Effects of traps on dynamics of two coupled Bose-Einstein condensates

Effects of the traps are investigated on the dynamics of two coupled Bose-Einstein condensates, and the atom population transfer between the two condensates is discussed. It is found that the traps and the initial condition determine the switching and self-trapping effects on the atom population imbalance. There are the critical potential amplitude and the critical potential width, by which the oscillation manner of the population transferring ratio can be analyzed as time changes.     

Interference of two Bose-Einstein condensates

The visibility of the density interference pattern of two Bose-Einstein condensates, which are produced in traps and overlap after the trapping potential is switched off, is investigated. Coherent wave packets are used to describe the order parameter in a second-quantization formalism. This results in a decrease of the visibility of the interference fringes with increasing time delay between the formation of the condensates and the observation of interference. In the two limiting cases of ideal and very dense gases the correlation time increases, τ→∞, and the result is identical to that obtained using an approach based on the Gross-Pitaevskii equation. Under the conditions of the experiment performed by M. R. Andrews, C. G. Townsend, H. J. Miesner et al., Science 275, 6367 (1997), the computed correlation time τ≈0.2 s is much longer than the confinement time of the condensate, and it is possible to observe the predicted decrease of visibility of the interference fringes of the density of the atoms. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 7, 491–496 (10 April 1999)     

噪声对双势阱玻色-爱因斯坦凝聚体系自俘获现象的影响

研究了对称双势阱玻色-爱因斯坦凝聚体系(BEC)存在均匀噪声或高斯噪声时的自俘获现象.结果发现噪声的存在破坏了自俘获现象的临界行为特征，使得原来约瑟夫森振荡和自俘获之间的临界点变成了一个过渡区域，而且噪声强度越大，这个过渡区域展得越宽.同时发现，对于确定的相互作用强度，当噪声强度增大到一定程度时，相平面会出现混乱，如果这时固定噪声强度增大相互作用强度，相平面中的轨道会重新出现.对纯量子系统加噪声后，自俘获同样不存在临界值，而是存在一个临界区域，且随噪声的增强临界区域会展宽.与平均场近似情况下不同的是，纯量子情况下噪声促进自俘获的产生，且噪声越强自俘获越明显. 关键词： 玻色-爱因斯坦凝聚 自俘获 双势阱 噪声     

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.     

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations.     

Production of 87Rb Bose-Einstein condensates in a hybrid trap

We report a rapid evaporative cooling method using a hybrid trap which is composed of a quadrupole magnetic trap and a one-beam optical dipole trap. It contains two kinds of evaporative coolings to reach the quantum degeneracy: initial radio-frequency (RF) enforced evaporative cooling in the quadrupole magnetic trap and further runaway evaporative cooling in the optical dipole trap. The hybrid trap does not require a very high power laser such as that in the traditional pure optical trap, but still has a deep trap depth and a large trap volume, and has better optical access than the normal magnetic trap like the quadrupole-Ioffe-configuration (QUIC) cloverleaf trap. A high trap frequency can be easily realized in the hybrid trap to enhance the elastic collision rate and shorten the evaporative cooling time. In our experiment, pure Bose-Einstein condensates (BECs) with about 1 × 105 atoms can be realized in 6 s evaporative cooling in the optical dipole trap.     

双势阱玻色-爱因斯坦凝聚体系的自俘获现象及其周期调制效应

研究了双势阱玻色-爱因斯坦凝聚体系(BEC)的自俘获现象(self-trapping). 在平均场近似下通过相平面(phase space)分析的方法研究了两种自俘获的机理：1)势阱中的粒子数在平衡位置附近振动，而相对相位随时间单调变化(running-phase); 2) 势阱中的粒子数和相对相位都在平衡点附近振动. 研究了周期调制场对自俘获现象的影响，发现发生自俘获现象的相变参数能够被周期场非常有效的调制，从而在弱相互作用BEC体系中也可以观察到自俘获现象. 还研究了多体量子涨落对自俘获现象的影响，讨论了在现有的实验条件下对凝聚体自俘获现象进行观察和周期调制. 关键词： 玻色-爱因斯坦凝聚 自俘获 双势阱 周期调制     

两个玻色-爱因斯坦凝聚体间相互作用的数值研究

本文采用辛算法数值求解一维含时Gross-Pitaevskii(GP)方程.研究了存在陷俘势和撤掉陷俘势时两个凝聚体间的相互作用.发现当存在陷俘势时两个凝聚体间发生弹性碰撞;在零时刻撤掉陷俘势时两个凝聚体间发生干涉现象;当t=2时撤掉陷俘势两个凝聚体间发生了复杂现象.     

