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.     

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.     

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 two-component 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.     

Self—Trapping State and Atomic Tunnelling Current of an Atomic Bose—Einstein Condensate Interacting with a Laser Field in a Double—Well Potential

We present a theoretical treatment of dynamics of an atomic Bose-Einstein condensation interacting with a single-mode quantized travelling-wave laser field in a double-well potential.When the atom-field system is initially in a coherent state,expressions for the energy exchange between atoms and photons are derived.It is revealed that atoms in the two wells can be in a self-trapping state when the tunnelling frequency satisfies two specific conditions,in which the resonant and far off-resonant cases are included.It is found that there is an alternating current with two different sinusoidal oscillations between the two wells,but no dc characteristic of the atomic tunnelling current occurs.It should be emphasized that when without the laser field,both the population difference and the atomic tunnelling current are only a single oscillation.But they will respectively become a superposition of two oscillations with different oscillatory frequencies in the presence of the laser field.For the two oscillations of the population difference,one always has an increment in the oscillatory frequency,the other can have an increment or a decrease under different cases.These conclusions are also suitable to those of the atomic tunnelling current.As a possible application,by measurement of the atomic tunnelling current between the two wells,the number of Bose-condensed atoms can be evaluated.By poperly selecting the laser field,the expected atomic tunnelling current can be obtained too.     

Quantum Tunneling of a Dipolar Bose-Einstein Condensate in Optical Lattice

We study quantum tunneling of a dipolar Bose-Einstein condensate in optical lattice when the spin system initially is prepared in a squeezed coherent state. It is found that there exists quantum tunneling 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, quantum tunneling disappears between lattices l and l ＋ 1, and that l and l - 1. Correspondingly, the magnetic soliton appears.     

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 Two-Species Molecular Bose-Einstein Condensates

We study tunneling dynamics of atomic group in two-species molecular Bose-Einstein condensates. It is shown that the tunneling of the atom group depends on not only the tunneling coupling constant between the atomic pair molecular condensate and the three-atomic group molecular condensate, but also the inter-molecular nonlinear interactions and the initial number of atoms in these condensates. It is discovered that besides oscillating tunneling current between the atomic pair molecular condensate and the three-atomic group molecular condensate, the nonlinear atomic group tunneling dynamics sustains a self-maintained population imbalance: a macroscopic quantum self-trapping effect.     

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.     

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.     

可控制光学双阱实验及非对称双阱的应用

根据用相位板产生可控制光学双阱的实验方案,制作了具有不同相位差的相位板,测量了不同相位差相位板衍射光强分布和从双阱到单阱演变过程中的衍射光强分布,得到了理论与实验一致的结果.进一步分析实验结果发现:相位差△ψ≠π的相位板,产生非对称光学双阱,在原子光学实验中也有很重要的应用,从而拓展了光学双阱在原子光学实验中的应用范围.     

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.     

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.     

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.     

Phase of a Bose-Einstein Condensate in a Double-Well Potential Modulated Periodically in Time

By using of the invariant theory, we have studied phase of a Bose-Einstein condensate in a double-well potential modulated periodically in time when the on-site interaction energy of a single pair of bosons occupying the same well equals the collision energy between two condensates, the dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained in the case of the cyclical evolution. PACS:03.65.Vf; 03.75.Mn     

Influence of External Magnetic Fields on Tunneling of Spin-1 Bose Condensate

In this letter, we have studied the influence of the external magnetic fields on tunneling of the spin-1 Bose condensate. We find that the population transfer between spin-0 and spin-±1 exhibits the step structure under the external cosinusoidal magnetic field and a combination of static and cosinusoidal one, respectively. Compared with the longitudinal component of the external magnetic field, the smaller the transverse component of the magnetic field is, the larger the time scale of exhibiting the step structure does. The tunneling current may exhibit periodically oscillation behavior when the ratio of the transverse component of the magnetic field is smaller than that of the longitudinal component, otherwise it exhibits a damply oscillating behavior. This means that the dynamical spin localization can be adjusted by the external magnetic fields.     

Bose-Einstein Condensate in a Linear Trap with a Dimple Potential

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.     

Josephson Dynamics of a Bose-Einstein Condensate Trapped in a Double-Well Potential

The Josephson equations for a Bose Einstein Condensate gas trapped in a double-well potential are derived with the two-mode approximation by the Gross Pitaevskii equation. The dynamical characteristics of the equations are obtained by the numerical phase diagrams. The nonlinear self-trapping effect appeared in the phase diagrams are emphatically discussed, and the condition EcN 〉 4E3 is presented.