The dynamics of Bose-condensate generation by a cw atom laser with simultaneous stimulated evaporative cooling in a magnetic trap was analyzed using a quantum-mechanical master equation. The model of the atom laser includes irreversible processes of incoherent trap mode pumping and spontaneous atomic transitions due to the interaction of the atomic ensemble with heat reservoirs. The inelastic atomic collisions in the trap and the continual coherent Bose-condensate output coupling from the trap were considered. At certain values of parameters, the Bose condensate created in this laser scheme occurs in a compressed sub-Poisson state. For large Bose condensates with a mean number of atoms ∼10 6 , the Fano factor may be as high as ≅0.5. The influence of spontaneous transitions from the excited trap modes on the statistics of Bose condensate was analyzed.
The dynamics of Bose-condensate generation by a cw atom laser with simultaneous stimulated evaporative cooling in a magnetic trap was analyzed using a quantum-mechanical master equation. The model of the atom laser includes irreversible processes of incoherent trap mode pumping and spontaneous atomic transitions due to the interaction of the atomic ensemble with heat reservoirs. The inelastic atomic collisions in the trap and the continual coherent Bose-condensate output coupling from the trap were considered. At certain values of parameters, the Bose condensate created in this laser scheme occurs in a compressed sub-Poisson state. For large Bose condensates with a mean number of atoms ∼10 6 , the Fano factor may be as high as ≅0.5. The influence of spontaneous transitions from the excited trap modes on the statistics of Bose condensate was analyzed.
A self-consistent quantum theory is developed for an atomic laser utilizing cooling of atoms in a trap by the method of stimulated evaporation. The model describes the pumping and extraction of the atomic field from a trap upon its interaction with independent atomic reservoirs. The stimulated collisions between atoms in the trap, which produce a Bose condensate in the lower state of the trap, are considered. The interaction of atoms with a phonon field causes spontaneous transitions between the discrete states of the trap. Calculations performed for the three-and four-level models of the trap showed the possibility of generation of a strongly squeezed sub-Poisson Bose condensate.
The first-order coherence dynamics of a Bose condensate generated by a cw atomic laser with evaporative cooling is analyzed. For the atomic-laser multimode model, the coherence functions and atomic field spectra are calculated by the master equation technique. Elastic collisions in the trapped atomic gas lead to significant broadening of the atomic laser line, a shift of its center, and a multi peak structure of the spectra. The oscillatory time dynamics of the atomic-field coherence function is studied. For the atomic laser, the free phase diffusion of the field typical of optical lasers, and characterized by monotonically decreasing mean field with a constant mean phase, is absent due to elastic collisions.
We consider the behavior of an atomic Bose-Einstein condensate in the presence of an atom in an (internal) excited electronic level. We analyze the boson-accumulation regime, defined by the relation N0\ensuremath{\gg}a,N-N0, where N is the total number of atoms in the ground electronic state, N0 is the number of atoms in the condensate, and a is the number of levels to which the excited atom can decay. In this regime, quantum statistical effects related to the boson nature of the atoms are predominant in the process of spontaneous emission. Simple arguments suggest that the proportion of atoms in the condensate decreases after the spontaneous decay. A more elaborated model based on a master equation description shows that, in general, these arguments may lead to erroneous conclusions. Under certain conditions it predicts that the proportion of atoms in the condensate increases. We give an interpretation of this phenomenon in terms of quantum interferences between processes that include reabsorption of the emitted photons, and dipole-dipole interactions between the atoms. The physical effect considered here may help to pump atoms into a condensate and to compensate for atomic losses in the atomic trap. \textcopyright{} 1996 The American Physical Society.
The quantum statistical properties of the radiation of a one-atom two-level laser with incoherent pumping are analyzed. Solution of the Liouville equation for the density operator in the basis of Fock states shows that stationary radiation from a single-mode laser with incoherent pumping can be in a squeezed (sub-Poissonian) stationary state if the rate of spontaneous decay is lower than the rate of cavity losses and the pump rate. Inside the cavity the Fano factor reaches F =0.85 (15% squeezing). Multiple squeezing ( F =0.19) is possible in the transient lasing regime. Significant squeezing obtains at the cavity output; the spectral Fano factor at zero frequency is 0.36 under optimal conditions.
We analyze the continuous pumping of atoms into a Bose-Einstein condensate via spontaneous emission from a thermal reservoir of atoms. We consider the case of atoms with a three-level $\ensuremath{\Lambda}$ scheme, in which one of the atomic transitions has a very much shorter lifetime than the other one. We found that in such a scenario the photon reabsorption in dense clouds at the frequency of the narrow transition can be considered negligible. If, in addition, inelastic processes can be kept negligible, we find that optical pumping can be used to continuously load and refill Bose-Einstein condensates, i.e., it provides a possible way to achieve a continuous atom laser.
We studied the creation of coherent atomic ensembles by various means, allof which are either already demonstrated experimentally or within reach ofcurrent experiments. We investigated the dynamics of the outcoupling of acoherent beam from an atomic Bose-Einstein condensate. Since this problemis well treated in present literature, we focused on another aspect of proposedatom-laser schemes, the pumping. To this end, we investigated the merging ofindependent condensates and paid particular attention to the role of the relativephase. We found that it emerges as a key parameter during the merging process,almost solely defining the resulting dynamics. More concretely, the phasedifference determines the depth of an adiabatically formed soliton as well as thedynamics of a dipole oscillation of the atomic cloud, which builds up during themerging process. Under the assumption of a coherent cooling, such as evaporationof higher energy atoms from the ensemble, we were able to empiricallyfind an analytic formula for the phase of the final condensate. We studied themerging as an independent process, not necessarily linked to the atom laseritself. Our results might shed light onto new, non-destructive ways of readingout phase-differences between condensates as it is necessary in matter-wavespectroscopy. Although not related to our work, it is worth mentioning thatin the mean-time, a different pumping mechanism was demonstrated. It relieson two electronic transitions, with a reservoir condensate and a separate lasingcondensate [74]. We turned towards a different way of producing matter wavepulses altogether, namely superradiance from condensates, which shows otherpromising aspects, such as well defined populations and momenta of the createdpulses. We constructed a quantum treatment for the early stages of the process,which, as we have shown, is not well described within the available mean-fieldmodels. This semi-classical model can, however, produce quantum expectationvalues by means of averaging over randomly seeded trajectories. We used thisrelations to investigate the statistics of delay– and passage-times of superradiantpulses. Beyond the mean-field treatment of the problem, the quantum modelpredicts long range order as well as atomic bunching in the side-modes and enhancedcross-correlations between forward and backwards scattered atoms. Inthe strong pulse regime, the two counter-propagating clouds become entangledand the number difference between them is squeezed.4.6.2 OutlookThe experimental verification of our results is within reach of current experiments,and the tools available to probe Bose-Einstein condensates are advancingat a fast rate. As far as our studies are concerned, there are still open questions.We found that, in general, the merging of condensates is related to the formationof a soliton. The decay of such a structure is a topic of current debate, but theconsensus that this depends highly on the geometry of the trapping potentialsused seems reached.We investigated the early stage of superradiance from condensates and it isnatural to ask what is to expect for later stages, or in other situations wheredepletion of the primary condensate, population of higher order side-modes or120interaction between end-fire modes become relevant. Our results suggest thatthe exotic correlations we found decay with time, but this is not conclusive