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Springer eBooks

Input-Output from Optical Cavities: Quasi-Mode Theory

Bryan J. Dalton, E. S. Guerra, P. L. Knight

Published Jan 1, 1996• 0 citations
Publisher
DOI
10.1007/978-1-4757-9742-8_160

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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.
The input-output formalism is the basis to study the response of an optical cavity to the external stimulations. The existing theories usually handle cavity systems with only one internal mode. However, there is growing interest in more complex systems, especially the hybrid cavity-matter systems, which contain at least two internal modes, one or more from both the optical cavity and the matter. Here we propose a graphical loop theory to calculate and visualize the reflection and transmission spectrum of such a multimode cavity, resembling the role of Feynman diagrams in the quantum field theory. This loop theory gives a unified picture to interpret the experimental observations of a hybrid magnet-light system and is extremely easy to apply to arbitrary complicated problems without any calculations.