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Acta Physica Sinica

Effect of detection efficiency on phase sensitivity in quantum-enhanced Mach-Zehnder interferometer

Shiyu Li, Tian Jian-feng, Yang Chen, Zuo Guan-Hua, Zhang Yu-Chi, Tiancai Zhang

Published Jan 1, 2018• 2 citations
Publisher

Abstract

Three kinds of quantum light sources:Fock state, correlated Fock-state and squeezed vacuum state, which serve as the injection end of Mach-Zehnder interferometer (MZI) are investigated. The effect of detection quantum efficiency on the sensitivity of phase measurement in MZI is analyzed by using the intensity difference detection scheme. By analyzing the MZI system, the quantitative relationship between the sensitivity of phase measurement and the detection efficiency is obtained. It is found that the phase sensitivity cannot go beyond the standard quantum limit in any case when the Fock state is injected into interferometer, that is, the Fock state does not realize quantum enhanced measurement (QEM). And the injection of correlated Fock-state or squeezed vacuum state of light can go beyond the standard quantum limit, but the conditions for realizing quantum enhancement are different, quantum enhancement can only be achieved when the detection efficiency is greater than 75% for correlated Fock-state, or the squeezed vacuum state of light is injected into interferometer. There is no limitation of the minimum detection efficiency for realizing quantum enhancement on squeezed vacuum state. In principle, quantum enhancement can be achieved as long as the squeezed vacuum state is injected. The influence of detection efficiency on the phase sensitivity is investigated when the correlated Fock-state and the squeezed vacuum state are injected into the MZI. It is found that the phase sensitivity or quantum enhancement becomes better as the quantum efficiency of the detection system turns higher. And it is the squeezed vacuum state injected into the interferometer that has better quantum enhancement effect than the correlated Fock-state. In this study, the requirements for the detection efficiency for realizing QEM in experiment are given, which is of great significance for studying the QEM, when taking the real experimental system into account. In addition, the conclusions obtained from the MZI model discussed can also be used to analyze the sensitivity of detecting the gravitational wave, it explains that the improvement of detector efficiency can indeed improve the sensitivity to gravitational wave detection, which will play an important role in exploring gravitational waves and understanding the time and space to reveal the mystery of the universe in the future.

