Quantum-jump approach to dissipative processes: application to amplification without inversion

Abstract

Several recent studies have shown that the time evolution of an atom submitted to coherent laser fields and to dissipative processes, such as spontaneous emission of photons or excitation by a broadband incoherent field, can be considered to consist of a sequence of coherent evolution periods separated by quantum jumps occurring at random times. A general statistical analysis of this random sequence is presented for the case in which the number of relevant atomic states is finite and the delay functions giving the distribution of the time intervals between two successive jumps can easily be calculated. These general considerations are then applied to a simple model recently proposed for demonstrating the possibility of amplification without inversion of populations. We show how the quantum-jump approach allows one to calculate the respective contributions of the various physical processes responsible for the amplification or the attenuation of the probe field and to get new insights into the relevant physical mechanisms.