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We analyze the anisotropic Dicke model in the presence of a periodic driveand under a quasiperiodic drive. The study of drive-induced phenomena in thisexperimentally accesible model is important since although it is simpler thanfull-fledged many-body quantum systems, it is still rich enough to exhibit manyinteresting features. We show that under a quasiperiodic Fibonacci (Thue-Morse)drive, the system features a prethermal plateau that increases as anexponential (stretched exponential) with the driving frequency before heatingto an infinite-temperature state. In contrast, when the model is periodicallydriven, the dynamics reaches a plateau that is not followed by heating. Ineither case, the plateau value depends on the energy of the initial state andon the parameters of the undriven Hamiltonian. Surprisingly, this value doesnot always approach the infinite-temperature state monotonically as thefrequency of the periodic drive decreases. We also show how the drive modifiesthe quantum critical point and discuss open questions associated with theanalysis of level statistics at intermediate frequencies.

Periodically and quasiperiodically driven-anisotropic Dicke model