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arXiv:1606.08966 · Physical Review A

Quantum optical metrology in the lossy SU(2) and SU(1,1) interferometers

Yang Gao

Published Aug 18, 2016• 24 citations
arXivHTMLPDF

Abstract

We study the phase sensitivity in the conventional SU(2) and nonconventional SU(1,1) interferometers with a coherent and squeezed vacuum input state via quantum Cramer-Rao bound. We explicitly construct the detection scheme that gives the optimal phase sensitivity. For practical purposes, we show that in the presence of photon loss, both interferometers with proper homodyne detections are nearly optimal. We also find that unlike the coherent state and the squeezed vacuum state, the effects of imperfect detector on the phase sensitivity cannot be asymptotically removed for a generic coherent-squeezed state.

DOI
10.1103/physreva.94.023834

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We study the phase sensitivity in the conventional SU(2) and nonconventional SU(1,1) interferometers with a coherent and squeezed vacuum input state via quantum Cramer-Rao bound. We explicitly construct the detection scheme that gives the optimal phase sensitivity. For practical purposes, we show that in the presence of photon loss, both interferometers with proper homodyne detections are nearly optimal. We also find that unlike the coherent state and the squeezed vacuum state, the effects of imperfect detector on the phase sensitivity cannot be asymptotically removed for a generic coherent-squeezed 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 propose a novel scheme that is used for the enhancement of phase sensitivity. The SU(1,1) interferometer with a two-mode squeezed coherent state input, using balanced homodyne detection (BHD) and intensity detection (ID), is shown. Our results demonstrate that the phase sensitivity achieved via BHD outperforms that of ID. The optimal phase sensitivity via BHD surpasses the Heisenberg limit (HL) and approaches the quantum Cramér–Rao bound. A larger photon number and parameter strength can make the phase sensitivity better. Furthermore, we show the effects of internal and external losses on phase sensitivity in detail. When external loss reaches 10%, the phase sensitivity can reach the HL. Next, we have a detailed discussion on the impact of the squeezing parameter and photon number on phase sensitivity, which shows that our scheme has better phase sensitivity and enhanced robustness. This interferometer system thus holds significant potential for applications in quantum precision measurement.
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.
We study the phase sensitivity of an SU(1,1) interferometer from two aspects, i.e., the phase estimation determined by the error propagation formula and that by the quantum Cramér-Rao bound (QCRB). The results show that the phase sensitivity by using the intensity detection reaches the sub-shot-noise limit with a coherent state and an m-photon-added squeezed vacuum state (m-PA-SVS) as inputs. The phase sensitivity gradually approaches the Heisenberg limit for increasing m, and the ultimate phase precision improves with the increase of m. In addition, the QCRB can be saturated by the intensity detection with inputting the m-PA-SVS.
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 present the quantum Cramér-Rao bounds (QCRB) of an SU(1,1) interferometer for Gaussian states input with and without the internal photonic losses. The phase shifts in the single arm and in the double arms are studied and the corresponding analytical expressions of quantum Fisher information with Gaussian input states are presented. Different from the traditional Mach-Zehnder interferometer, the QCRB of single arm case is slightly higher or lower than that of double arms case depending on the input states. With a fixed mean photon number and for pure Gaussian state input, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other. We compare the QCRB with the standard quantum limit and Heisenberg limit. In the case of small internal losses the QCRB can beat the standard quantum limit.