Rosen Zener model in cold molecule formation
Abstract
The RosenZener model for association of atoms in a BoseEinstein condensate is studied. Using a nonlinear Volterra integral equation, we obtain an analytic formula for final probability of the transition to the molecular state for weak interaction limit. Considering the strong coupling limit of high field intensities, we show that the system reveals two different timeevolution pictures depending on the detuning of the frequency of the associating field. For both limit cases we derive highly accurate formulas for the molecular state probability valid for the whole range of variation of time. Using these formulas, we show that at large detuning regime the molecule formation process occurs almost nonoscillatory in time and a RosenZener pulse is not able to associate more than one third of atoms at any time point. The system returns to its initial allatomic state at the end of the process and the maximal transition probability 1/6 is achieved when the field intensity reaches its peak. In contrast, at small detuning the evolution of the system displays largeamplitude oscillations between atomic and molecular populations. We find that the shape of the oscillations in the first approximation is defined by the field detuning only. Finally, a hidden singularity of the RosenZener model due to the specific timevariation of the field amplitude at the beginning of the interaction is indicated. It is this singularity that stands for many of the qualitative and quantitative properties of the model. The singularity may be viewed as an effective resonancetouching.
 Publication:

Optics Communications
 Pub Date:
 January 2009
 DOI:
 10.1016/j.optcom.2008.10.008
 arXiv:
 arXiv:0909.0546
 Bibcode:
 2009OptCo.282..218I
 Keywords:

 Condensed Matter  Quantum Gases
 EPrint:
 Optics Communications 282, 218 (2009)