Atomic Tunneling Effect in Two-Component Bose-Einstein Condensates with a Coupling Drive

In this paper, we have studied the atomic population difference and the atomic tunneling current of twocomponent Bose-Einstein condensates with a coupling drive. It is found that when the two-component Bose-Einstein condensates are initially in the coherent states, the atomic population difference may exhibit the step structure, in which the numbers of the step increase with the decrease of the Rabi frequency and with the increment of the initial phase difference. The atomic population difference may exhibit collapses, and revivals, in which their periods are affected dramatically by the Rabi frequency and the initial phase difference. The atomic tunneling current may exhibit damping oscillation behaviors, and exist the step structure for the time range of 10-10 ～ 10-9 second.     

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.     

Interference of Two-Component Bose-Einstein Condensates with a Coupling Drive in Presence of Dissipation

The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the coherent states, for the smaller dissipation parameters compared with that of the rf frequency ωrf, the interference intensity exhibits damply oscillation behavior, whereas when the dissipation parameters are larger than that of the ωry, the interference intensity exhibits a fast attenuation behavior. As a comparison, the interference intensity in the absence of the dissipation is also studied. We conclude that the dissipation of the system can be evaluated by selecting the ωrf experimentally.     

Interference of Two-Component Bose-Einstein Condensates with a Coupling Drive in Presence of Dissipation

The interference of the two-component Bose-Einstein condensates with a coupling drive in the presence of the dissipation is studied. We find that when the two-component Bose-Einstein condensates are initially in the coherent states, for the smaller dissipation parameters compared with that of the rf frequency ωrf, the interference intensity exhibits damply oscillation behavior, whereas when the dissipation parameters are larger than that of the ωrf, the interference intensity exhibits a fast attenuation behavior. As a comparison, the interference intensity in the absence of the dissipation is also studied. We conclude that the dissipation of the system can be evaluated by selecting the ωrf experimentally.     

Rabi Oscillations in Two-Component Bose-Einstein Condensates with a Coupling Drive

The Rabi oscillations in two-component Bose-Einstein condensates with a coupling drive are studiedby means of a pair of bosonic operators. The coupling drive and initial phase difference will affect the amplitudeand the period of the Rabi oscillations. The Rabi oscillations will vanish in the evolution of the condensate densityfor some special initial phase differences (ψ = 0 or π). Our theory provides not only an analytical framework forquantitative predictions for two-component condensates, but also gives an intuitive understanding of some mysteriousfeatures observed in experiments and numerical. simulations.     

Landau-Zener Tunnelling of Two-Component Bose-Einstein Condensates inOptical Lattices

We investigate the Landau--Zener tunnelling of two-componentBose-Einstein condensates (BECs) in optical lattices. In the neighborhood of the Brillouin zone edge, the system can be reduced to two coupled nonlinear two-level models. From the models, we calculate the change of the tunnelling probability for each component with the linear sweeping rate. It is found that the probability for each component exhibits regular oscillating behavior for the larger sweeping rate, but for smaller rate the oscillation is irregular. Moreover, the asymmetry of the tunnelling between the two components can be induced by the unbalanced initial populations or the inequality of the twoself-interactions when the cross-interaction between the components exists. The result can not be found in the single component BECs.     

Landau-Zener Tunnelling of Two-Component Bose-Einstein Condensates in Optical Lattices

We investigate the Landau-Zener tunnelling of two-component Bose-Einstein condensates （BECs） in optical lattices. In the neighborhood of the Brillouin zone edge, the system can be reduced to two coupled nonlinear two-level models. From the models, we calculate the change of the tunnelling probability for each component with the linear sweeping rate. It is found that the probability for each component exhibits regular oscillating behavior for the larger sweeping rate, but for smaller rate the oscillation is irregular. Moreover, the asymmetry of the tunnelling between the two components can be induced by the unbalanced initial populations or the inequality of the two self-interactions when the cross-interaction between the components exists. The result can not be found in the single component BECs.     

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 populationdifference of atoms, and exist Shapiro-like steps of atomic tunneling current. Both the population difference and theatomic tunneling current depend strongly on the total number of atoms and the initial phase difference.     

Phase of Two-Component Bose-Einstein Condensates with a Coupling Drive

By using the invariant theory, we study the phases of two-component Bose-Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the interspecies interaction. The dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Stability of Two-Component Bose-Einstein Condensates in Bessel Optical Lattices

The stability of the ground state of two-component Bose-Einstein condensates （BEGs） loaded into the central well of an axially symmetric Bessel lattices （BLs） potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross-Pitaevskii equation （GPE）. By using the variational method, we find that stable ground state of two-component BEGs can exist in BLs. The BLs＇s depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BEGs in BLs is also studied and a collapse condition for trapped two-component BEGs is obtained. It is shown that the two-component BEGs exhibit rich collapse dynamics. That is, the two-component BEGs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BEGs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BEGs can be controlled by temporal modulation of the atom interaction.     

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

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.     

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.     

Stationary States and Modulational Instability of Coupled Two-Component Bose-Einstein Condensates in a Ring Trap

We investigate modulational instability (MI) of a coupled two-component Bose-Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent. Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intra-component interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose-Einstein condensates by modulating its coupling strength and interaction strength.     

Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l 1, l and l - 1,respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l 1, and l and l - 1. In this case the fluctuations are a constant,and the magnetic soliton appears.     

Atomic Tunnelling Dynamics of Two Squeezed Bose-Einstein Condensates

In this paper, tunnelling dynamics of squeezed Bose-Einstein condensates (BEC's) in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunnelling interaction is investigated by using the second quantization approach. The influence of BEC squeezing on macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunnelling is analyzed in detail. It is shown that the MQST and coherent atomic tunnelling between two squeezed BEC's can be manipulated through changing squeezing amplitude and squeezing phase of BEC squeezed states.     

Analyzing Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

We analyze the dynamics of a bright soliton in atomic scattering length in an expulsive parabolic potential. Bose-Einstein condensates （BECs） with time-dependent Under a safe ravage of parameters in which the Gross-Pitaevskii （GP） equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomic scattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.     

Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices I and l＋ 1, and I and l - 1. In this case the fluctuations are a constant, and the magnetic soliton appears.     

Analyzing Dynamics of a Bright Soliton in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

We analyze the dynamics of a bright soliton in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross-Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomicscattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.