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Photonics

Single-Port Homodyne Detection in a Squeezed-State Interferometry with Optimal Data Processing

Likun Zhou, Pan Liu, Guangri Jin

Published Jul 21, 2021• 5 citations
Publisher

Abstract

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.

DOI
10.3390/photonics8080291

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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.
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.
Quantum metrology can beat the shot-noise limit (SNL) with nonclassical resources, yet simultaneously realizing sub-Rayleigh resolution and sub-SNL sensitivity in a deployable interferometer remains challenging. Here we experimentally validate a deterministic phase-measurement protocol that combines single-port balanced homodyne detection in a Mach-Zehnder interferometer with ternary-binning post-processing. For a coherent probe with a mean photon number of about 67, ternary binning preserves sub-Rayleigh resolution while mitigating the near-zero-phase ill-conditioning of binary-binning readout, yielding a 7.15-fold resolution enhancement relative to the unprocessed interferometer. With 5.99 ± 0.13 dB squeezed-state injection into the vacuum port, the resolution enhancement increases to 13.69-fold, and sub-SNL sensitivity is achieved; the minimum sensitivity improves by a factor of 1.78 compared with the coherent probe. The protocol is deterministic and experimentally accessible, offering a practical route to multiparameter estimation and quantum-enhanced microscopy.
Abstract Photon counting measurement has been regarded as the optimal measurement scheme for phase estimation in the squeezed-state interferometry, since the classical Fisher information equals to the quantum fisher information and scales as n ¯ 2 for given input number of photons n ¯ . However, it requires photon-number-resolving detectors with a large enough resolution threshold. Here we show that a collection of N -photon detection events for N up to the resolution threshold ∼ n ¯ can result in the ultimate estimation precision beyond the shot-noise limit. An analytical formula has been derived to obtain the best scaling of the fisher information.
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.
Summary form only given. The use of quantum states of light in optical interferometry improves the precision in the estimation of a phase shift, paving the way for applications in quantum metrology, computation and cryptography. Sub-shot noise phase sensing can for example be achieved by injecting a squeezed vacuum into an interferometer . However, this approach leads to enhanced sensitivity only for small phase shifts. In this work we aim for ab initio sub-shot noise estimation of an unknown phase shift using a pre-determined squeezed probe and an adaptive measurement approach. We experimentally investigate the performances of such protocol under the realistic assumption of thermalization of the probe state. Indeed, adaptive phase estimation schemes with squeezed states and Bayesian processing of homodyne data have been shown to be asymptotically optimal in the pure case, thus approaching the quantum Cramér-Rao bound. In our protocol we take advantage of the enhanced sensitivity of homodyne detection in proximity of the optimal phase which maximizes the homodyne Fisher information. A squeezed thermal probe state (signal) undergoes an unknown phase shift. The first estimation step involves interference on a beam splitter of the signal and a local oscillator followed by homodyne detection. Homodyne data is then processed to compute a rough estimation of the phase through Bayesian inference. The rough estimation is fed back to the local oscillator in order to match the optimal relative phase with the signal. A second estimation step leads to the final estimation of the phase shift. Thermalization of the probe state prevents the attainability of the quantum Cramér-Rao bound. Nevertheless, we show that the studied adaptive scheme still saturates the classical Cramér-Rao bound, showing sub-shot noise behaviour and therefore extracting the maximum available information from homodyne data. In contrast to previous approaches, our scheme is optimized for Gaussian states.