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Physical Review A

Multimode quantum analysis of an interferometer with moving mirrors

Alfredo Luis, Luis Lorenzo Sánchez-Soto

Published Jun 1, 1992• 20 citations
Publisher

Abstract

A multimode quantum analysis of noise reduction in interferometric measurements is presented. A unitary transformation relating the output modes with the input ones for a Michelson interferometer with moving mirrors is given. The evaluation of the noise spectrum shows that with a proper choice of the input states, the sensitivity of the interferometer can be pushed beyond the standard quantum limit. The results are compared with a semiclassical analysis.

DOI
10.1103/physreva.45.8228

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A multimode quantum analysis of noise reduction in interferometric measurements is presented. A unitary transformation relating the output modes with the input ones for a Michelson interferometer with moving mirrors is given. The evaluation of the noise spectrum shows that with a proper choice of the input states, the sensitivity of the interferometer can be pushed beyond the standard quantum limit. The results are compared with a semiclassical analysis.
A full quantum theory of the Fabry-Perot interferometer is presented. The quantum limits on the determination of small changes in the cavity length are considered, studying the case in which the interferometer is simultaneously excited by coherent and squeezed-vacuum inputs. The contributions to the limiting resolution from photon noise and radiation pressure uncertainty are evaluated in a unified calculation by means of a unitary transformation which relates the input modes to the output modes. These results are compared with the corresponding results for the Michelson interferometer.
We consider the situation when the signal propagating through each arm of an interferometer has a complicated multimode structure. We demonstrate that the shot-noise level for such a setup is the same as for the common two-mode case for as long as the interferometric transformation treats each arm as a whole and does not penetrate its inner structure. We find the relation between the particle entanglement and the possibility to surpass the shot-noise limit of the phase estimation. Our results are general---they apply to pure and mixed states of identical and distinguishable particles (or combinations of both) for a fixed and fluctuating number of particles. An important result is that the method for detecting the entanglement often used in a two-mode system---based on the measurement of the visibility of fringes and the population imbalance fluctuations---can give misleading results when applied to the multimode case. Our main result is that the additional modes do not boost the sensitivity for as long as they are not interacting. Therefore, the improvement above the shot-noise level established for the two-mode systems can safely be treated as an entanglement criterion also in the complex multimode case.
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.