NON-MARKOVIAN DYNAMICS OF THE MICROMASER DUE TO DISCRETE AND CONTINUOUS NON-POISSONIAN PUMPING

We investigate the effect of non-Poissonian pump fluctuations on the m icromaser dynamics. Non-Poissonian micromaser pumping has been describ ed by two, seemingly unrelated, theoretical approaches. The first empl oys a discrete pumping process where the pump atoms are allowed to arr ive, with certain probability p, only at regularly spaced instants of time, whereas the second refers to continuously distributed arrival ti mes of the pump atoms. Based on a generalization of the latter, we pre sent a unified approach that can handle both situations on an equal fo oting. We find that for any kind of non-Poissonian pumping the resulti ng dynamics of the micromaser field is a non-Markovian one. For a micr omaser with discrete non-Poissonian pumping, we show the equivalence o f ensemble averaging and time averaging, providing a rare example wher e the validity of the ergodic hypothesis can be explicitly demonstrate d. Moreover, we investigate the time-delayed field-field correlation f unction and a generalized k-photon spectrum of the cavity field, which for k=1 corresponds to the usual power spectrum. For the case that th e micromaser is operated under the k-photon trapping condition, we der ive exact analytical expressions for the k-photon spectrum and the cor responding correlation functions that result from the exact solution o f a non-Markovian evolution problem. Provided that p > 1/2, the spectr um is found to be split into several equidistant peaks for certain val ues of the interaction parameters.