Rosen–Zener model in cold molecule formation
| Autor: | B. Joulakian, Ruzan Sokhoyan, Artur Ishkhanyan, Kalle-Antti Suominen |
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| Rok vydání: | 2009 |
| Předmět: |
Field (physics)
FOS: Physical sciences Weak interaction 01 natural sciences Volterra integral equation 010305 fluids & plasmas law.invention symbols.namesake Singularity Optics law Quantum mechanics 0103 physical sciences Electrical and Electronic Engineering Physical and Theoretical Chemistry 010306 general physics Condensed Matter::Quantum Gases Physics business.industry Time evolution Atomic and Molecular Physics and Optics Electronic Optical and Magnetic Materials Gross–Pitaevskii equation Amplitude Quantum Gases (cond-mat.quant-gas) symbols Condensed Matter - Quantum Gases business Bose–Einstein condensate |
| Zdroj: | Optics Communications. 282:218-226 |
| ISSN: | 0030-4018 |
| DOI: | 10.1016/j.optcom.2008.10.008 |
| Popis: | The Rosen–Zener model for association of atoms in a Bose–Einstein 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 time-evolution 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 non-oscillatory in time and a Rosen–Zener pulse is not able to associate more than one third of atoms at any time point. The system returns to its initial all-atomic 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 large-amplitude 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 Rosen–Zener model due to the specific time-variation 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 resonance-touching. |
| Databáze: | OpenAIRE |
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