Tripartite multiphoton Jaynes-Cummings model: Analytical solution and Wigner nonclassicalities

TL;DR

This paper provides an analytical solution for a tripartite quantum system involving a qubit and two oscillators under multiphoton Jaynes-Cummings interactions, exploring nonclassical Wigner negativities and excitation transfer.

Contribution

It derives exact analytical solutions for the tripartite system and demonstrates how nonlinear multiphoton interactions enhance nonclassical states and enable excitation transfer.

Findings

Exact solutions for system dynamics in various cases.

Perfect excitation transfer between oscillators under specific parameters.

Nonlinear interactions increase Wigner negativity beyond initial states.

Abstract

We investigate a generic tripartite quantum system featuring a single qubit interacting concurrently with two quantized harmonic oscillators via nonlinear multiphoton Jaynes-Cummings (MPJC) interactions. Assuming the qubit is initially prepared in a superposition state and the two oscillators are in arbitrary Fock states, we analytically trace the temporal evolution of this tripartite pure initial state. We identify four broad cases, each further divided into two subcases, and derive exact analytical solutions for most cases. Notably, we obtain perfect transfer of excitations between the oscillators by carefully selecting system parameters. In addition, we extensively examine the manner in which the nonclassicalities of various initial oscillator Fock states, quantified by the volume of negative regions in the associated Wigner functions, evolve under the MPJC Hamiltonian, considering diverse system parameters including environmental effects. Besides producing substantial enhancements in the initial value for higher photon number states, our analysis reveals that driven solely by the initial qubit energy, with both oscillators initialized in the vacuum state, the nonlinear MPJC interaction yields a significant amount of nontrivial Wigner negativity in the oscillators. The additional nonlinearity introduced by the multiphoton process plays a pivotal role in surpassing the initial nonclassicalities of the photon number states.