Landau-Zener extension of the Tavis-Cummings model: structure of the solution

TL;DR

This paper analyzes the driven Tavis-Cummings model with a linearly time-dependent bosonic mode, providing new exact solutions, efficient formulas for transition probabilities, and exploring its semiclassical limit and connection to q-deformed statistics.

Contribution

It derives compact, tractable expressions for transition probabilities in the driven Tavis-Cummings model, enabling faster calculations and deeper analytical understanding.

Findings

Derived exact transition probability formulas using special functions

Compared semiclassical limit with previous approximations

Revealed connection to q-deformed binomial statistics

Abstract

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and $q$-deformed binomial statistics.