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Optics Express

Waveguide Mach-Zehnder interferometer to enhance the sensitivity of quantum parameter estimation

X. N. Feng, Huaiyuan Liu, L. F. Wei

Published Apr 14, 2023• 2 citations
Publisher

Abstract

The waveguide Fabry-Perot interferometer (FPI) (see, e.g., in Phys. Rev. Lett.113, 243601 (2015)10.1103/PhysRevLett.115.243601 and Nature569, 692 (2019)10.1038/s41586-019-1196-1), instead of the free space's one, have been demonstrated for the sensitive quantum parameter estimations. Here, we propose a waveguide Mach-Zehnder interferometer (MZI) to further enhance the sensitivity of the relevant parameter estimations. The configuration is formed by two one-dimensional waveguides coupled sequentially to two atomic mirrors, which are served as the beam splitters of the waveguide photons to control the probabilities of the photons being transferred from one waveguide to another. Due to the quantum interference of the waveguide photons, the acquired phase of the photons when they pass through a phase shifter can be sensitively estimated by measuring either the transmitted or reflected probabilities of the transporting photons. Interestingly, we show that, with the proposed waveguide MZI the sensitivity of the quantum parameter estimation could be further optimized, compared with the waveguide FPI, in the same condition. The feasibility of the proposal, with the current atom-waveguide integrated technique, is also discussed.

DOI
10.1364/oe.487793

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The waveguide Fabry-Perot interferometer (FPI) (see, e.g., in Phys. Rev. Lett.113, 243601 (2015)10.1103/PhysRevLett.115.243601 and Nature569, 692 (2019)10.1038/s41586-019-1196-1), instead of the free space's one, have been demonstrated for the sensitive quantum parameter estimations. Here, we propose a waveguide Mach-Zehnder interferometer (MZI) to further enhance the sensitivity of the relevant parameter estimations. The configuration is formed by two one-dimensional waveguides coupled sequentially to two atomic mirrors, which are served as the beam splitters of the waveguide photons to control the probabilities of the photons being transferred from one waveguide to another. Due to the quantum interference of the waveguide photons, the acquired phase of the photons when they pass through a phase shifter can be sensitively estimated by measuring either the transmitted or reflected probabilities of the transporting photons. Interestingly, we show that, with the proposed waveguide MZI the sensitivity of the quantum parameter estimation could be further optimized, compared with the waveguide FPI, in the same condition. The feasibility of the proposal, with the current atom-waveguide integrated technique, is also discussed.
A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cram\'er-Rao bound. The effects of photon loss on phase sensitivity are discussed. Our scheme can also provide some estimates for units of ${\ensuremath{\chi}}^{(3)}$, due to the relation between the nonlinear phase shift and the susceptibility ${\ensuremath{\chi}}^{(3)}$ of the Kerr medium.
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.
Recent progress in atom optics has culminated in several demonstrations of atom interferometers. These rely on the passage of atoms through mechanical or light gratings and may be roughly characterized as Mach–Zehnder interferometers. In this communication, we propose a scheme to realize a Fabry–Perot interferometer for atoms. The mirrors are realized by the field gradient resulting from the spatial mode structure in optical or microwave cavities. When ultra- cold atoms impinge on such cavities, they experience quantum mechanical reflection and transmission that result in the appearance of longitudinal modes for the atomic wave function. We present a model of such a Fabry–Perot interferometer for two-level atoms. We discuss the intra-cavity matter–wave mode structure as well as the transmittivity and reflectivity characteristics of the interferometer. The potential generation of macroscopic quantum waves using such a device, as well as its potential as a sensitive photon detector, will be addressed.
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.
The Mach-Zehnder interferometer (MZI) is a two-path phase-to-intensity transducer that becomes "mysterious" mainly when one conflates operational facts, minimal predictive calculus, and ontological storytelling.Controlled phase shifts are the central "knob" of the MZI: a tunable relative phase Φ converts directly into complementary output intensities at the two ports.In this model, photons enter the MZI with classical instructions: the "white" photons with E 2 = 1 (where E is the electric field of the sinusoidal electromagnetic wave at the given moment) are reflected on the beamsplitters, the "grey" photons with E 2 = 0.5 can be both reflected and transmitted through the beamsplitters (with 50:50 ratio), and the "black" photons with E 2 = 0 transmit through the beamsplitters.The movable mirrors and the second beamsplitter modify the "color" of photons.The 50:50 mixture of "white" and "black" photons at the input is separated by the first beamsplitter.The phase shifts are modified by movable mirrors so that the second beamsplitter organizes the resulting structure of photons at the two detectors.The interference patterns have been formed from two sub-ensembles of photons with their relative phase shift ΔΦ = π at the given port.We assume that this classical behavior of photons in the MZI can clarify the "riddle-like" discussions (e.g., delayed choice switching, the meaning of a dark port, and the role of which-way information).
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.