On the suppression of the diffusion and the quantum nature of a cavity mode. Optical bistability; forces and friction in driven cavities

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Abstract
A new analytical method is presented here, offering a physical view of driven cavities where the external field cannot be neglected. We introduce a new dimensionless complex parameter, intrinsically linked to the cooperativity parameter of optical bistability, and analogous to the scaled Rabbi frequency for driven systems where the field is classical. Classes of steady states are iteratively constructed and expressions for the diffusion and friction coefficients at lowest order also derived. They have in most cases the same mathematical form as their free-space analog. The method offers a semiclassical explanation for two recent experiments of one atom trapping in a high Q cavity where the excited state is significantly saturated. Our results refute both claims of atom trapping by a quantized cavity mode, single or not. Finally, it is argued that the parameter newly constructed, as well as the groundwork of this method, are at least companions of the cooperativity parameter and its mother theory. In particular, we lay the stress on the apparently more fundamental role of our structure parameter.

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