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


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:

  1. 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.
  2. A generalized version of the quantum Bloch sphere for this non-linear case is straightforwardly derived in the dual space of the Lagrange multipliers.
  3. The invariants of motion of the problem are given.
  4. The thermodynamical treatment can be obtained via the MEP density operator which allows one to find properly, the initial conditions of the relevant operators.
  5. 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