Optimal Phase Measurements In A Lossy Laser Interferometer

Laser interferometer is a high-precision precision measurement tool,which is widely used to detect various physical quantities,such as gravitational field,distance,rotational angular velocity,etc.Phase sensitivity is the core parameter of interferometer,and how to improve the phase sensitivity of interferometer has been one of the frontier hotspots in the field of precision measurement.In the classical domain,the phase measurement limit of laser interferometer is the standard quantum limit.In order to further improve the phase sensitivity of laser interferometer,breaking the limit of standard quantum limit has been one of the main research objectives in the field of precision measurement.In the last two decades,a large number of research advances have realized quantum interferometers with phase sensitivity beyond the standard quantum limit,such as the Mach-Zehnder interferometer(MZI)with squeezed light injection and the SU(1,1)-type quantum correlation interferometer based on dual-mode squeezed light.However,in practice,interferometers will inevitably face various types of environmental losses,such as propagation losses,detection losses,etc.,which will all cause the interferometer phase sensitivity to degrade.In particular,the quantum advantage of quantum interferometer will disappear rapidly with the increase of losses,which is the main bottleneck for the practicalization of quantum interferometer.In this paper,we address the internal loss problem of classical MZI(coherent state +vacuum state)and quantum MZI(coherent state + squeezed vacuum state)in practical applications,and investigate the theory of optimal quantum phase estimation in lossy environment and the methods and techniques of resource optimization,which effectively improve the phase sensitivity in lossy environment.The details of the study are as follows:(1).Quantum Fisher information can give the best phase accuracy of an interferometric system without considering a specific detection scheme.In this paper,the quantum phase estimation of interferometer in lossy environment is given based on the parameter estimation model of open quantum system.Based on this,the optimal Quantum Cramér-Rao Bound for lossy classical MZI and lossy quantum MZI and the corresponding optimal resource allocation scheme are obtained.The results of this theoretical study provide a solid basis for the experimental optimization study of lossy MZI.(2).To address the problem of phase sensitivity degradation of classical MZI under large environmental losses,an optimization scheme for coherent resource allocation is proposed to enhance the phase sensitivity of lossy interferometer to the theoretical limit value.In this paper,the optimal resource optimization scheme and detection method of classical MZI are firstly introduced in theoretical details,and then the MZI with adjustable beam splitting ratio is constructed in experiments to demonstrate this optimization scheme.The experimental results confirm that the phase sensitivity can be enhanced by optimising the beam splitting ratio of the interferometer to reach the optimization limit in the lossy case.(3).Quantum laser interferometers with squeezed vacuum state injection have measurement sensitivity beyond the standard quantum limit and have been successfully used by LIGO to enhance the accuracy of gravitational wave measurements.However,in lossy environments,the quantum advantage of such interferometers is rapidly lost with increasing loss.In this paper,we theoretically analyse the quantum Fisher information and phase sensitivity of lossy quantum MZI,and by optimising the coherent and quantum resource allocation of the interferometer,we are able to effectively preserve the quantum resources and enhance the interferometer measurement sensitivity under large losses.This optimization scheme is experimentally demonstrated in a quantum MZI with 2.0d B squeezed light injection,where the phase sensitivity is still improved by about 1.6d B compared to conventional MZI at losses up to 90%.the optimised phase sensitivity reaches the theoretical optimization limit of the quantum interferometer,and the quantum noise advantage is well preserved.