Berry phases in the generalized Rabi model with dispersive-type interaction

Jean-Paul Saucier Calderón, F. De Zela

We address Berry phases that have been predicted to appear when a two-level system interacts with a quantized field, including the vacuum state. The issue became controversial after it was argued that the appearance of such Berry phases is an artifact of the rotating-wave approximation (RWA). As is widely believed, whenever the RWA applies, one may replace the Rabi model of a two-level system interacting with a quantized field by the analytically solvable Jaynes-Cummings model. Conflicting predictions of these two models under conditions that validate the RWA would signal a serious inconsistency of this approximation. We show that this is not the case and that claims to the contrary are inconsistent with analytical results concerning the Rabi model. We provide also numerical evidence supporting our analytical approach. Furthermore, we argue that the appearance of Berry phases in the addressed cases does not depend on adiabatic conditions nor on any particular Hamiltonian, but on the underlying vector space. Thus, the appropriate framework is given by the kinematic approach to geometric phases, which contains Berry's phase as a special case.

Clemens Müller

Wenwu Deng, Gao‐xiang Li

The Berry phase of the Rabi model beyond the rotating-wave approximation is investigated. By use of two unitary transformations, the analytical expressions of the Berry phase are obtained approximately for the Rabi model. The obtained analytical solutions reproduce accurately the high-accuracy numerical results of the Berry phase in the strong coupling regime. It is found that the Berry phase of the ground state is relevant to the second-order terms of the coupling strength, and the Berry phases of the first and second excited states are mainly relevant to the first-, second- and third-order terms of the coupling strength when the effect of the counter-rotating-wave terms is taken into account.

S. A. Bulgadaev

Guanyu Zhu, Sebastian Schmidt, Jens Koch

Jonas Larson

I revisit a longstanding question in quantum optics; when is the rotating wave approximation justified? In terms of the Jaynes–Cummings and Rabi models I demonstrate that the approximation in general breaks down in the adiabatic limit regardless of system parameters. This is explicitly shown by comparing Berry phases of the two models, where it is found that this geometrical phase is strictly zero in the Rabi model contrary to the non-trivial Berry phase of the Jaynes–Cummings model. The source of this surprising result is traced back to different topologies in the two models.