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Optics Express

Enhancing phase sensitivity by a nonlinear-feedback-assisted interferometer

Gao-Feng Jiao

Published Nov 26, 2024• 2 citations
Publisher

Abstract

Nonlinear feedback utilizing nonlinear elements usually provides better performance in preparation and manipulation of quantum states compared to linear feedback using linear elements. In this work, by employing nonlinear feedback, we propose a nonlinear-feedback-assisted interferometer for quantum metrology. We theoretically analyze the phase sensitivity via homodyne detection on both of output ports. It is found that this proposal can realize phase sensitivity enhancement by manipulating the nonlinear feedback strength. Furthermore, the phase sensitivity can saturate the classical and quantum Cramér-Rao bound, respectively. Moreover, we demonstrate that this proposal is superior to the linear-feedback-assisted interferometer.

DOI
10.1364/oe.546024

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Nonlinear feedback utilizing nonlinear elements usually provides better performance in preparation and manipulation of quantum states compared to linear feedback using linear elements. In this work, by employing nonlinear feedback, we propose a nonlinear-feedback-assisted interferometer for quantum metrology. We theoretically analyze the phase sensitivity via homodyne detection on both of output ports. It is found that this proposal can realize phase sensitivity enhancement by manipulating the nonlinear feedback strength. Furthermore, the phase sensitivity can saturate the classical and quantum Cramér-Rao bound, respectively. Moreover, we demonstrate that this proposal is superior to the linear-feedback-assisted interferometer.
Abstract The topology of feedback optical parametric amplifier (FOPA) renders a number of significant advantages over the topology of traditional optical parametric amplifier (TOPA) such as a higher degree of quantum correlation, all-phase entanglement enhancement, and the robustness of the losses. Here, we propose a feedback-assisted interferometer based on the topology of FOPA for quantum metrology. We theoretically study the phase sensitivity with the method of homodyne detection and product detection. By manipulating the feedback strength of the FOPA, the phase sensitivity can be further enhanced, and approach the quantum Cramér-Rao bound. Furthermore, we demonstrate that our proposal is superior to the SU(1,1) interferometer based on the topology of TOPA.
Estimating nonlinear phase shifts is useful to analyze many dynamical processes. In this work, with respect to the second-order nonlinear phase shifts, we propose an estimation scheme with a coherent state as the input and balanced homodyne detection as the readout strategy. The measurement setup is a nonlinear-linear hybrid interferometer composed of an optical parametric amplifier and a beam splitter. We analyze the precision and determine the optimal parameters of our scheme. The precision is compared with the quantum Cramér–Rao bound as well as the precision of a conventional nonlinear interferometer. In view of the fact that photon loss is ubiquitous, the effects of transmission loss and detection loss on the precision are addressed. At low gain, our scheme is superior to the scheme using a conventional nonlinear interferometer, and the precision can saturate the quantum Cramér–Rao bound.
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.
We propose a high-precision phase estimation scheme in a hybrid interferometer by synergistically combining a Kerr nonlinear phase shifter and multi-photon subtraction operations. Using a coherent state and a vacuum state as input resources, we systematically evaluate the phase sensitivity via homodyne detection and analyze the quantum Fisher information as well as the quantum Cramér-Rao bound under both ideal and lossy conditions. Our results show that the joint integration of Kerr nonlinearity and multi-photon subtraction yields remarkable advantages over either technique used alone. The proposed scheme enables the phase sensitivity to surpass the standard quantum limit, exceed the conventional Heisenberg scaling (1/N1/N1/N), and approach the super-Heisenberg scaling (1/N21/N^{2}1/N2)-a direct consequence of Kerr nonlinearity. More precisely, the super-Heisenberg scaling $\propto $ 1/N21/N^{2}1/N2 is the ultimate precision limit permitted by the k=2k=2k=2 Kerr nonlinearity and does not violate the fundamental Heisenberg limit for linear phase accumulation. Even under moderate internal photon loss, the system maintains high precision and exhibits enhanced robustness to decoherence. The Kerr nonlinearity introduces an intensity-dependent phase shift proportional to the squared photon number, while multi-photon subtraction tailors non-Gaussian states to strengthen phase information extraction. Compared with existing schemes based on hybrid interferometers or SU(1,1) interferometers, our architecture achieves superior precision and stronger loss resilience. All components are experimentally accessible with current quantum optical technologies. This work provides a promising route for practical high-precision quantum metrology and quantum sensing.
Abstract We investigate the enhancement of phase sensitivity of a nonlinear-linear hybrid interferometer with the input of the two-mode squeezed coherent state (TMSCS). With the TMSCS produced by four-wave mixing, the quantum Cramér-Rao bounds (QCRB) can beat the Heisenberg limit (HL). Under the phase matched conditions, the optimal phase sensitivity with the balanced homodyne detection measurement can beat the HL and approach QCRB. The effects of internal and external losses on the measurement accuracy are also discussed. The results demonstrate that the scheme is robustness against to internal losses and this protocol can resist external detection loss which is up to 39%. Our results improve the performance of hybrid interferometers and this scheme can find important practical applications in quantum metrology.
Classical and quantum states working in concert play an essential role in high-precision interferometry. In this regard, coherent combined with squeezed vacuum states are the most promising candidate. Here we complement this subject by comparing nonlinear and nonlinear-linear hybrid interferometers with homodyne detection as a readout strategy. For a high-photon coherent state, either of the two interferometers can provide the phase sensitivity approaching the quantum Cramer-Rao bound. Additionally, we discuss the impacts of photon loss during the transmission and readout stages. We find that a nonlinear interferometer is advantageous over a nonlinear-linear hybrid interferometer. With increasing photon number of the coherent state, the maximal tolerable lossy rate ensuring phase sensitivity beyond the shot-noise limit is close to 50%. Our work may deepen the understanding of quantum-enhanced interferometry using nonlinear dynamics.