dorsal/arxiv
View SchemaTheory of nonlinear Landau-Zener tunneling
| Authors | Jie Liu, Li-Bin Fu, Bi-Yiao Ou, Shi-Gang Chen, Qian Niu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0105140 |
| URL | https://arxiv.org/abs/quant-ph/0105140 |
| DOI | 10.1103/PhysRevA.66.023404 |
| Journal | Phys. Rev. A Vol.66,023404 (2002) |
Abstract
A nonlinear Landau-Zener model was proposed recently to describe, among a number of applications, the nonadiabatic transition of a Bose-Einstein condensate between Bloch bands. Numerical analysis revealed a striking phenomenon that tunneling occurs even in the adiabatic limit as the nonlinear parameter $C$ is above a critical value equal to the gap $V$ of avoided crossing of the two levels. In this paper, we present analytical results that give quantitative account of the breakdown of adiabaticity by mapping this quantum nonlinear model into a classical Josephson Hamiltonian. In the critical region, we find a power-law scaling of the nonadiabatic transition probability as a function of $C/V-1$ and $\alpha $, the crossing rate of the energy levels. In the subcritical regime, the transition probability still follows an exponential law but with the exponent changed by the nonlinear effect. For $C/V>>1$, we find a near unit probability for the transition between the adiabatic levels for all values of the crossing rate.
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"abstract": "A nonlinear Landau-Zener model was proposed recently to describe, among a\nnumber of applications, the nonadiabatic transition of a Bose-Einstein\ncondensate between Bloch bands. Numerical analysis revealed a striking\nphenomenon that tunneling occurs even in the adiabatic limit as the nonlinear\nparameter $C$ is above a critical value equal to the gap $V$ of avoided\ncrossing of the two levels. In this paper, we present analytical results that\ngive quantitative account of the breakdown of adiabaticity by mapping this\nquantum nonlinear model into a classical Josephson Hamiltonian. In the critical\nregion, we find a power-law scaling of the nonadiabatic transition probability\nas a function of $C/V-1$ and $\\alpha $, the crossing rate of the energy levels.\nIn the subcritical regime, the transition probability still follows an\nexponential law but with the exponent changed by the nonlinear effect. For\n$C/V\u003e\u003e1$, we find a near unit probability for the transition between the\nadiabatic levels for all values of the crossing rate.",
"arxiv_id": "quant-ph/0105140",
"authors": [
"Jie Liu",
"Li-Bin Fu",
"Bi-Yiao Ou",
"Shi-Gang Chen",
"Qian Niu"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.023404",
"journal_ref": "Phys. Rev. A Vol.66,023404 (2002)",
"title": "Theory of nonlinear Landau-Zener tunneling",
"url": "https://arxiv.org/abs/quant-ph/0105140"
},
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