Acta Physica Sinica

Many-body quantum fluctuation effects of Rosen-Zener transition in Bose-Einstein condensates

Jianzhong Wang, Hui Cao, Dou Fu-Quan

Published Jan 1, 2012• 2 citations

Abstract

We investigate many-body quantum fluctuation effects of Rosen-Zener transition of Bose-Einstein condensate (BEC) in a symmetric double-well potential through the relation between the average population imbalance of the final state (APIFS) and scanning period. In the linear case, we deduce the analytical expression of the APIFS which has the same behavior as in the mean-field level. We also employ numerical calculation to demonstrate it. In the nonlinear case, numerical results show that the APIFS in the sudden limit also accords with that in the mean-field level whereas in the adiabatic limit the many-body result is quite different from that of the mean-field case: the behavior of APIFS with respect to scanning period is similar to sinusoidal rather than rectangular oscillation, besides the oscillation period increases with both the total number N and the nonlinear parameter c increasing.

DOI: 10.7498/aps.61.220305

Related papers

Rosen–Zener transition of two-component Bose–Einstein condensates

Xin Yu Jiang, Wen-Shan Duan, Sheng-Chang Li +1 more

Rosen–Zener transitions of two-component Bose–Einstein condensates in a nonlinear two-level system are studied. The intensities of interspecies interactions which can be adjusted by Feshbach resonance can affect the quantum transition dramatically. The percentage of both components also has an important effect on the quantum transition probabilities. It is also found that the quantum transition can be completely blocked by either strong interspecies interactions or large percentage of the component. In the sudden limit, the approximated transition probabilities for each component are obtained analytically. In the adiabatic limit, the equivalent classical Hamiltonian is obtained. The fixed points and the eigenenergy level structures are also obtained. Finally, for some special cases, the period of the rectangular oscillation as a function of the percentage of the number density and the interspecies interaction is obtained analytically. All the analytical results are compared with numerical simulations and good agreement is obtained.

Journal of Physics B Atomic Molecular and Optical PhysicsSep 8, 20097 citations

Rosen-Zener transition in a nonlinear two-level system

Difa Ye, Libin Fu, Jie Liu

We study the Rosen-Zener transition (RZT) in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. We find that the nonlinearity could affect the quantum transition dramatically. At certain nonlinearity the 100% population transfer between two levels is observed and found to be robust over a very wide range of external parameters. On the other hand, the quantum transition could be completely blocked by a strong nonlinearity. In the sudden and adiabatic limits we have derived analytical expressions for the transition probability. Numerical explorations are made for a wide range of parameters of the general case. Possible applications of our theory to Bose-Einstein condensates (BECs) and solid-state physics are discussed.

arXiv:0709.3161Physical Review AJan 9, 200857 citations

Deformation scheme of nonlinear Rosen–Zener tunneling for Bose–Einstein condensates in a triple-well potential

Hong Cao

Abstract We investigate Rosen-Zener tunneling for Bose-Einstein condensates in a triple-well potential within the framework of mean-field treatment. Firstly, we exactly calculate tunneling dynamics for triple-well in the linear case, where the population evolution of each well is robust, and all atoms are finally trapped in the single well, that is initially uploaded. In this case, tunneling dynamics are symmetrical when all atoms are populated in the first well and third well. However, as the nonlinear interaction is introduced, tunneling dynamics will be significantly changed. On the one hand, the symmetry will be broken, some atoms will not be confined to the starting well. On the other hand, nonlinear Josephson oscillation will be presented within a fixing interval. When the interaction exceeds this interval, the self-trapping solution emerges.

Nonlinear DynamicsMay 3, 20232 citations

Nonlinear Rosen-Zener transition of Fermi superfluid gases

Hongjuan Meng, Yang Yang, Wen-Yuan Wang +5 more

By considering the contribution of the higher order term representing the lowest approximation of beyond mean field correction and taking Roser-Zener tunneling as the underling process, we study the nonlinear Rosen-Zener transition of Fermi superfluid gas in a two-level system. We find that the nonlinearity can affect the quantun trasition in the fast scan limit and the adiabatic limit. We also derive the analytical expression for the of rectangular oscillation period dependent on nonlinear parameter. This provides a theoretical basis for a deeper understanding of the basis properties of Fermi gases.

Acta Physica SinicaJan 1, 20123 citations

Quantum entanglement manifestation of transition to nonlinear self-trapping for Bose-Einstein condensates in a symmetric double well

Liu Fu, Jie Liu

We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.

arXiv:cond-mat/0609337Physical Review ADec 13, 200695 citations

Self-trapping and its periodic modulation of Bose-Einstein condensates in double-well trap

Guanfang Wang, Fu Li-Bin, Zhao Hong +2 more

Self-trapping of Bose-Einstein condensates (BEC) in double-well trap is investigated. Two kinds of self-trapping are discussed through phase space analysis in the mean-field approximation: 1) The number of atoms oscillates near an equilibrium point in the phase space, while relative phase increases monotonously with time (running-phase); 2) Both the number of particles and the relative phase oscillate near an equilibrium point in the phase space. In particular, we investigate how an external periodic filed influence the self-trapping. It is found that the external periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. With this, we can observe self-trapping phenomenon in a dilute Bose-Einstein condensate with a very weak interaction as well. Finally, the effect of many-body quantum fluctuation on self-trapping is also studied. We also discuss how to observe the self-trapping phenomenon with present experimental techniques.

Acta Physica SinicaJan 1, 200529 citations