Abstract
We apply the time-delayed Pyragas control scheme to the dissipative Dicke model via a modulation of the atom-field-coupling. The feedback creates an infinite sequence of non-equilibrium phases with fixed points and limit cycles in the primary superradiant regime. We analyse this Hopf bifurcation scenario as a function of delay time and feedback strength and determine analytical conditions for the phase boundaries.
Highlights
Interacting quantum systems with time-dependent Hamiltonians offer rich and exciting possibilities to study many-body physics beyond equilibrium conditions
There has been a recent surge in generating correlated nonequilibrium dynamics in a controlled way by changing the interaction parameters as a function of time, for example, by periodically modulating the coupling constants or by abruptly quenching them
The timedelayed Pyragas control scheme [5] that we propose here has been successfully employed in a classical context over the past twenty years, for example, as a tool to stabilize certain orbits in chaotic systems or networks [6,7,8,9]
Summary
Interacting quantum systems with time-dependent Hamiltonians offer rich and exciting possibilities to study many-body physics beyond equilibrium conditions. There has been a recent surge in generating correlated nonequilibrium dynamics in a controlled way by changing the interaction parameters as a function of time, for example, by periodically modulating the coupling constants or by abruptly quenching them. Our key idea is to generate new non-equilibrium phases via Pyragas control of the interaction between the single bosonic cavity mode and the collection of quantum two-level systems [10] in Dicke–Hepp–Lieb superradiance. The superradiant transition without control, which has been observed only recently in cold atoms within a photonic cavity [11,12,13,14], with applied quenches [15] or using cavity-assisted Raman transitions [16], has an underlying semi-classical bifurcation, which makes it an ideal candidate to study feedback at the boundary between non-linear (classical) dynamics and quantum many-body systems [17]. The structure of this paper is as follows: In section 2 we introduce the model with the conditioned coupling constant g(t) and perform the linearized stability analysis based on semiclassical equations of motion; in section 3 we visualize and discuss the results and go beyond the linear stability analysis and give more details on the numerical procedure; in section 4 we summarize our findings, discussing them in a more general context
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