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OSA Continuum

Simultaneously estimating two phase shifts with a power-recycled tri-port interferometer fed by coherent states

Jiandong Zhang, Zijing Zhang, Longzhu Cen, Jun-Yan Hu, Yuan Zhe Zhao

Published Dec 13, 2018• 2 citations
Publisher

Abstract

Supersensitive phase estimation was and is one of the principal goals in the field of precision measurements. In this paper, we study a power-recycled tri-port interferometer that enables the protocol to estimate two phase shifts simultaneously. Each sensitivity of the phase shift is the shot-noise limit 1/N with two coherent states as inputs (3N/2 photons on average), and the balanced homodyne detection is performed on the outputs. Fundamental sensitivity limits of two estimated phases are studied by calculating the quantum Fisher information. Finally, we discuss the effects of photon loss on the phase sensitivity.

DOI
10.1364/osac.1.001437

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Supersensitive phase estimation was and is one of the principal goals in the field of precision measurements. In this paper, we study a power-recycled tri-port interferometer that enables the protocol to estimate two phase shifts simultaneously. Each sensitivity of the phase shift is the shot-noise limit 1/N with two coherent states as inputs (3N/2 photons on average), and the balanced homodyne detection is performed on the outputs. Fundamental sensitivity limits of two estimated phases are studied by calculating the quantum Fisher information. Finally, we discuss the effects of photon loss on the phase sensitivity.
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.
Abstract We have theoretically investigated the phase sensitivity of the hybrid interferometer with two coherent beams using the method of balance homodyne detection. The measurement device is a nonlinear–linear hybrid interferometer consisting of an optical parametric amplifier and a beam splitter. We prove that the phase sensitivity can beat the shot noise limit in the optimal conditions. Furthermore, we derive the quantum Cramér–Rao bound of the hybrid interferometer. The effects of transmission loss and detection loss on the measurement accuracy are discussed. The detection accuracy of this scheme is compared with that of the conventional SU (1,1) interferometer. Our results show that this scheme outperforms the conventional SU (1,1) interferometer scheme at high parametric strength. This scheme can be implemented with existing experimental techniques and will have important applications in quantum precision measurements.
We propose a protocol for the second-order nonlinear phase estimation with a coherent state as input and balanced homodyne detection as measurement strategy. The sensitivity is sub-Heisenberg limit, which scales as N−3/2N^{-3/2}N−3/2 for NNN photons on average. By ruling out hidden resources in quantum Fisher information, the fundamental sensitivity limit is recalculated and compared to the optimal sensitivity of our protocol. In addition, we investigate the effect of photon loss on sensitivity, and discuss the robustness of measurement strategy. The results indicate that our protocol is nearly optimal and robust.
We study a Mach-Zehnder interferometer fed by a coherent state in one input port and vacuum in the other. We explore a Bayesian phase estimation strategy to demonstrate that it is possible to achieve the standard quantum limit independently from the true value of the phase shift and specific assumptions on the noise of the interferometer. We have been able to implement the protocol by using parallel operation of two photon-number-resolving detectors and multiphoton coincidence logic electronics at the output ports of a weakly illuminated Mach-Zehnder interferometer. This protocol is unbiased, saturates the Cramer-Rao phase uncertainty bound, and, therefore, is an optimal phase estimation strategy.
We propose an alternative scheme for phase estimation in a Mach-Zehnder interferometer (MZI) with photon recycling. It is demonstrated that with the same coherent-state input and homodyne detection, our proposal possesses a phase sensitivity beyond the traditional MZI. For instance, it can achieve an enhancement factor of ∼9.32 in the phase sensitivity compared with the conventional scheme even with a photon loss of 10% on the photon-recycled arm. From another point of view, the quantum Cramér-Rao bound (QCRB) is also investigated. It is found that our scheme is able to achieve a lower QCRB than the traditional one. Intriguingly, the QCRB of our scheme is dependent of the phase shift ϕ while the traditional scheme has a constant QCRB regardless of the phase shift. Finally, we present the underlying mechanisms behind the enhanced phase sensitivity. We believe that our results provide another angle from which to enhance the phase sensitivity in a MZI via photon recycling.
SU(1,1) interferometers, based on the usage of nonlinear elements, are superior to passive interferometers in phase sensitivity. However, the SU(1,1) interferometer cannot make full use of photons carrying phase information as the second nonlinear element annihilates some of the photons inside. Here we focus on improving phase sensitivity and propose a different protocol based on a modified SU(1,1) interferometer, where the second nonlinear element is replaced by a beam splitter. We utilize two coherent states as inputs and implement balanced homodyne measurement at the output. Our analysis suggests that the protocol we propose can achieve the sub-shot-noise-limited phase sensitivity and is robust against photon loss as well as background noise. Our work is important for practical quantum metrology using SU(1,1) interferometers.