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Optics Continuum

Phase sensitivity of a modified Grover-Michelson interferometer

Chaoping Wei, Chuting Xu, Qi Li

Published May 23, 2025• 2 citations
Publisher

Abstract

Power recycling techniques are usually used to improve the phase sensitivity of interferometers by reusing the input light energy, and can beat the shot noise level. Recent studies have demonstrated that the phase sensitivity of the interferometer is significantly improved via the addition of a recycling cavity, that is, coupling the interferometer with an external optical device. This study reviewed such types of interferometers named Grover-Michelson interferometers (GMI), and discusses their phase sensitivity with coherent states as inputs. Subsequently, a detailed comparison in terms of the scale of 1/ N and the standard quantum limit (SQL) is presented. The results demonstrate that the phase sensitivity of GMI improved owing to the power recycling and exceeded the value of 1/ N . Further, we proposed a modified Grover-Michelson interferometer (MGMI) with two input ports and examined its phase sensitivity with single photon or coherent states, respectively. Finally, in the presence of photon losses, we investigated the phase sensitivity of the four different interferometers, including MGMI, GMI, Mach-Zehnder interferometer (MZI), and SU(1,1) interferometer (SU(1,1)I), and conducted detailed comparisons. The results of this study indicated that the phase sensitivity of MGMI significantly improved owing to the increase in input energy, and MGMI exhibited the strongest robustness against photon number loss. These theoretical results are expected to facilitate improvements in interferometers and the detection of weak signals.

DOI
10.1364/optcon.546829

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Power recycling techniques are usually used to improve the phase sensitivity of interferometers by reusing the input light energy, and can beat the shot noise level. Recent studies have demonstrated that the phase sensitivity of the interferometer is significantly improved via the addition of a recycling cavity, that is, coupling the interferometer with an external optical device. This study reviewed such types of interferometers named Grover-Michelson interferometers (GMI), and discusses their phase sensitivity with coherent states as inputs. Subsequently, a detailed comparison in terms of the scale of 1/ N and the standard quantum limit (SQL) is presented. The results demonstrate that the phase sensitivity of GMI improved owing to the power recycling and exceeded the value of 1/ N . Further, we proposed a modified Grover-Michelson interferometer (MGMI) with two input ports and examined its phase sensitivity with single photon or coherent states, respectively. Finally, in the presence of photon losses, we investigated the phase sensitivity of the four different interferometers, including MGMI, GMI, Mach-Zehnder interferometer (MZI), and SU(1,1) interferometer (SU(1,1)I), and conducted detailed comparisons. The results of this study indicated that the phase sensitivity of MGMI significantly improved owing to the increase in input energy, and MGMI exhibited the strongest robustness against photon number loss. These theoretical results are expected to facilitate improvements in interferometers and the detection of weak signals.
The Michelson interferometric phase detection resolution can be enhanced by replacing conventional beam splitters with novel directionally unbiased four-port scatterers, such as Grover coins. We present a quantitative analysis of the noise-to-signal ratio of sideband frequencies generated by gravitational wave-induced phase perturbations in a Grover-Michelson interferometer (GMI). We discuss the principles of GMI signal enhancement and demonstrate how combining this configuration with additional light-recycling arrangements further enhances the performance.
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.
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.
A Michelson-type interferometer with two-mode squeezed coherent state input is considered. Such an interferometer has a better phase sensitivity over the shot-noise limit by a factor of e2re^{2r}e2r, where rrr is the squeezing parameter [Phys. Rev. A 102,022614 (2020)]. We show that when photon loss and noise in the two arms is asymmetric an optimal choice of the squeezing angle can allow improvement in phase sensitivity without any increase in input or pump power. In particular, when loss occurs only in one arm of the interferometer, we can have improvement in phase sensitivity for photon loss up to 80\%. Hence, a significant improvement can be made in several applications such as LiDAR, gyroscopes and measuring refractive indices of highly absorptive/reflective materials.
A Michelson-type interferometer with two-mode squeezed coherent state input is considered. Such an interferometer has a better phase sensitivity over the shot-noise limit by a factor of e2r, where r is the squeezing parameter [Phys. Rev. A 102, 022614 (2020)]. We show that when photon loss and noise in the two arms are asymmetric, an optimal choice of the squeezing angle can allow improvement in phase sensitivity without any increase in input or pump power. In particular, when loss occurs only in one arm of the interferometer, we can have improvement in phase sensitivity for photon loss up to 80%. Hence, a significant improvement can be made in several applications such as LiDAR, gyroscopes, and measuring refractive indices of highly absorptive/reflective materials.
Michelson interferometer can be applied to not only the building block of the fundamental research of physics, but also the precise measurement, such as the direct observation of gravity wave signal. Therefore, high performance Michelson interferometer is the key step towards the implementation of direct observation of weak gravity wave signal. Recently, the vacuum noise was reduced by injecting squeezed vacuum into the unused port of Michelson interferomter, and the phase signal optical field in Mach-Zender interferometer is amplified based on the four-wave mixing in hot Rubidium atom. Here we study high sensitivity quantum Michelson interferometer. In the Michelson interferometer, the linear optical beam splitter is replaced by a non-degenerated optical parametric amplifier to realize the splitting and combining of optical fields, and the squeezed vacuum is also injected into the unused port of interferomter, so that the high signal-to-noise ratio and high sensitivity of phase measurement can be realized. Due to the inevitable optical losses, the losses inside and outside the Michelson interferometer are considered in our theoretical model. We investigate the influences of the losses inside and outside the Michelson interferometer on the sensitivity of phase measurement. By theoretical calculation, we analyze the dependence of sensitivity of phase measurement on system parameters, such as intensity of optical fields for phase sensing, gain factor of non-degenerated optical parametric amplifier, the losses inside and outside the Michelson interferometer, and the squeezing parameter of input squeezed vacuum, and thus the condition of high sensitivity nonlinear Michelson interferometer can be obtained. In a broad system parametric range, the quantum Michaleson interferometer can surpass standard quantum limit, and the nonlinear Michaleson interferometer with squeezed state injection can provide the optimal sensitivity for phase measurement. The nonlinear Michelson interferometer with squeezed state is suitable for weak signal measurement. While the gain factor of non-degenerated optical parametric amplifier is large enough, the nonlinear Michelson interferometer without injecting the squeezed vacuum can still reach the optimal sensitivity, which reduces the use of quantum resources. When the phase sensing optical field is strong, the linear Michelson interferometer with injecting the squeezed vacuum can also reach the optimal sensitivity, and the sensitivity is robust for both losses inside and outside the interferometer. All the kinds of interferometers are more sensitive to the loss inside the interferometer than outside the interferometer, and the sensitivity of phase measurement can be improved by reducing the loss inside the interferometer. Our result provides direct reference of experimental implementation of high performance interferometer for high precision quantum metrology.