We investigate the band structure and the dynamics of Bose-Einstein condensates in a triple-well trap, which are located in a high-finesse optical cavity. For the noninteracting atoms, the band structure of the eigenenergies are obtained using the numerical methods under the mean-field approximation. It is demonstrated that the energy band structure is strongly dependent on the value of reduced cavity detuning. Under some conditions, the atomic band structure develops loop structures and swallowtail structure, which mean the atom-cavity system exhibits bistability. We attribute the appearance of new states to the nonlinearity of the cavity-field-induced tilt. For the interacting atoms, the structure of the eigenenergy band appears more complicated for the interaction between atoms.
We investigate the band structure and the dynamics of Bose-Einstein condensates in a triple-well trap, which are located in a high-finesse optical cavity. For the noninteracting atoms, the band structure of the eigenenergies are obtained using the numerical methods under the mean-field approximation. It is demonstrated that the energy band structure is strongly dependent on the value of reduced cavity detuning. Under some conditions, the atomic band structure develops loop structures and swallowtail structure, which mean the atom-cavity system exhibits bistability. We attribute the appearance of new states to the nonlinearity of the cavity-field-induced tilt. For the interacting atoms, the structure of the eigenenergy band appears more complicated for the interaction between atoms.
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.
We calculate the band structure of ultracold atoms located inside a laser-driven optical cavity. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (noncavity) optical lattices. However, in our case the nonlinearity derives from the cavity back-action rather than from direct interatomic interactions. We find both bi- and tristable regimes associated with the lowest band, and show that the multistability we observe can be analyzed in terms of swallowtail catastrophes. Dynamic and energetic stability of the mean-field solutions is also discussed, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the atomic band structure has important implications for proposals concerning Bloch oscillations of atoms inside optical cavities [Peden et al., Phys. Rev. A 80, 043803 (2009); Prasanna Venkatesh et al., Phys. Rev. A 80, 063834 (2009)].
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.
By employing a nonlinear three-mode model, we study the band structure of Bose-Einstein condensates in Fourier-synthesized optical lattices, where the nonlinearity comes from the mean field treatment of interaction between atoms. In the linear case, we present the band structure of the system. It is observed that the energy band structure is strongly dependent on the relative phase between the two lattice harmonics. In the nonlinear case, we show that the eigenenergy as a function of energy bias has a striking bowl structure in the middle energy level. It is found that there exist four critical values of interaction strength where the band structure undergoes interesting changes. Because of these topological distortions on the energy levels, we expect that the tunnelling dynamics make a dramatic change. The tunnelling probability is nonzero when the nonlinear term is very small and the energy levels keep the same topological structure as that in the linear case. Especially, the tunnelling probability as a function of the sweeping rate shows an irregular oscillation for the state on the middle level.
Abstract We theoretically investigate the energy band structure and Josephson dynamics of a spin-orbit coupled Bose–Einstein condensate in a double-well potential. We study the energy band structure and the corresponding tunneling dynamics of the system by properly adjusting the SO coupling, Raman coupling, Zeeman field and atomic interactions. The coupled effects of SO coupling, Raman coupling, Zeeman field and atomic interactions lead to the appearance of complex energy band structure including the loop structure. Particularly, the emergence of the loop structure in energy band also depends on SO coupling, Raman coupling, Zeeman field and atomic interactions. Correspondingly, the Josephson dynamics of the system are strongly related to the energy band structure. Especially, the emergence of the loop structure results in complex tunneling dynamics, including suppression-revival transitions and self-trapping of atoms transfer between two spin states and two wells. This engineering provides a possible means for studying energy level and corresponding dynamics of two-species SO coupled BECs.
We study experimentally the stability of excited, interacting states of bosons in a double-well optical lattice in regimes where the nonlinear interactions are expected to induce ``swallowtail'' looped band structure. A dynamic homogeneous Gross-Pitaevskii calculation indicates that the double-well lattice both stabilizes the looped band structure and allows for dynamic preparation of different initial states, including states within the loop structure. The homogeneous calculation predicts that the loop states, unlike the ground states, should be dynamically stable. An inhomogeneous mean-field calculation including the trap potential, however, implies that the decay is dominated by inhomogeneous effects and that there is little variation in the decay rate among the states prepared within the loop structure. By experimentally preparing different initial coherent states and observing their subsequent decay, we observe distinct decay rates in regimes where multivalued looped band structure is expected, although not the stability predicted by the homogeneous calculation.