Understanding the role of counter-rotating terms of Rabi Model under dissipation

Chunjian Zhao, Hang Zheng

The quantum dynamics of the dissipative two-level system in the Ohmic bath with Rabi driving is studied by means of a modified Bloch-Redfield approach based on a unitary transformation. The main purpose is to understand the effect of counter-rotating terms of the system-environment interaction on the dynamics of the two-level system and, in particular, if it is possible to control the effective system-environment coupling by their effect on the interference between driving and dissipation. By calculating the nonequilibrium correlation $P(t)$ for a finite driving it is shown that the counter-rotating terms of the system-environment interaction play an important role in the dynamic evolution with a longer coherent time and a weaker amplitude of the long-time driven oscillation.

Raphael C. Drumond, Maria Carolina Nemes

Clemens Müller

Jin‐Feng Huang, C. K. Law

We present an interaction scheme to control counter-rotating terms in the quantum Rabi model. We show that by applying a sequence of $\ensuremath{\pi}/2$ phase kicks to a two-level atom and a single-mode quantized field, the natural dynamics of the Rabi model can be interrupted in a way that counter-rotating transitions can be significantly enhanced. This is achieved by a suitable timing of the phase kicks determined by a phase-matching condition. If the time between successive kicks is sufficiently short, our scheme is turned into a dynamical decoupling problem in which the effects of counter-rotating terms can be strongly suppressed under ultrastrong coupling.

Guofeng Zhang, Han‐Jie Zhu

The anisotropic Rabi model, which was proposed recently, differs from the original Rabi model: the rotating and counter-rotating terms are governed by two different coupling constants. This feature allows us to vary the counter-rotating interaction independently and explore the effects of it on some quantum properties. In this paper, we eliminate the counter-rotating terms approximately and obtain the analytical energy spectrums and wavefunctions. These analytical results agree well with the numerical calculations in a wide range of the parameters including the ultrastrong coupling regime. In the weak counter-rotating coupling limit we find out that the counter-rotating terms can be considered as the shifts to the parameters of the Jaynes-Cummings model. This modification shows the validness of the rotating-wave approximation on the assumption of near-resonance and relatively weak coupling. Moreover, the analytical expressions of several physics quantities are also derived, and the results show the break-down of the U(1)-symmetry and the deviation from the Jaynes-Cummings model.

Alexander Moroz