DOI
10.7498/aps.67.20181193

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Three kinds of quantum light sources:Fock state, correlated Fock-state and squeezed vacuum state, which serve as the injection end of Mach-Zehnder interferometer (MZI) are investigated. The effect of detection quantum efficiency on the sensitivity of phase measurement in MZI is analyzed by using the intensity difference detection scheme. By analyzing the MZI system, the quantitative relationship between the sensitivity of phase measurement and the detection efficiency is obtained. It is found that the phase sensitivity cannot go beyond the standard quantum limit in any case when the Fock state is injected into interferometer, that is, the Fock state does not realize quantum enhanced measurement (QEM). And the injection of correlated Fock-state or squeezed vacuum state of light can go beyond the standard quantum limit, but the conditions for realizing quantum enhancement are different, quantum enhancement can only be achieved when the detection efficiency is greater than 75% for correlated Fock-state, or the squeezed vacuum state of light is injected into interferometer. There is no limitation of the minimum detection efficiency for realizing quantum enhancement on squeezed vacuum state. In principle, quantum enhancement can be achieved as long as the squeezed vacuum state is injected. The influence of detection efficiency on the phase sensitivity is investigated when the correlated Fock-state and the squeezed vacuum state are injected into the MZI. It is found that the phase sensitivity or quantum enhancement becomes better as the quantum efficiency of the detection system turns higher. And it is the squeezed vacuum state injected into the interferometer that has better quantum enhancement effect than the correlated Fock-state. In this study, the requirements for the detection efficiency for realizing QEM in experiment are given, which is of great significance for studying the QEM, when taking the real experimental system into account. In addition, the conclusions obtained from the MZI model discussed can also be used to analyze the sensitivity of detecting the gravitational wave, it explains that the improvement of detector efficiency can indeed improve the sensitivity to gravitational wave detection, which will play an important role in exploring gravitational waves and understanding the time and space to reveal the mystery of the universe in the future.
Phase-shifting interferometry (PSI) promises excellent performance for quantitative phase measurement. However, the PSI is commonly realized by utilizing the Mach-Zehnder interferometer (MZI) fed with classical resources, and hence its phase sensitivity is hindered by the photon shot noise. In this paper, we propose to introduce specific phase-shifting algorithms into the well-established quantum-enhanced MZI, seeded by coherent and squeezed vacuum states and followed by single-mode intensity detection and difference intensity detection, to achieve quantitative phase measurement with sensitivity beyond that achieved by the corresponding Mach-Zehnder-type PSI with classical input. We show that when the average photon number of the coherent state is dominant, the optimal phase sensitivity of the Mach-Zehnder-type PSI with coherent plus squeezed vacuum input is better than the phase sensitivity of the Mach-Zehnder-type PSI with single coherent input under the same phase-sensing intensity condition in both of detection setups. We also show that for the typical MZI seeded with a high-power coherent state and a finitely squeezed vacuum state, the combination of intensity detection and phase-shifting algorithm can still improve the sensitivity of quantitative phase measurement. Furthermore, we derive the phase sensitivity of the fixed MZI as well as the quantum Cramér-Rao bound for two detection schemes. Finally, we explore the impacts of photon losses on the phase sensitivity enhancements of the Mach-Zehnder-type PSI and the fixed MZI in the high-intensity regime for each detection setup. The robustness to losses is compared between the Mach-Zehnder-type PSI and the fixed MZI. Our results may be helpful to promote the exploration of quantum-enhanced quantitative phase sensing.
We study the improvement in the phase sensitivity of a Mach–Zehnder interferometer using the superposition of Schrödinger’s cat-like state with the Fock state (SCFS) and the coherent state as inputs. With this setup, we examine the effect on phase sensitivity of the interferometer using a two-channel detection (TCD) scheme [ Opt. Express 29 , 95 ( 2021 ) OPEXFF 1094-4087 10.1364/OE.413391 ] in which we take the optimal combination of the intensities of both output ports. We find better phase sensitivity under some conditions for this setup as compared to other known combinations of inputs such as squeezed vacuum and coherent states, vacuum and coherent states, etc. Therefore, we expect that the SCFS may be an alternative nonclassical resource for improvement in the phase sensitivity of a Mach–Zehnder interferometer, having potential application in quantum sensing.
We study the phase super–sensitivity of a Mach–Zehnder interferometer (MZI) with the squeezed Kerr state (SKS) and coherent state as the inputs. We discuss the lower bound in phase sensitivity by considering the quantum Fisher information and the corresponding quantum Cramér–Rao bound. With the help of single intensity detection, intensity difference detection, and homodyne detection schemes, we find that our scheme gives a better sensitivity under both lossless and lossy conditions as compared to the well–known results of the combinations of inputs, such as coherent plus vacuum, coherent plus squeezed vacuum, and double coherent states. Because of the possibility of the generation of SKS with the present available quantum optical techniques, we expect that SKS may be an alternative nonclassical resource for the improvement in the phase super–sensitivity of the MZI in realistic scenarios.
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.
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.
We quantitatively investigate phase measurement in a Mach-Zehnder interferometer (MZI), which is injected with a weak coherent and a squeezed vacuum generated from a spontaneous parametric down-conversion. The measured three-photon coincidence in this system is quantified as a function of a ratio between the amplitude of the coherent state and the squeezed parameter of squeezed vacuum when the photon number is detected at one output of MZI. It shows that the phase sensitivity reaches the Heisenberg limit when an optimal ratio is chosen. This may introduce one approach to quantify phase sensitivity in precision phase measurement.