We investigate the tunneling dynamics of Bose-Einstein condensates (BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunneling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poincar\'e section method that visualizes the motions of BECs in a reduced phase plane.
We investigate the tunneling dynamics of Bose-Einstein condensates (BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunneling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poincar'e section method that visualizes the motions of BECs in a reduced phase plane.
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.
We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.
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.
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.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.
We present particular examples of tunneling and transport dynamics of Bose–Einstein condensate (BEC) in a two-well trap: Josephson oscillations (JO), macroscopic quantum self-trapping (MQST) and complete adiabatic transport. Being quite general, these dynamical regimes have close analogies with Josephson junctions in superconductors and transport problems in nanosystems. The calculations are performed within the time-dependent mean-field prescription within (transport) and beyond (JO and MQST) two-mode approximation. For the transport a universal adiabatic population transfer scheme is proposed, allowing a robust and complete transport even under strong nonlinear effects.