Matter-wave interferometry with phase fluctuating Bose-Einstein condensates

Elongated Bose-Einstein condensates (BECs) exhibit strong spatial phase fluctuations even well below the BEC transition temperature. We demonstrate that atom interferometers using such condensates are robust against phase fluctuations; i.e., the relative phase of the split condensate is reproducible despite axial phase fluctuations. However, larger phase fluctuations limit the coherence time, especially in the presence of some asymmetries in the two wells of the interferometer.     

Quantum coherent oscillations between two coupled bose-einstein condensates

The theoretical investigation of quantum coherent atomic oscillations between two coupled Bose-Einstein condensates(BECs) is studied. We apply the inseparable wave function of time-space to describe two trapped BECs in a double-well magnetic trap. According to Thomas-Fermi approximation, dynamical equations of the interwell phase difference and population imbalance are obtained. Using numerical method, coherent atomic tunneling and macroscopic quantum self-trapping(MQST) effect are investigated.     

两耦合玻色-爱因斯坦凝聚体间的量子相干振荡

理论上考察了两耦合玻色-爱因斯坦凝聚体间的相干原子振荡,我们用时空不能完全分离的波函数去描述囚禁在双磁阱中的玻色-爱因斯坦凝聚体,根据托马斯-费米近似,得到两凝聚体的相位差和布局数随时间的演化方程,应用数值计算的方法,考察了相干原子遂穿和宏观量子自囚禁效应.这些研究结果和采用双模时空分离波函数近似法得到的结果进行了比较.     

Disorder-induced order in two-component Bose-Einstein condensates

We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for XY spin models. We show that a random Raman coupling induces a relative phase of pi/2 between the two BECs and that the effect is robust. We demonstrate it in one, two, and three dimensions at T=0 and present evidence that it persists at small T>0. Applications to phase control in ultracold spinor condensates are discussed.     

Erratum to: Collisional dynamics of symmetric two-dimensional quantum droplets

Frontiers of Physics - We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose—Einstein condensates (BECs) with tunable spin—orbit (SO) coupling in...     

Hyperchaos of two coupled Bose--Einstein condensates with a three-body interaction

We investigate the dynamics of two tunnel-coupled Bose--Einstein condensates (BECs) in a double-well potential. The effects of the three-body recombination loss and the feeding of the condensates from the thermal cloud are studied in the case of attractive interatomic interaction. An imaginary three-body interaction term is considered and a two-mode approximation is used to derive three coupled equations which describe the total atomic numbers of the two condensates, the relative population and relative phase respectively. Theoretical analyses and numerical calculations demonstrate the existence of chaotic and hyperchaotic behaviour by using a periodically time-varying scattering length.     

Quantum phase transition of two-component Bose–Einstein condensates in optical lattices

In this Letter we study the superfluid–Mott-insulator (SMI) phase transition of two-component Bose–Einstein condensates (BECs) in an optical lattice. The analytic exciation energy spectrum is obtained by means of Bogoliubov transformation and hence the SMI phase transition condition is determined explicitly. Moreover, the characteristics of superfluid phase are explained from the energy spectrum.     

Analytical studies of two-component Bose-Einstein condensates in two-dimensional optical lattices

The two-component Bose-Einstein condensates (BECs) trapped in 2D optical lattice potential is studied analytically. A new family of stationary exact solutions of the coupled Gross-Pitaevskii (GP) equations with 2D periodic potential are obtained. In particular, the phase diagram of the system in the trigonometric limit is determined analytically according to the nontrivial phase macroscopic wave functions of the condensates.     

光晶格中玻色-爱因斯坦凝聚体的自旋和磁研究

近年应用光晶格（optical lattice)控制原子玻色－爱因斯坦凝聚体（BEC）的研究取得了突破性的进展。德国Munich研究小组首次在三维光晶格中观察到了超冷原子从BEC超流状态向Mott insulator状态的量子相变。这样的量子相变现象不仅具有重大的理论研究价值，而且为BEC的实际应用提供了新的途径。文章介绍了作者近来在光晶格中BEC的自旋和磁特性方面的一些研究进展，并探讨了它们在磁传感器及量子计算中的可能应用。     

A variational approach to the modulational-oscillatory instability of Bose–Einstein condensates in an optical potential

We use the time-dependent variational approach to demonstrate how the modulational and oscillatory instabilities can be generated in Bose–Einstein condensates (BECs) trapped in a periodic optical lattice with weak driving harmonic potential. We derive and analyze the ordinary differential equations for the time evolution of the amplitude and phase of the modulational perturbation, and obtain the instability condition of the condensates through the effective potential. The effect of the optical potential on the dynamics of the BECs is shown. We perform direct numerical simulations to support our theoretical findings, and good agreement is found.     

