# Jaynes-Cummings hamiltonian with a Kerr-like medium

## J.L. Gruver, J. Aliaga, H. Cerdeira and A.N. Proto

Grupo de Sistemas Dinamicos. Universidad de Buenos Aires CRN

C.C.2 (1638) V. Lopez Argentina

### Abstract

The combination of two solvable models, a Kerr medium inside a
cavity usually modeled by an anharmonic oscillator, and the
time-dependent Jaynes-Cummings hamiltonian (TJCH), leads to a model
which describes the interaction of a two-level system, with a single
mode of an electromagnetic field in the presence of the Kerr-like
medium.
In the present effort, we find the dynamical and thermodynamical
description of the proposed hamiltonian, in the frame of the Maximum
Entropy Principle formalism. Our main results are:

- The addition of
a nonlinear term to the JCH induces a nontrivial discrete dynamics for
the correlations of the system. The number of possible links among the
infinite set of relevant operators generated by the closure
relationship with the hamiltonian, is represented by a Fibonacci
series.
- A generalized version of the quantum Bloch sphere for this
non-linear case is straightforwardly derived in the dual space of the
Lagrange multipliers.
- The invariants of motion of the problem are
given.
- The thermodynamical treatment can be obtained via the MEP
density operator which allows one to find properly, the initial
conditions of the relevant operators.
- The time-independent case is
solved, and we show that the nonlinearity of the problem is
characterized by a weighted sum over correlations, where the weights
are related to the Fibonacci series.

MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk