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Communications in Theoretical Physics

Double-port homodyne detection in a squeezed-state interferometry with a binary-outcome data processing

Likun Zhou, Pan Liu, Guangri Jin

Published Aug 15, 2022• 2 citations
Publisher

Abstract

Abstract Performing homodyne detection at a single output port of a squeezed-state light interferometer and then separating the measurement quadrature into two intervals can realize super-resolving and super-sensitive phase measurements, which is equivalent to a binary-outcome measurement. Obviously, the single-port homodyne detection may lose almost part of the phase information, reducing the estimation precision. Here, we propose a data-processing technique over the double-port homodyne detection, where the two-dimensional measurement quadrature (p 1, p 2) has been divided into two regions. With such a binary-outcome measurement, we estimate the phase shift accumulated in the interferometer by inverting the output signal. By analyzing the full width at half maximum of the signal and the phase sensitivity, we show that both the resolution and the achievable sensitivity are better than that of the previous binary-outcome scheme.

DOI
10.1088/1572-9494/ac8974

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Abstract Performing homodyne detection at a single output port of a squeezed-state light interferometer and then separating the measurement quadrature into two intervals can realize super-resolving and super-sensitive phase measurements, which is equivalent to a binary-outcome measurement. Obviously, the single-port homodyne detection may lose almost part of the phase information, reducing the estimation precision. Here, we propose a data-processing technique over the double-port homodyne detection, where the two-dimensional measurement quadrature (p 1, p 2) has been divided into two regions. With such a binary-outcome measurement, we estimate the phase shift accumulated in the interferometer by inverting the output signal. By analyzing the full width at half maximum of the signal and the phase sensitivity, we show that both the resolution and the achievable sensitivity are better than that of the previous binary-outcome scheme.
Performing homodyne detection at a single output port of a squeezed-state light interferometer and then separating the measurement quadrature into several bins can realize superresolving and supersensitive phase measurements. However, the phase resolution and the achievable phase sensitivity depend on the bin size that is adopted in the data processing. By maximizing classical Fisher information, we analytically derive an optimal value of the bin size and the associated best sensitivity for the case of three bins, which can be regarded as a three-outcome measurement. Our results indicate that both the resolution and the achievable sensitivity are better than that of the previous binary–outcome case. Finally, we present an approximate maximum Likelihood estimator to asymptotically saturate the ultimate lower bound of the phase sensitivity.
Performing homodyne detection at one port of a squeezed-state light interferometer and then binarizing the measurement data are important to achieve superresolving and supersensitive phase measurements. Here we propose an alternative data-processing technique by dividing the measurement quadrature into three bins (equivalent to a multi-outcome measurement), which leads to a higher improvement in the phase resolution and the phase sensitivity under realistic experimental conditions. Furthermore, we develop an alternative phase-estimation protocol based on a combination of the inversion estimators of each outcome and show that the estimator can saturate the Cram\'er-Rao lower bound, similar to the asymptotically unbiased maximum likelihood estimator.
Optimal measurement scheme with an efficient data processing is important in quantum-enhanced interferometry. Here we prove that for a general binary-outcome measurement, the simplest data processing based on inverting the average signal can saturate the Cram\'er-Rao bound. This idea is illustrated by binary-outcome homodyne detection, even-odd photon counting (i.e., parity detection), and zero-nonzero photon counting that have achieved super-resolved interferometric fringe and shot-noise limited sensitivity in coherent-light Mach-Zehnder interferometer. The roles of phase diffusion are investigated in these binary-outcome measurements. We find that the diffusion degrades the fringe resolution and the achievable phase sensitivity. Our analytical results confirm that the zero-nonzero counting can produce a slightly better sensitivity than that of the parity detection, as demonstrated in a recent experiment.
Abstract We theoretically investigate the phase sensitivity of a truncated SU(1,1) interferometer fed with a two-mode coherent state and employing double-port homodyne detection. On the one hand, we analytically demonstrate that the two-mode coherent state provides better phase sensitivity than the single-mode coherent state. In addition, we show that the double-port homodyne detection is a quasi-optimal measurement. For a bright coherent-state input, the sensitivity of this scheme saturates the phase-sensitivity bound determined by the quantum Fisher information. On the other hand, we quantitatively illustrate the advantage of double-port homodyne detection over the single-port scheme under ideal conditions and in the presence of photon loss, respectively. Furthermore, our analysis indicates that the scheme we propose is robust against photon loss.
There has been much recent interest in high precision angular rotation measurement using photon orbital angular momentum to realize super-resolving angular rotation measurement. It is well known that quantum detection strategies can obtain a quantum-enhanced performance. Here, we prove that binary-outcome homodyne detection method can obtain a narrower signal peak, showing better resolution compared with the existing data processing method. Since the photon loss is unavoidable in the actual non-ideal optical system, this paper further discusses the impact of photon loss on the resolution and sensitivity of angular rotation measurement with binary-outcome homodyne detection method.
An important part of optical sensing is interferometry, where direct or homodyne detection at the output of an interferometer yields information about small phase shifts. Classical interferometry operates at the shot-noise limit (SNL), caused by the photon structure of light and reached when an interferometer is fed with coherent light. The use of nonclassical light at the input of an interferometer enables overcoming the SNL. In particular, squeezed light is known to be less noisy than coherent light. An interferometer fed with strongly squeezed light can, in principle, provide the phase sensitivity at the Heisenberg limit, the ultimate limit allowed by the laws of physics. However, this supersensitive operation is strongly degraded by loss – both inside the interferometer and outside it, at the stage of detection. While the former (internal loss) seems to be inevitable, the latter (detection loss) can be overcome, and we demonstrate it in our recent experiment. The clue is to amplify light at the interferometer output using a phase-sensitive optical parametric amplifier. This device does not introduce additional noise, but it amplifies the fragile quantum signal and thus makes it tolerant to loss at the detection stage. In a proof-of-principle experiment, we build a polarization Mach-Zehnder interferometer and feed it with coherent light in one port and a squeezed vacuum in another port. At one output port, we amplify light with an optical parametric amplifier and measure a phase sensitivity of 13 mrad for 1500 photons in the interferometer. This result, achieved with 50% detection efficiency, overcomes the SNL by 3 dB. Moreover, by using stronger amplification, we can overcome the SNL under detection efficiency as low as 13%. Our results outline a way to use squeezed light for real-life sensing, where the detection efficiency cannot be very high, especially in spectral ranges like middle-infrared or terahertz.