Transmission resonances in above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential - Condensed Matter > Quantum GasesReportar como inadecuado




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Abstract: Quantum above-barrier reflection of ultra-cold atoms by the Rosen-Morsepotential is analytically considered within the mean field Gross-Pitaevskiiapproximation. Reformulating the problem of reflectionless transmission as aquasi-linear eigenvalue problem for the potential depth, an approximation forthe specific height of the potential that supports reflectionless transmissionof the incoming matter wave is derived via modification of theRayleigh-Schroedinger time-independent perturbation theory. The approximationprovides highly accurate description of the resonance position for all theresonance orders if the nonlinearity parameter is small compared with theincoming particles chemical potential. Notably, the result for the firsttransmission resonance turns out to be exact, i.e., the derived formula for theresonant potential height gives the exact value of the first nonlinearresonances position for all the allowed variation range of the involvedparameters, the nonlinearity parameter and chemical potential. This has beenshown by constructing the exact solution of the problem for the firstresonance. Furthermore, the presented approximation reveals that, in contrastto the linear case, in the nonlinear case reflectionless transmission may occurnot only for potential wells but also for potential barriers with positivepotential height. It also shows that the nonlinear shift of the resonanceposition from the position of the corresponding linear resonance isapproximately described as a linear function of the resonance order. Finally, acompact yet, highly accurate analytic formula for the n-th order resonanceposition is constructed via combination of analytical and numerical methods.



Autor: H. A. Ishkhanyan, V. P. Krainov, A. M. Ishkhanyan

Fuente: https://arxiv.org/







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