Abstract

We consider a N-atom micromaser model, described by the following hamiltonian: $\widehat{\text{H}}=\left(\omega ·{\widehat{a}}^{+}\widehat{a}+{\omega }_0\left({\widehat{S}}_3+\frac{N}{2}\right)\right)+g\left({\widehat{a}}^{+}·{\widehat{S}}_{-}+\widehat{a}·{\widehat{S}}_{+}\right)$, where ${\widehat{S}}_{+},{\widehat{S}}_{-},{\widehat{S}}_3$ operators, defined in the Hilbert space of N two-level particles’ states. Taking into account field relaxation between consecutive N-atom packets we study dynamics and quasi-stationary states of subsystems in the model. Experimentally, such a system may be realized on a high-density atom flux prepared with help of ultrashort time pulses of exciting laser, in order to achieve small packets and avoid large dispersion of entrance times. For initially diagonal density operator of atoms, the system dynamics and particularly of the field reduced density matrix (RDM) have significant simplification, called diagonal invariance. Under such conditions it was found that the field dynamics might be divided into two stages, a rapid stage and a quasi-stationary stage. This behavior is determined by quasi-trapped states, which are a generalization of well known trapped states in the one-atom micromaser. The quasi-trapped states do not exactly satisfy the trapping condition. However they are distinctively localized in the Fock space and have very long lifetimes. In general the RDM dynamics can be characterized as follows: first rapid creation of a quasi-trapped state and then a slow “leak” of probability to the stationary state. One can find some analogy with a population tunneling through walls of the effective potential in Fokker-Plank approach of the one-atom micromaser [1]. We find that a quasi-trapped state becomes more narrow and an evolution to quasi-stationary state become faster, when the number of atoms in the packet becomes larger. We proposed a scheme for very powerful field cooling by injecting unexcited flux with a large number of atoms in the packet. Another interesting effect may be observed on atoms in the so-called Dicke’s state when only half number of atoms in the packet is excited. It is intuitively evident that if for excited atoms field evolves to larger photon numbers while for unexcited–to smaller numbers, for Dicke’s state these mechanisms have to work simultaneously. On the rapid stage of dynamics the initial state of the field (coherent, for instance) is split to several quasi-trapped states, each of them formed by population fluxes coming from both sides. It is why we may expect that such a mechanics is less sensitive to relaxation, and we observed this effect. In order to change a lifetime of quasi-trapped states and consequently to identify the most stable one in the Fock’s space we used off-resonance regime with different values of detuning. This regime also has some interesting applications. It was found that even for unpolarized atoms squeezing of the field can be achieved for appropriately chosen interaction times. To detect all the effects one has to identify them in statistical properties of passed atom packets. In order to do that we have constructed an approximation for dynamics of the atom packet’s RDM through a system of differential equations. In conclusion we wish to note that our consideration is a traditional quantum mechanical approach based on the ensemble of identical systems. The recent experiments[2] carry out measurements on individual quantum system. We want to emphasize that our work raises important questions on a possibility to apply formalism of density matrix for description of such experiments.

© 2000 IEEE