interferometry and imaging with undetected photons.

Infrared (IR) imaging and spectroscopy is invaluable to many disciplines for its ability to probe molecular responses, from material analysis to diagnostic medicine. However, these applications are often limited by inefficient, noisy detectors. Non-degenerate nonlinear interferometers (NLIs) offer an alternative route through a technique known as imaging with undetected photons [1]. For an NLI producing visible-IR photon pairs, a change in the IR due to an object can be observed as a change to the interference of the visible photons. The IR does not need to be detected, bypassing the need for IR detectors completely.

The standard quantum limit (SQL) describes the best precision that can be achieved for phase measurements using a classical interferometer. For such an interferometer, this limit is given by

1/\sqrt{N}

where

N

is the total number of photons launched into the interferometer. The SQL can be circumvented through the utilisation of quantum states combined with advanced low-loss detection schemes. Such overcoming of the SQL has been demonstrated, for example, by replacing the unused vacuum input port of the linear interferometer with a non-classical state [1], and by exploiting nonlinear SU (1,1) interferometers in the high-gain regime [2]. However, the impact of the experimental losses on the ability of nonlinear interferometers to beat the SQL is often neglected, particularly in the low-gain regime. In this work, we close this gap by studying the performance of lossy SU (1,1) interferometers in the single-photon pair regime, with particular attention to the different amount of information contained in the measurement of single counts and of coincidences at the output of the interferometer.

SU(1,1) interferometers, based on nonlinear optical processes, potentially offer better phase sensitivity than traditional instruments. Bright-seeded variants are important for applications with large numbers of photons, yet have remained uncharacterized experimentally, for lack of a real-time technique to measure phase sensitivity. This study uses a direct intensity-detection technique to demonstrate the quantum enhancement of phase sensitivity in real time for a bright-seeded SU(1,1) system, compared to the classical shot-noise limit. It is hoped that these results will promote applications of this class of interferometer in quantum metrology.

In an unseeded SU(1,1) interferometer composed of two cascaded degenerate parametric amplifiers, with direct detection at the output, we demonstrate a phase sensitivity overcoming the shot noise limit by 2.3 dB. The interferometer is strongly unbalanced, with the parametric gain of the second amplifier exceeding the gain of the first one by a factor of 2, which makes the scheme extremely tolerant to detection losses. We show that by increasing the gain of the second amplifier, the phase supersensitivity of the interferometer can be preserved even with detection losses as high as 80%. This finding can considerably improve the state-of-the-art interferometry, enable sub-shot-noise phase sensitivity in spectral ranges with inefficient detection, and allow extension to quantum imaging.