Fidelity of Interference Between Two Bose-Einstein Condensates with Collision and Dissipation

Interference between the two Bose-Einstein condensates with collision and dissipation is investigated. Itis found that when the two condensates are initially in the coherent state, the interference intensity is affected by thecollision and dissipation, but for the initial Fock state, it is only related to the dissipation. Whether the initial stateis in the coherent state or in a Fock state, the fidelity time has nothing to do with collision. For the initial coherentstate, the fidelity loss rate is zero, but for the initial Fock state, it is determined by the initial particle number of thetwo condensates and dissipation.     

Fidelity of Interference Between Two Bose-Einstein Condensates with Collision and Dissipation

Interference between the two Bose-Einstein condensates with collision and dissipation is investigated. It is found that when the two condensates are initially in the coherent state, the interference intensity is affected by the collision and dissipation, but for the initial Fock state, it is only related to the dissipation. Whether the initial state is in the coherent state or in a Fock state, the fidelity time has nothing to do with collision. For the initial coherent state, the fidelity loss rate is zero, but for the initial Fock state, it is determined by the initial particle number of the two condensates and dissipation.     

一维含时Gross-Pitaevskii方程下三个玻色-爱因斯坦凝聚体间的干涉

从理论上应用辛算法数值求解一维含时GP方程,研究存在陷浮势和陷浮势为零时三个玻色-爱因斯坦凝聚体间的干涉.当陷浮势存在时,玻色-爱因斯坦凝聚体间发生弹性碰撞;如果在t=0时陷浮势为零,三个凝聚体间发生干涉现象,并且发现几率密度随着时间的演化是振荡的.     

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 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.     

Atomic Coherent State, Entangled State and Phase Operator for Studying Interference Between Two Bose-Einstein Condensates

For studying the interference between two Bose-Einstein condensates we introduce the atomic coherentstate （ACS） in the Schwinger bosonic realization along with the phase operator to directly calculate the interference pattern with steady relative phase cos Ф. Eigenstates of the density operator of condensates are classified as ACS is also demonstrated. The entangled state representation is used in some calculations.     

Soliton Solutions in Three-Component Bose-Einstein Condensates

We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.     

The Weak-Coupling of Bose-Einstein Condensates

The coherent characteristics of four trapped Bose-Einstein condensates (BEC) conjunct one by one in aring shape which is divided by two far off-resonant lasers, are studied. Four coupled Gross-Pitaevskii equations are usedto describe the dynamics of the system. Two kinds of self-trapping effects are discussed in the coupled BECs, and thephase diagrams for different initial conditions and different coupling strengths are discussed. This study can be used todetermine interaction parameters between atoms in BEC.     

Stability and Chaos of Two Coupled Bose-Einstein Condensates with Three-Body Interaction

We study the dynamics of two Bose-Einstein condensates （BECs） tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time- varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.     

Stability and Chaos of Two Coupled Bose-Einstein Condensates with Three-Body Interaction

We study the dynamics of two Bose-Einstein condensates (BECs) tunnel-coupled by a double-well potential.A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations,which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time-varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.     

Two-Dimensional Soliton Interaction for Multi-component Bose-Einstein Condensates

For two-component disk-shaped Bose-Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev-Petviashvili-Ⅰ equation at the lowest order from the originai coupled Gross-Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev- Petviashvili-1 equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.     

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.     

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.     

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 Atomic Bose-Einstein Condensate Interacting with Laser Field

Interference of an atomic Bose-Einstein condensate interacting with a laser field in a double-well potential with dissipation is investigated. If properly selecting the laser field and the initial states of the atoms in the two wells, we find that the intensity exhibits revivals and collapses. The fidelity of interference is affected by the total number of atoms in the two wells and dissipation.     

Two-Dimensional Soliton Interaction for Multi-component Bose-Einstein Condensates

For two-component disk-shaped Bose-Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev-Petviashvili-I equation at the lowest order from the original coupled Gross-Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev-Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.     

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.     

Quantum Effects of Bose-Einstein Condensates

In this paper, we study quadrature squeezings of two Bose-Einstein condensates with collision and nonclassical properties of pair entanglement in four wave mixing in Bose-Einstein condensates. With the aid of a numerical method, we find that the two modes (pair entanglement modes) a₁ and a₂ may exhibit quadrature squeezing, in which they are affected by the initial phase. It is shown that the two pump modes exhibit the same super-Poissonian distribution. The analysis for the mode-mode correlation shows that there always exists a violation of the Cauchy-Schwartz inequality, which means that correlation between the two pump modes is nonclassical.