Dynamics of the rotated Dicke model

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We study quantum dynamics of the rotationally driven Dicke model where the collective spin is rotated around the z axis with a finite velocity. In the absence of the rotating wave approximation we observe that for several physically relevant initial states the position of the quantum critical point is shifted by the amount given by the applied rotation velocity. This allows us to probe the quantum criticality "from a distance" in parameter space without actual crossing of the quantum critical surface but instead by encircling it in the parameter space. This may provide a useful experimental hint since the quantum state is not destroyed by this protocol. Moreover, for the coherent initial state we observe an interesting non-equilibrium reentrant phenomenon of quantum critical behavior as a function of the driving velocity and construct a non-equilibrium phase diagram of the driven model.