Abstract
We propose a time-delayed feedback control scheme for open quantum systems that can dramatically reduce the time to reach steady state. No measurement is performed in the feedback loop, and we suggest a simple all-optical implementation for a cavity QED system. We demonstrate the potential of the scheme by applying it to a driven and dissipative Dicke model, as recently realized in a quantum gas experiment. The time to reach steady state can be reduced by two orders of magnitude for the parameters taken from the experiment, making previously inaccessible long time attractors reachable within typical experimental run times. The scheme also offers the possibility of slowing down the dynamics, as well as qualitatively changing the phase diagram of the system.
Highlights
Steady states of open quantum systems, where driving forces and internal dynamics are balanced by dissipation and/or other types of environmental noise, are often of experimental interest
We propose an all-optical feedback scheme relevant, for example, to circuit quantum electrodynamics (CQED) systems, that can be used to (i) change the stability of long time attractors, so that one can switch between different behaviors, and (ii) change the characteristic time-scale for approaching a steady state, potentially speeding up the convergence
This is relevant for the Bose–Einstein condensate (BEC) realization of the Dicke model where, as we will discuss in more detail below, the approach to steady state can be slow compared to typical experimental run times
Summary
Steady states of open quantum systems, where driving forces and internal dynamics are balanced by dissipation and/or other types of environmental noise, are often of experimental interest. The control is based on coherent feedback, i.e. no measurement is performed in the feedback loop, which can be advantageous, or even necessary, for stabilizing the high frequency dynamics of optical systems or high speed electrical circuits [13, 14] Another great strength of the approach is that it does not require the steady state to be known a priori. We will take advantage of this dissipative channel as well, by using it as the input to a noninvasive feedback loop that can alter the characteristic time-scale for the relaxation of the system, as well as the stability of the long-time attractors This is relevant for the BEC realization of the Dicke model where, as we will discuss in more detail below, the approach to steady state can be slow compared to typical experimental run times.
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