Dynamical symmetry breaking of lambda and vee-type three-level systems on quantization of the field modes

TL;DR

This paper constructs Hamiltonians for three-level atomic systems using SU(3) generators, compares classical and quantum field dynamics, and shows how quantization affects dynamical symmetry, which can be restored with large photon numbers.

Contribution

It introduces a novel SU(3)-based scheme for Hamiltonian construction and analyzes the impact of field quantization on dynamical symmetry in three-level systems.

Findings

Classical fields show similar Rabi oscillations in lambda and vee models.

Quantization destroys the symmetry observed in semiclassical models.

Large photon numbers in coherent states restore symmetry through collapse and revival phenomena.

Abstract

We develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well defined selection rule to give different Hamitonians for each configurations. The lambda and vee type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields . For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when the field modes are both in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.