Long-lived states of the quantized field in a laser

Abstract

The lifetimes of different pure states of the quantized field in a single-mode laser (Scully-Lamb model) are considered. For operation high above threshold, I have shown number states to have extremely short lifetimes: Long lifetimes require coherent superpositions of neighboring number states with a width of the order of the square root of the average photon number. Thus, the long-lived states approach classical states. I propose a definition of the lifetime, which is found to be maximized by states that resemble the conventional Glauber coherent states, although they are slightly narrower in photon-number distribution. This is in contrast to the steadystate photon-number distribution for an ensemble of identical lasers (as given by the diagonal steady-state density matrix), which is wider than a coherent state. Possible interpretations and implications of these results are discussed.