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arXiv:2104.09718 · Journal of the Optical Society of America B

SU(1,1) interferometry with parity measurement

Shuai Wang, Jiandong Zhang

Published Aug 2, 2021• 11 citations
arXivHTMLPDF

Abstract

We present a new operator method in the Heisenberg representation to obtain the signal of parity measurement within a lossless SU(1,1) interferometer. Based on this method, it is convenient to derive the parity signal directly in terms of input states, including general Gaussian and non-Gaussian states. As applications, we revisit the signal of parity measurement within an SU(1,1) interferometer when a coherent or thermal state and a squeezed vacuum state are considered as input states. In addition, we obtain the parity signal of an arbitrary single-mode state when it passes through an SU(1,1) interferometer, which is also a new result. Then, we analytically prove that parity measurement can saturate the quantum Cramér–Rao bound when the estimated phase approaches zero. Therefore, the operator method proposed in this work may bring convenience to the study of quantum metrology, particularly the phase estimation based on an SU(1,1) interferometer.

DOI
10.1364/josab.430759

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We present a new operator method in the Heisenberg representation to obtain the signal of parity measurement within a lossless SU(1,1) interferometer. Based on this method, it is convenient to derive the parity signal directly in terms of input states, including general Gaussian and non-Gaussian states. As applications, we revisit the signal of parity measurement within an SU(1,1) interferometer when a coherent or thermal state and a squeezed vacuum state are considered as input states. In addition, we obtain the parity signal of an arbitrary single-mode state when it passes through an SU(1,1) interferometer, which is also a new result. Then, we analytically prove that parity measurement can saturate the quantum Cramér–Rao bound when the estimated phase approaches zero. Therefore, the operator method proposed in this work may bring convenience to the study of quantum metrology, particularly the phase estimation based on an SU(1,1) interferometer.
In this paper, we derive a general expression of the quantum Fisher information of an SU(1,1) interferometer with an arbitrary state and a Fock state as inputs by the phase-averaging method. Our results show that the same quantum Fisher information can be obtained regardless of the specific form of the arbitrary state. Then, we analytically prove that the parity measurement can saturate the quantum Cramer-Rao bound when the estimated phase sits at the optimal working point. For practical reasons, we investigate the phase sensitivity when the arbitrary state is a coherent or thermal state. We further show that a Fock state can indeed enhance the phase sensitivity within a constraint on the total mean photon number inside the interferometer.
We derive a general expression of the expectation value of the parity operator in a Mach–Zehnder interferometer with a Fock state in one input port and an arbitrary state in the other input. We obtain the quantum Crámer–Rao bound via the error propagation method from parity detection for the phase shift around zero. In addition, for an arbitrary state with the same mean photon number, our results show that the same phase resolution and the same phase uncertainty can be obtained for the phase shift around zero. That is to say, when a Mach–Zehnder interferometer is powered by a Fock state into one input port, all quantum states with same mean photon number at the other input may have the same performance in the phase estimation via parity detection. As some specific applications, we consider the arbitrary state being a Fock state, a coherent state, and a squeezed-vacuum state.
Abstract The SU(1,1) interferometer, a nonlinear analog of the traditional Mach–Zehnder interferometer, has emerged as a powerful tool for achieving phase sensitivity beyond the standard quantum limit. In this work, we propose the use of a superposition of even and odd coherent states as input state to enhance the phase sensitivity of an SU(1,1) interferometer. These non-classical states exhibit unique properties such as squeezing, entanglement, and quantum interference, which can be harnessed to improve metrological precision. Phase sensitivity is analyzed using single-intensity detection and homodyne detection schemes under both ideal and photon loss cases, which demonstrates significant improvements over classical and squeezed-vacuum inputs. In addition, we evaluate the quantum Cramér-Rao lower bound by employing the quantum Fisher information formalism, showing that it surpasses the standard quantum limit and approaches the Heisenberg limit under optimal conditions. Our results highlight the potential of the even and odd coherent states superposition in quantum metrology and provide a pathway for achieving ultra-precise phase measurements in SU(1,1) interferometers for applications in optical sensing, and quantum information processing.
We develop a quantum sensing framework for the phase independent detection of weak coherent optical displacements based on SU(1,1) interferometry. Unlike conventional quantum measurement protocols that require prior knowledge of the signal phase and coherent homodyne detection, the proposed approach estimates the displacement magnitude independently of its phase. We show that, under ideal lossless conditions, a conventional SU(1,1) interferometer employing only total intensity detection saturates the quantum Cramer Rao bound for displacement magnitude estimation. We further derive the analytical expression of the quantum Cramer Rao bound and the sensitivity of the conventional SU(1,1) interferometer with total intensity detection and systematically investigate its performance in the presence of optical loss. The proposed phase-independent intensity detection scheme achieves comparable performance over experimentally relevant operating regimes while eliminating the need for local oscillators, phase locking, and quadrature tracking. These results establish SU(1,1) based intensity detection as a practical platform for phase independent quantum sensing.
We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of phase estimation approaches the Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cram\'er-Rao bound of the SU(1,1) interferometer.