Tavis-Cummings model beyond the rotating wave approximation: Quasi-degenerate qubits

TL;DR

This paper extends the Tavis-Cummings model beyond the rotating wave approximation to analyze multi-qubit interactions with a common oscillator, revealing new dynamics and entanglement features in the ultra-strong coupling regime.

Contribution

It generalizes the adiabatic approximation to multi-qubit systems and provides analytical formulas for complex dynamics beyond the RWA.

Findings

Identification of three-state manifolds of close-lying energy levels

Differences in two-qubit dynamics compared to single qubit case

Analytical expressions for collapse and revival signals

Abstract

The Tavis-Cummings model for more than one qubit interacting with a common oscillator mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the frequencies of the qubits are much smaller than the oscillator frequency and the coupling strength is allowed to be ultra-strong. The application of the adiabatic approximation, introduced by Irish, et al. (Phys. Rev. B \textbf{72}, 195410 (2005)), for a single qubit system is extended to the multi-qubit case. For a two-qubit system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intra-manifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-qubit dynamics that are different from the single qubit case, including calculations of qubit-qubit entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.