Abstract:
We study the effect of spontaneous emission and incoherent atomic pumping on
the nonlinear semiclassical dynamics of the unbalanced Dicke model -- a
generalization of the Dicke model that features independent coupling strengths
for the co- and counter-rotating interaction terms. As well as the ubiquitous
superradiant behavior the Dicke model is well-known for, the addition of
spontaneous emission combined with the presence of strong counter-rotating
terms creates laser-like behavior termed counter-lasing. These states appear in
the semiclassical model as stable periodic orbits. We perform a comprehensive
dynamical analysis of the appearance of counter-lasing in the unbalanced Dicke
model subject to strong cavity dissipation, such that the cavity field can be
adiabatically eliminated to yield an effective Lipkin-Meshkov-Glick (LMG)
model. If the coupling strength of the co-rotating interactions is small, then
the counter-lasing phase appears via a Hopf bifurcation of the de-excited
state. We find that if the rate of spontaneous emission is small, this can lead
to resurgent superradiant pulses. However, if the co-rotating coupling is
larger, then the counter-lasing phase must emerge via the steady-state
superradiant phase. Such a transition is the result of the competition of the
coherent and incoherent processes that drive superradiance and counter-lasing,
respectively. We observe a surprisingly complex transition between the two,
associated with the formation of a chaotic attractor over a thin transitional
parameter region.