Tunneling Dynamics of Two-Species Bose-Einstein Condensates with Feshbach Resonances

We investigate tunneling dynamics of atomic group consisting of three atoms in Bose-Einstein condensates with Feshbach resonance. It is shown that the tunneling of the atom group depends not only on the inter-atomic nonlinear interactions and the initial number of atoms in these condensates, but also on the tunneling coupling between the atomic condensate and the three-atomic molecular condensate. It is found that besides oscillating tunneling current between the atomic condensate and the molecular condensate, the nonlinear atomic group tunneling dynamics sustains a self-maintained population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate atoms on the tunneling dynamics is studied. It is indicated that de-coherence suppresses the atomic group tunneling.     

Tunneling Dynamics Between Atomic and Molecular Bose-Einstein Condensates

Tunneling dynamics of multi-atomic molecules between atomic and multi-atomic molecular Bose-Einstein condensates with Feshbach resonance is investigated.It is indicated that the tunneling in the two Bose-Einstein condensates depends on not only the inter-atomic-molecular nonlinear interactions and the initial number of atoms in these condensates,but also the tunneling coupling between the atomic condensate and the multi-atomic molecular condensate.It is discovered that besides oscillating tunneling current between the atomic condensate and the multi-atomic molecular condensate,the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance:a macroscopic quantum self-trapping effect.The influence of de-coherence caused by non-condensate atoms on the tunneling dynamics is studied.It is shown that de-coherence suppresses the multi-atomic molecular tunneling.Moreover,the conception of the molecular Bose-Einstein condensate,which is different from the conventional single-atomic Bose-Einstein condensate,is specially emphasized in this paper.     

Tunneling Dynamics of Two-Species Bose-Einstein Condensates with Feshbach Resonances

We investigate tunneling dynamics of atomic group consisting of three atoms in Bose-Einstein condensateswith Feshbach resonance. It is shown that the tunneling of the atom group depends not only on the inter-atomicnonlinear interactions and the initial number of atoms in these condensates, but also on the tunneling coupling betweenthe atomic condensate and the three-atomic molecular condensate. It is found that besides oscillating tunneling currentbetween the atomic condensate and the molecular condensate, the nonlinear atomic group tunneling dynamics sustains aself-maintained population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence causedby non-condensate atoms on the tunneling dynamics is studied. It is indicated that de-coherence suppresses the atomicgroup tunneling.     

The Atomic Tunneling Current in Two—Species Bose—Einstein Condensates

It is shown that the atomic tunneling current and the Shapiro-like steps strongly depend on the initial number of atoms in each condensate and the initial phase difference between the two condensates which are initially in even(odd) coherent states.The nonlinearity of interatomic interactions in the two condensates may lead to the atomic tunneling current and Shapiro-like step between the two condensates.It is found that the interatomic nonlinear interactions can induce the atomic tunneling current and Shapiro-like step between two condensates even though there does not exist the interspecies Josephson-like tunneling coupling.The static atomic tunneling current flows in positive or negative direction,which depends on the phase difference of the two-species condensates.     

Tunneling Dynamics Between Any Two Multi-atomic-molecular Bose-Einstein Condensates

Tunneling dynamics of multi-atomic molecules between any two multi-atomic molecular Bose-Einstein condensates with Feshbach resonance is investigated. It is indicated that the tunneling in the two Bose-Einstein condensates depends not only on the inter-molecular nonlinear interactions and the initial number of molecule in these condensates, but also on the tunneling coupling between them. It is discovered that besides oscillating tunneling current between the multi-atomic molecular condensates, the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate molecule on the tunneling dynamics is studied. It is shown that de-coherence suppresses the multi-atomic molecular tunneling.     

Quantum Statistical Properties in Two—Species Bose—Einstein Condensates

We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species,the interspecies nonlinear interaction,and the Jisephson-like tunneling interaction.It is found that the two condensates may periodically exhibit sub-Poissonian distribution.It is revealed that the correlation between the two condensates can be nonclassical,which means that there exists a violation of Cauchy-Schwartz inequality.The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.     

Quantum coherent tunneling between two atomic-molecular Bose-Einstein condensates

We study the quantum coherent tunneling dynamics of two weakly coupled atomic-molecular Bose-Einstein condensates (AMBEC). A weak link is supposed to be provided by a double-well trap. The regions of parameters where the macroscopic quantum localization of the relative atomic population occurs are revealed. The different dynamical regimes are found depending on the value of nonlinearity, namely, coupled oscillations of population imbalance of atomic and molecular condensate, including irregular oscillations regions, and macroscopic quantum self trapping regimes. Quantum means and quadrature variances are calculated for population of atomic and molecular condensates and the possibility of quadrature squeezing is shown via stochastic simulations within P-positive phase space representation method. Linear tunnel coupling between two AMBEC leads to correlations in quantum statistics.Received: 22 May 2004, Published online: 10 August 2004PACS: 03.75.-b Matter waves - 03.75.Gg Entanglement and decoherence in Bose-Einstein condensates - 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 05.30.Jp Boson systems     

Formation of parametric solitons in coupled atom–molecule quantum gases via controlled nonlinear interactions

We consider an atomic Bose–Einstein condensate parametrically coupled to a molecular condensate with tunable interactions. The space distribution and nonlinear dynamics of this coupled system, especially the parametric solitons, are investigated within the full parameter space accounts for all the nonlinear two-body collisions, together with the atom–molecule conversion coupling and the bare formation energy of the molecular species. The results show that the exact parametric solitons can be formed via controlled nonlinear interactions, and the atom–molecule transfer term can provide an effective potential which can be used to stable the coupled system even in the absence of the external potential. We also give an experimental setup and detection of the atomic–molecular Bose–Einstein condensates in future experiments.     

