ENTROPY STUDIES FOR THE DAMPED AND THE UNDAMPED JAYNES-CUMMINGS MODEL

On the basis of a representation in terms of photon-number states we d erive an analytically solvable set of ordinary differential equations for the matrix elements of the density operator belonging to the Jayne s-Cummings model. We allow for atomic detuning, spontaneous emission, and cavity damping, but we do not take into account the presence of th ermal photons. The exact results are employed to perform a careful inv estigation of the evolution in time of atomic inversion and von Neuman n entropy. A factorization of the initial density operator is assumed, with the privileged field mode being in a coherent state. We invoke t he mathematical notion of maximum variation of a function to construct a measure for entropy fluctuations. In the undamped case the measure is found to increase during the first few revivals of Rabi oscillation s. Hence, the influence of the surroundings on the atom does not decre ase monotonically from time zero onwards. A further non-Markovian feat ure of the dynamics is given by the strong dependence of our measure o n the initial atomic state, even for times at which damping brings abo ut irreversible decay. For weak damping and high initial energy densit y the atomic evolution exhibits a crossover between quasireversible re vival dynamics and irreversible Markovian decay. During this stage the state of maximum entropy acts as an attractor for the trajectories in atomic phase space. Subsequently, all trajectories follow a unique ro ute to the atomic ground state, for which the off-diagonals of the ato mic density matrix equal zero. From our entropy studies one learns wha t kind of difficulties must be overcome in establishing formulae for e ntropy production, the use of which is not limited to semigroup-induce d dynamics.