Quantum switching or quantum tunneling in optical bistability?

Abstract

The problem of the global stability of steady states in optical bistability is considered with emphasis toward the distinction between quantum switching (characterized by a classical diffusive process) and quantum tunneling (characterized by a nonclassical process with a singular and nonpositive Glauber-Sudarshan distribution). Relative to treatments of quantum switching in optical bistability for which nonpositive definite diffusion is excluded, we address the issue of global stability when the atom-field interaction is purely radiative and nonclassical processes (such as squeezing and antibunching) are involved. In the 1-D approximation, we point out certain anomalous features in the eigenvalue structure of the switching problem associated with a change in sign of the diffusion coefficient in the Glauber-Sudarshan representation. To substantiate the validity of the 1-D approximation, we explore the topology of the 2-D generalized potential. Finally, we compare our result with those previously obtained to emphasize in qualitative terms the distinction between switching and tunneling for bistable optical systems. Our analysis is motivated by an attempt to identify explicit experimental signatures of quantum tunneling.