Bloch space structure, the qutrit wave function and atom-field entanglement in three-level systems

TL;DR

This paper presents a novel SU(3)-based formulation for three-level atomic systems, analyzing their Bloch space structure, qutrit wave functions, and atom-field entanglement, revealing distinct subspace structures and entanglement dynamics.

Contribution

It introduces an SU(3) basis approach for exact solutions, proposes a qutrit wave function representation, and explores entanglement and collapse-revival phenomena in three-level systems.

Findings

Bloch space splits into two subspaces at resonance.

Distinct nonlinear constants for different configurations.

Collapse and revival phenomena observed in cascade systems.

Abstract

We have given a novel formulation of the exact solutions for the lambda, vee and cascade three-level systems where the Hamiltonian of each configuration is expressed in the SU(3) basis. The solutions are discussed from the perspective of the Bloch equation and the atom-field entanglement scenario. For the semiclassical systems, the Bloch space structure of each configuration is studied by solving the corresponding Bloch equation and it is shown that at resonance, the eight-dimensional Bloch sphere is broken up into two distinct subspaces due to the existence of a pair of quadratic constants. Because of the different structure of the Hamiltonian in the SU(3) basis, the non-linear constants are found to be distinct for different configurations. We propose a possible representation of the qutrit wave function and show its equivalence with the three-level system. Taking the bichromatic cavity modes to be in the coherent state, the amplitudes of all three quantized systems are calculated by developing an Euler angle based dressed state scheme. Finally following the Phoenix-Knight formalism, the interrelation between the atom-field entanglement and population inversion for all configurations is studied and the existence of collapses and revivals of two different types is pointed out for the equidistant cascade system in particular.