Energy spectrum and entanglement of two tunnel- coupled Bose--Einstein condensates

This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose--Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions. The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs. The strong parity effect in the weak tunnelling region is also investigated.     

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.     

Symmetry Breaking Ground States of Bose-Einstein Condensates in 1D Double Square Well and Optical Lattice Well

We investigate the phenomena of symmetry breaking and phase transition in the ground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an optical lattice well, respectively. By using standing-wave expansion method, we present symmetric and asymmetric ground state solutions of nonlinear Schrödinger equation (NLSE) with a symmetric double square well potential for attractive nonlinearity. In particular, we study the ground state wave function's properties by changing the depth of potential and atomic interactions (here we restrict ourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal a phase transition of BECs trapped in one-dimensional optical lattice potential.     

Effects of localized impurity of trap on characteristics of two Bose-Einstein condensates

The characteristics of solitons with a localized impurity in Bose-Einstein condensates (BECs) are investigated with numerical simulations of the Gross-Pitaevskii (GP) equation, the effects of the impurity on BEC solitons are discussed, and the atom population transferring ratios between the two BECs as time goes on are analyzed. It is found that population transfer depends on the impurity strength and the parameters of the system of BECs.     

Phase fluctuations in Bose–Einstein condensates

We demonstrate the existence of phase fluctuations in elongated Bose–Einstein condensates (BECs) and study the dependence of these fluctuations on the system parameters. A strong dependence on temperature, atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase-coherence length is significantly smaller than the condensate size. Our method of detecting phase fluctuations is based on their transformation into density modulations after ballistic expansion. An analytic theory describing this transformation is developed. Received: 13 July 2001 / Revised version: 28 September 2001 / Published online: 23 November 2001     

Vortex formation by merging of multiple trapped Bose-Einstein condensates

We report observations of vortex formation by merging and interfering multiple (87)Rb Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or for high-energy barriers, the BECs can be merged together by barrier removal after their formation. Either process may instigate vortex formation in the resulting BEC, depending on the initially indeterminate relative phases of the condensates and the merging rate.     

Effects of spacing on dynamics of two coupled Bose-Einstein condensates in two finite traps

Interaction between two coupled Bose-Einstein condensates (BECs) is investigated by the variational approach in two finite traps, and the effects of the spacing between the two traps on dynamics of the two BECs are analyzed. The spacing determines the stable condition of stationary states, affects the existence condition of each BEC, and changes the switching and self-trapping effects on the two BECs. The dynamic mechanism is demonstrated by performing a coordinate of classical particle moving in an effective potential field, and confirmed by the evolution of the atom population transferring ratio.     

First principle explanation of phase transition for Bose-Einstein condensates in optical lattices

In this paper we consider Bose-Einstein condensates (BECs) in one-, two- and three-dimension lattice potentials. The key argument for the explanation of the transition from Superfluidity phase to Mott-Insulator phase is suggested to be the spontaneous symmetry breaking effect which occurs for critical values of the ratio between the on-site interaction term and the hopping matrix element. Such an effect can be directly seen in the Gross-Pitaevskii equation with double-well potentials and it also explains the different behavior between one-dimensional models and two/three-dimensional models.     

稀薄原子气体玻色-爱因斯坦凝聚近期研究进展简介

论述了自1999年涡旋态在稀薄碱金属原子气体的玻色-爱因斯坦凝聚体(BEC)中成功实现以来有关的BEC理论和实验研究的进展及作近期的部分探索，并介绍了相关的基本概念和理论。     

A Dynamical Phase Transition of Binary Species BECs Mixtures in a Double Well Potential

We investigate the critical behavior in tunneling dynamics of a binary mixture of Bose-Einstein condensates (BECs) trapped in a symmetric double well potential. By gradually increasing the interspecies interaction, we characterize a continuous dynamical phase transition behavior which involves power law scaling. This dynamical phase transition is a consequence of separatrix crossing as we revealed by poincaré section analysis.