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arXiv:2406.08007 · Journal of the Optical Society of America B

Enhancing phase sensitivity in a Mach-Zehnder interferometer with various detection schemes using SU(1,1) coherent states

Nour-Eddine Abouelkhir, Abdallah Slaoui, El Hassan Saidi, R. Ahl Laamara, Hanane El Hadfi

Published Dec 23, 2024• 14 citations
arXivHTMLPDF

Abstract

Improving interferometric phase sensitivity is crucial for high-precision measurements in rapidly developing quantum technologies. The Mach–Zehnder interferometer (MZI) is a versatile tool for analyzing this phenomenon. By splitting and recombining a light beam using beam splitters, the MZI allows for precise phase sensitivity analysis using tools like the quantum Cramér–Rao bound (QCRB) and the quantum Fisher information (QFI). This paper analyzes the phase sensitivity of an MZI in various scenarios using different detection schemes and input states. We compare the single- and two-parameter quantum estimation and their associated QCRB for three phase-shift situations: in both arms; only in the upper arm (asymmetric); and in both arms symmetrically. We then investigate the phase sensitivity under three detection schemes: intensity difference; single-mode intensity; and balanced homodyne. Additionally, we explore the use of Perelomov and Barut–Girardello coherent states, two types of SU(1,1) coherent states, in all scenarios. Notably, we demonstrate that, under optimal conditions, all detection schemes can achieve the QCRB by utilizing SU(1,1) coherent states as input states.

DOI
10.1364/josab.543874

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Improving interferometric phase sensitivity is crucial for high-precision measurements in rapidly developing quantum technologies. The Mach–Zehnder interferometer (MZI) is a versatile tool for analyzing this phenomenon. By splitting and recombining a light beam using beam splitters, the MZI allows for precise phase sensitivity analysis using tools like the quantum Cramér–Rao bound (QCRB) and the quantum Fisher information (QFI). This paper analyzes the phase sensitivity of an MZI in various scenarios using different detection schemes and input states. We compare the single- and two-parameter quantum estimation and their associated QCRB for three phase-shift situations: in both arms; only in the upper arm (asymmetric); and in both arms symmetrically. We then investigate the phase sensitivity under three detection schemes: intensity difference; single-mode intensity; and balanced homodyne. Additionally, we explore the use of Perelomov and Barut–Girardello coherent states, two types of SU(1,1) coherent states, in all scenarios. Notably, we demonstrate that, under optimal conditions, all detection schemes can achieve the QCRB by utilizing SU(1,1) coherent states as input states.
We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.
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.
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.
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.
Interferometry is a widely used technique for precision measurements in both classical and quantum contexts. One way to increase the precision of phase measurements, for example, in a Mach-Zehnder interferometer (MZI), is to use high-intensity lasers. In this paper we study the phase sensitivity of a MZI in two detection setups (difference intensity detection and single-mode intensity detection) and for three input scenarios (coherent, double coherent, and coherent plus squeezed vacuum). For the coherent and double coherent input, both detection setups can reach the quantum Cram\'er-Rao bound, although at different values of the optimal phase shift. The double coherent input scenario has the unique advantage of changing the optimal phase shift by varying the input power ratio.
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.