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Journal of Changsha University of Science & Technology

Input-output relation in the cavity filled with material media

Yu Jing Guo

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The influence of the material media on the input and output fields of optical cavity were analyzed.The input-output theory developed by Collett and Gardiner to the single-mode cavity filled with material media was extended.It can be controlled the input-output relation of cavity by adjusting the parameters of the two-level atoms of material media.

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The influence of the material media on the input and output fields of optical cavity were analyzed.The input-output theory developed by Collett and Gardiner to the single-mode cavity filled with material media was extended.It can be controlled the input-output relation of cavity by adjusting the parameters of the two-level atoms of material media.
In this paper, we present a very simple approach to input-output relations in optical cavities, limiting ourselves to one- and two-photon states of the field. After field quantization, we derive the nonunitary transformation between inside and output annihilation and creation operators. Then we express the most general two-photon state generated by inside creation operators, through base states generated by output creation operators. After renormalization of coefficients of the inside two-photon state, we calculate the outside photon-number probability distribution in a general case; then we treat with some detail the single-mode and symmetrical cavity case. We found that the statistics of emitted photons may exhibit either quantum or classical behavior, depending both on source properties and on cavity characteristics.
We generalize the quantum optical input-output theory developed for optical cavities to ultracold fermionic atoms confined in a trapping potential, which forms an ``atom cavity.'' In order to account for the Pauli exclusion principle, quantum Langevin equations for all cavity modes are derived. The dissipative part of these multimode Langevin equations includes a coupling between cavity modes. We also derive a set of boundary conditions for the Fermi field that relate the output fields to the input fields and the field radiated by the cavity. Starting from a constant uniform current of fermions incident on one side of the cavity, we use the boundary conditions to calculate the occupation numbers and current density for the fermions that are reflected and transmitted by the cavity.
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.
An obvious question is, how to relate the internal cavity mode to externallymeasured fields. Normally, themeasuring instruments are external to the cavity. In this case, the input-output formalism is use- ful. Strictly speaking, the input-output results are approximations, and can be obtained from considering the boundary conditions at lossy cavity mirrors. In this chapter, we consider the input-output formalism for a single-sided cavity in which the cavity mode is coupled to an external multi-mode environment through a partially transparent broadband mirror.
The quantized electromagnetic field inside and outside an absorbing high-QQQ cavity is studied, with special emphasis on the absorption losses in the coupling mirror and their influence on the outgoing field. Generalized operator input-output relations are derived, which are used to calculate the Wigner function of the outgoing field. To illustrate the theory, the preparation of the outgoing field in a Schrödinger cat-like state is discussed.