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Advanced Quantum Technologies

Phase Sensitivity Optimization For a Hybrid Mach‐Zehnder Interferometer With Internal Parametric Amplifiers and One Input in the Vacuum State

Karunesh Kumar Mishra, Stefan Ataman

Published Oct 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT In this work, we address the problem of phase sensitivity optimization for a hybrid interferometer. The device we consider is composed of a usual Mach–Zehnder interferometer (MZI), however with parametric amplifiers (PA) inserted in each of its arms. We consider a generic pure input having one port in the vacuum state, and the MZI is assumed to be unbalanced. We address this optimization problem for both detection schemes having access – or not – to an external phase reference. As applications, we discuss a number of input states showing a potential interest in quantum metrology and thoroughly evaluate their performance. We discuss both the QFI and phase sensitivity scaling in respect with the average number of PA photons. We show that the PA‐enhanced MZI can outperform both the usual Mach–Zehnder and also the standard SU(1,1) interferometer having the same input resources. We also address the effect of both internal and external losses on the performance of the hybrid interferometer.

DOI
10.1002/qute.70497

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ABSTRACT In this work, we address the problem of phase sensitivity optimization for a hybrid interferometer. The device we consider is composed of a usual Mach–Zehnder interferometer (MZI), however with parametric amplifiers (PA) inserted in each of its arms. We consider a generic pure input having one port in the vacuum state, and the MZI is assumed to be unbalanced. We address this optimization problem for both detection schemes having access – or not – to an external phase reference. As applications, we discuss a number of input states showing a potential interest in quantum metrology and thoroughly evaluate their performance. We discuss both the QFI and phase sensitivity scaling in respect with the average number of PA photons. We show that the PA‐enhanced MZI can outperform both the usual Mach–Zehnder and also the standard SU(1,1) interferometer having the same input resources. We also address the effect of both internal and external losses on the performance of the hybrid interferometer.
This paper provides a theoretical analysis of a Mach–Zehnder interferometer (MZI) enhanced by optical parametric amplifiers (OPA) placed inside its arms and fed by a coherent input source. Contrary to most cases found in literature, we perform a wider analysis by considering the MZI unbalanced and two internal phase shifts. We discuss the theoretical best-case phase sensitivity of this setup via the quantum Cramér–Rao bound (QCRB) and we consider scenarios having – or not – access to an external phase reference. We also assess the realistic performance of the OPA-enhanced MZI by employing a balanced homodyne detection (asymmetric and symmetric phase shifts) scheme and a difference-intensity detection scheme. We are thus able to find the optimum beam splitter (BS) transmissivity (transmission coefficient) of the first BS via the quantum Fisher information (QFI), while for the second one, we need to take the detection scheme into account. We are able to find these optimal values for all considered scenarios and thus assess the best-case phase sensitivity provided by this setup.
Abstract In this work we address the problem of phase sensitivity optimization for an unbalanced Mach-Zehnder interferometer. While the quantum Fisher information can be employed in order to obtain the optimum transmission coefficient for the first beam splitter, this is no longer true for the second one, whose optimization is detection-scheme dependent. We thus consider three commonly used detection schemes and provide the optimal solution for each case. We also provide applications of the optimization method showing that for some input states a non-balanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.
This work discusses the single-intensity and difference-intensity detection schemes for lossy Mach–Zehnder Interferometer (MZI) and gives the corresponding optimal conditions to achieve the best phase measurements. The interferometer is fed by a coherent state in one port and a vacuum state in the other. When the core parameters (reflectivities, phase difference) are optimal, the phase sensitivity of these two detection schemes can reach a generalized precision bound: the standard interferometric limit (SIL). In the experiment, we design an MZI with adjustable beam splitters to verify the phase sensitivity optimization compared to the conventional MZI with 50:50 beam splitters. The sensitivity improvements at loss rates from 0.4 to 0.998 are demonstrated based on difference-intensity detection, matching the theoretical results well. With a loss up to 0.998 in one arm, we achieve a sensitivity improvement of 2.5 dB by adjusting reflectivity, which equates to a 5.5 dB sensitivity improvement in single-intensity detection. Such optimal phase measurement methods provide practical solutions for the correct use of resources in lossy interferometers.
We theoretically study the phase sensitivity of an SU(1,1) interferometer with a coherent state in one input port and a squeezed-vacuum state in the other input port using the method of homodyne detection. In this interferometer, beam splitting and recombination are generated by the parametric amplifiers instead of the beam splitters. Compared with the traditional Mach–Zehnder interferometer, the phase sensitivity of this interferometer can be improved due to the amplification process of the parametric amplifiers. Combined with the squeezed state input, the sensitivity can be improved further due to the noise reduction. The phase sensitivity of our scheme can approach the Heisenberg limit and the associated optimal condition is analyzed. The scheme can be implemented with current experimental technology.
We address in this work the phase sensitivity of a Mach-Zehnder interferometer with Gaussian input states. A squeezed-coherent plus squeezed vacuum input state allows us to unambiguously determine the optimal phase-matching conditions in order to maximize the quantum Fisher information. Realistic detection schemes are described and their performance compared with respect to the quantum Cram\'er-Rao bound. The core of this paper discusses in detail the most general Gaussian input state, without any a priori parameter restrictions. Prioritizing the maximization of various terms in the quantum Fisher information has the consequence of imposing the input phase-matching conditions. We discuss in detail when each scenario yields an optimal performance. Realistic detection scenarios are also considered and their performance compared to the theoretical optimum. The impact of the beam splitter types employed on the optimum phase-matching conditions is also discussed. We find a number of potentially interesting advantages of these states over the coherent plus squeezed vacuum input case.
An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are 12\frac{1}{2}21​. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cram\'er-Rao bound. Our results may contribute to the development of practical quantum sensing.