Analytic Approximation of the Tavis-Cummings Ground State via Projected States

TL;DR

This paper introduces a semi-classical projected state that accurately approximates the ground state of the Tavis-Cummings model, enabling analytical calculations of key quantum properties with high fidelity.

Contribution

The authors develop an analytical projected state approximation for the Tavis-Cummings ground state, simplifying calculations and closely matching the exact quantum solution.

Findings

Fidelity between the projected and exact ground states is near 1.

Analytical expressions for observables are derived and match numerical results.

The approximation breaks down near classical phase transitions.

Abstract

We show that an excellent approximation to the exact quantum solution of the ground state of the Tavis-Cummings model is obtained by means of a semi-classical projected state. This state has an analytical form in terms of the model parameters and, in contrast to the exact quantum state, it allows for an analytical calculation of the expectation values of field and matter observables, entanglement entropy between field and matter, squeezing parameter, and population probability distributions. The fidelity between this projected state and the exact quantum ground state is very close to 1, except for the region of classical phase transitions. We compare the analytical results with those of the exact solution obtained through the direct Hamiltonian diagonalization as a function of the atomic separation energy and the matter-field coupling.