有效质量法调控原子玻色-爱因斯坦凝聚体的双阱动力学

操控原子玻色-爱因斯坦凝聚体在双势阱中的动力学通常是通过改变势阱深度来实现,本文提出了一种基于调节原子有效质量的控制方案,可以在不改变双阱势的前提下操控凝聚体的双阱动力学.利用双模近似,本文解析地导出了超冷原子在双阱势中的隧穿强度和相互作用强度对有效质量的依赖关系,并基于平均场近似数值模拟了在有效质量调节下的凝聚体动力学演化,展示了隧穿振荡和自束缚等典型的双阱动力学行为.此外,本文的研究还发现,借助负有效质量效应,这一方案甚至可以等效地实现对负散射长度原子凝聚体双阱动力学行为的操控.     

Tunneling Dynamics of Two-Species Bose-Einstein Condensates

We have studied the tunneling dynamics of two-species Bose-Einstein condensates. It is shown that the population difference and the Josephson-like tunneling current between the two condensates exhibit oscillation behaviors and there exists macroscopic quantum self-trapping, which strongly depends on the initial state, interatomic nonlinear self-interaction, interspecies nonlinear interaction, and the total number of atoms in the two condensates.     

Nonlinear dissipative dynamics of a two-component atomic condensate coupling with a continuum

We investigate the nonlinear dissipative coherence bifurcation and population dynamics of a two-component atomic Bose-Einstein condensate coupling with a continuum. The coupling between the two-component condensates and the continuum brings effective dissipations to the two-component condensates. The steady states and the coherence bifurcation depend on both dissipation and the nonlinear interaction between condensed atoms. The coherence among condensed atoms may be even enhanced by the effective dissipations. The combination of dissipation and nonlinearity allows one to control the switching between different self-trapped states or the switching between a self-trapped state and a non-self-trapped state.     

凝聚体中亮孤子和暗孤子的交替演化

利用Darboux变换法，解析地研究了局限于恒定不变外部势阱中的玻色-爱因斯坦凝聚体的非线性动力学性质.结果发现凝聚体中的粒子之间的相互作用强度对其非线性动力学特征有重要的影响.当玻色子之间的相互排斥作用相当强时，凝聚体中只会存在亮孤子；而玻色子之间的相互排斥作用相当弱(小于临界值)时，凝聚体中会出现亮孤子和暗孤子交替演化. 关键词： 玻色-爱因斯坦凝聚 Darboux变换 孤子     

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau-Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate (BEC) with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters (i.e., the modulation amplitude and frequency) and the strength of periodic potential.     

Phases of atom-molecule vortex matter

We study ground state vortex configurations in a rotating atom-molecule Bose-Einstein condensate. It is found that the coherent coupling between the atomic and molecular condensates can render a pairing of atomic and molecular vortices into a composite structure that resembles a carbon dioxide molecule. Structural phase transitions of vortex lattices are also explored through different physical parameters including the rotational frequency of the system.     

Energy transfer in weakly coupled nonlinear oscillator chains: Transition from a wandering breather to nonlinear self-trapping

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic wandering of the low-amplitude breather between the chains, and the one-chain-localization of the high-amplitude breather. These two modes of coupled breathers can be mapped exactly onto two solutions of a pendulum equation, detached by a separatrix mode. We also show that these two regimes of the coupled breathers are similar, and are described by a similar pair of equations, to the two regimes in the nonlinear tunneling dynamics of two weakly coupled Bose-Einstein condensates. On the basis of this analogy, we predict a new tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around π/2 modulo π.     

Probing fermionic condensates by fast-sweep projection onto Feshbach molecules

Fast-sweep projection onto Feshbach molecules has been widely used as a probe of fermionic condensates. By determining the exact dynamics of a pair of atoms in time-varying magnetic fields, we calculate the number of condensed and noncondensed molecules created after fast magnetic field sweeps from the BCS to the Bose-Einstein condensate side of the resonances in 40K and 6Li, for different sweep rates and a range of initial and final fields. We discuss the relation between the initial fermionic condensate fraction and the molecular condensate fraction measured after the sweep.     

Tunneling of Boseben-Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

The tunneling effect of Bose-Einstein condensate (BEC) in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.     

Vortex lattices in planar Bose-Einstein condensates with dipolar interactions

In this Letter, we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with quantum tunneling processes, which affects the relative displacement of two neighboring vortex lattices and leads to the loss of phase coherence between different condensates.     

Tunneling Dynamics of the Halves of a Double-Well Trap Containing a Bose-Einstein Condensate

In this paper, we have studied tunneling dynamics of the halves of a double-well trap containing a Bose-Einstein condensate. It is found that there exist step structure and macroscopic quantum self-trapping of population difference of atoms, and exist Shapiro-like steps of atomic tunneling current. Both the population difference and the atomic tunneling current depend strongly on the total number of atoms and the initial phase difference.