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Optics Communications

Simultaneously estimating two phases in three-mode nonlinear interferometer

Ying-Wang, Liyun Hu, Zhi‐Ming Zhang, Chaoping Wei

Published Jun 30, 2018• 5 citations
Publisher
DOI
10.1016/j.optcom.2018.06.072

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In this work we investigate the problem of simultaneous estimation of phases using generalised three- and four-mode Mach-Zehnder interferometer. In our setup, we assume that the phases are placed in each of the modes in the interferometer, which introduces correlations between estimators of the phases. These correlations prevent simultaneous estimation of all these phases, however we show that we can still obtain the Heisenberg-like scaling of precision of joint estimation of any subset of [Formula: see text] phases, d being the number of modes, within completely fixed experimental setup, namely with the same initial state and set of measurements. Our estimation scheme can be applied to the task of quantum-enhanced sensing in three-dimensional interferometric configurations.
We investigate the simultaneous estimation of two optical phases in a three-mode interferometer assisted by optical parametric amplification (OPA). By employing the normally ordered characteristic-function formalism, we analytically obtain all photon-number moments of the output quantum state, enabling an explicit evaluation of the quantum Fisher information matrix for multiparameter phase estimation. In the lossless scenario, we show that uniformly applied OPA significantly enhances the attainable precision beyond that of an unamplified interferometer. By analyzing the second-order correlation functions, we demonstrate that this enhancement originates from the amplification of intra-mode photon-number correlations, rather than from inter-mode correlations. We further extend our analysis to realistic interferometers with photon loss using a purification-based variational approach. Although loss degrades the achievable precision, the OPA-assisted scheme retains a clear advantage for moderate loss, indicating a degree of robustness against dissipation. Our results clarify the physical mechanism underlying OPA-enhanced multiparameter quantum metrology and provide guidelines for optimizing phase estimation protocols in realistic noisy environments.
In this paper, we propose a nonlinear interferometer with feedback loops and explore its efficiency for phase estimation. We analyse two feedback schemes, one where both modes of the interferometer are fed-back into the device and another where only one mode is fed-back. The quantum Fisher information (QFI) for phase estimation in each feedback scheme increases with each feedback loop, and similar to the standard SU(1,1) nonlinear interferometer, phase estimation in this scheme is sensitive to photon loss when the inputs are vacuum state. In terms of resources, we show that, in the low-loss regime, our scheme performs better than standard nonlinear interferometer. The feedback scheme provides the minimum phase variance when the unknown phase is small. We have also provided a special case where feedback scheme provided enhanced QFI even for large phase values. This is achieved by switching between squeezing and anti-squeezing operators after every few loops.