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arXiv:quant-ph/0603043 · Physical Review A

Leaky cavities with unwanted noise

А. А. Семенов, Dmytro Vasylyev, W. Vogel, M. Khanbekyan, D.‐G. Welsch

Published Sep 8, 2006• 9 citations
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Abstract

A phenomenological approach is developed that allows one to completely describe the effects of unwanted noise, such as the noise associated with absorption and scattering, in high-$Q$ cavities. This noise is modeled by a block of beam splitters and an additional input-output port. The replacement schemes enable us to formulate appropriate quantum Langevin equations and input-output relations. It is demonstrated that unwanted noise renders it possible to combine a cavity input mode and the intracavity mode in a nonmonochromatic output mode. Possible applications to unbalanced and cascaded homodyning of the intracavity mode are discussed and the advantages of the latter method are shown.

DOI
10.1103/physreva.74.033803

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A phenomenological approach is developed that allows one to completely describe the effects of unwanted noise, such as the noise associated with absorption and scattering, in high-QQQ cavities. This noise is modeled by a block of beam splitters and an additional input-output port. The replacement schemes enable us to formulate appropriate quantum Langevin equations and input-output relations. It is demonstrated that unwanted noise renders it possible to combine a cavity input mode and the intracavity mode in a nonmonochromatic output mode. Possible applications to unbalanced and cascaded homodyning of the intracavity mode are discussed and the advantages of the latter method are shown.
The problem of the description of absorption and scattering losses in high- Q cavities is studied. The considerations are based on quantum noise theories, hence the unwanted noise associated with scattering and absorption is taken into account by introduction of additional damping and noise terms in the quantum Langevin equations and input-output relations. Completeness conditions for the description of the cavity models obtained in this way are studied and corresponding replacement schemes are discussed.
The problem of the description of absorption and scattering losses in high-Q cavities is studied. The considerations are based on quantum noise theories, hence the unwanted noise associated with scattering and absorption is taken into account by introduction of additional damping and noise terms in the quantum Langevin equations and input--output relations. Completeness conditions for the description of the cavity models obtained in this way are studied and corresponding replacement schemes are discussed.
Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-QQQ cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in general, as the exact calculation shows. On the basis of the operator input-output relations the problem of extracting the quantum state of an initially excited cavity mode is studied and input-output relations for the sss-parametrized phase-space function are derived, with special emphasis on the relation between the Wigner functions of the quantum states of the outgoing field and the cavity field.
Quantum input-output relations for a generic nnn-port ring cavity are obtained by modeling the ring as a cascade of nnn interlinked beam splitters. Cavity response to a beam impinging on one port is studied as a function of the beam-splitter reflectivities and the internal phase-shifts. Interferometric sensitivity and stability are analyzed as a function of the number of ports.
For a leaky cavity driven by an active medium, we clarify the connection between the concepts of single-quasimode squeezing (for the intracavity field) and spectral squeezing (for the input and output fields). Our analysis is based on a rigorous construction of the Fox-Li quasimodes of an empty cavity by a superposition of the true modes of a perfect, large (infinitely large in the limit) cavity which fully subsumes the leaky cavity. To illustrate the physical importance of spectral squeezing (as defined here and as used by other authors), we consider a novel model of a microscopic system that is sensitive to the generalized quadratures of the field. We obtain a simple picture of the reasons why the quantum-noise reduction is in general different inside and outside the cavity. An important special case of our picture is that if the intracavity field is perfectly squeezed, then the output field shows no squeezing at all. Our considerations apply to a wide class of systems, examples of which are discussed in the companion paper.