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Physical Review A

Effect of the detector efficiency on the phase sensitivity in a Mach-Zehnder interferometer

Taesoo Kim, Yang Ha, Jong-Tae Shin, Heonoh Kim, Goo-Dong Park, Kisik Kim, Tae-Gon Noh, Chung Ki Hong

Published Jul 1, 1999• 48 citations
Publisher

Abstract

The effect of quantum efficiencies of detectors on the phase sensitivity of a Mach-Zehnder is analyzed for the Fock state input. The phase uncertainty of two different interference experiments, the second order and the fourth order, are compared with two practical detectors with less than unit quantum efficiencies. It is found out that in the second-order interference experiment we cannot beat the classical limit in the phase sensitivity, even with ideal detectors. We show that almost ideal detectors are required to get the Heisenberg limit in the phase sensitivity of the fourth-order interference for two Fock state light inputs. There exists an optimum angle given by the efficiency of the detectors.

DOI
10.1103/physreva.60.708

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The effect of quantum efficiencies of detectors on the phase sensitivity of a Mach-Zehnder is analyzed for the Fock state input. The phase uncertainty of two different interference experiments, the second order and the fourth order, are compared with two practical detectors with less than unit quantum efficiencies. It is found out that in the second-order interference experiment we cannot beat the classical limit in the phase sensitivity, even with ideal detectors. We show that almost ideal detectors are required to get the Heisenberg limit in the phase sensitivity of the fourth-order interference for two Fock state light inputs. There exists an optimum angle given by the efficiency of the detectors.
The phase sensitivity of the coincidence detection in one output port of a Mach-Zehnder interferometer is analysed for twin Fock state inputs. Firstly, the ideal detectors with quantum efficiency of unity are assumed for the detection of the output photons. The sensitivity is found out to be independent of the photon number of input light, which means that the Heisenberg limit cannot be reached in the coincidence detection even with ideal detectors. Secondly, the practical detectors with quantum efficiencies less than unity are discussed.
We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one 1m\frac{1}{\sqrt{m}}m​1​ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.
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.
We investigate the phase sensitivity of the SU(1,1) interfereometer [SU(1,1)I] and the modified Mach–Zehnder interferometer (MMZI) with the entangled coherent states (ECS) as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU(1,1)I can beat the shot-noise limit (SNL) and approach the Heisenberg limit (HL). In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU(1,1)I, and the MMZI is more robust against internal photon losses than the SU(1,1)I.
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.