Vortices in attractive Bose-Einstein condensates in two dimensions

The form and stability of quantum vortices in Bose-Einstein condensates with attractive atomic interactions is elucidated. They appear as ring bright solitons, and are a generalization of the Townes soliton to nonzero winding number m. An infinite sequence of radially excited stationary states appear for each value of m, which are characterized by concentric matter-wave rings separated by nodes, in contrast to repulsive condensates, where no such set of states exists. It is shown that robustly stable as well as unstable regimes may be achieved in confined geometries, thereby suggesting that vortices and their radial excited states can be observed in experiments on attractive condensates in two dimensions.     

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     

Noise thermometry with two weakly coupled Bose-Einstein condensates

Here we report on the experimental investigation of thermally induced fluctuations of the relative phase between two Bose-Einstein condensates which are coupled via tunneling. The experimental control over the coupling strength and the temperature of the thermal background allows for the quantitative analysis of the phase fluctuations. Furthermore, we demonstrate the application of these measurements for thermometry in a regime where standard methods fail. With this we confirm that the heat capacity of an ideal Bose gas deviates from that of a classical gas as predicted by the third law of thermodynamics.     

Macroscopic oscillations between two weakly coupled Bose-Einstein condensates

We demonstrate, both from a theoretical and an experimental point of view, the possibility of realizing a weak coupling between two Bose-Einstein condensates trapped in different Zeeman states. The weak coupling drives macroscopic quantum oscillations between the condensate populations and the observed current-phase dynamics is described by generalized Josephson equations. In order to highlight the superfluid nature of the oscillations, we investigate the response of a ⁸⁷Rb non-condensate (thermal) gas in the same conditions, showing that the thermal oscillations damp more quickly than those of the condensate. Received 2 May 2002 / Received in final form 19 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: smerzi@sissa.it     

Bose-Einstein condensates in the presence of a magnetic trap and optical lattice

In this paper we consider solutions of a nonlinear Schrodinger equation with a parabolic and a periodic potential motivated from the dynamics of Bose-Einstein condensates. Our starting point is the corresponding linear problem which we analyze through regular perturbation and homogenization techniques. We then use Lyapunov-Schmidt theory to establish the persistence and bifurcation of the linear states in the presence of attractive and repulsive nonlinear inter-particle interactions. Stability of such solutions is also examined and a count is given of the potential real, complex and imaginary eigenvalues with negative Krein signature that such solutions may possess. The results are corroborated with numerical computations.     

Anomalous tunneling of phonon excitations between two Bose-Einstein condensates

We discuss the tunneling of phonon excitations across a potential barrier separating two condensates. It is shown that a strong barrier proves to be transparent for the excitations at low energy epsilon. Moreover, the transmission is reduced with increasing epsilon in contrast to the standard dependence. This anomalous behavior is due to the existence of a quasiresonance interaction. The origin of this interaction is a result of the formation of a special well determined by the density distribution of the condensate in the vicinity of a high barrier.     

Optical weak link between two spatially separated Bose-Einstein condensates

Two spatially separate Bose-Einstein condensates were prepared in an optical double-well potential. A bidirectional coupling between the two condensates was established by two pairs of Bragg beams which continuously outcoupled atoms in opposite directions. The atomic currents induced by the optical coupling depend on the relative phase of the two condensates and on an additional controllable coupling phase. This was observed through symmetric and antisymmetric correlations between the two outcoupled atom fluxes. A Josephson optical coupling of two condensates in a ring geometry is proposed. The continuous outcoupling method was used to monitor slow relative motions of two elongated condensates and characterize the trapping potential.     

Chaotic atomic tunneling between two periodically driven Bose-Einstein condensates

The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.     

Effects of external magnetic trap on two dark solitons of a two-component Bose-Einstein condensate

Two dark solitons are considered in a two-component Bose-Einstein condensate with an external magnetic trap, and effects of the trap potential on their dynamics are investigated by the numerical simulation. The results show that the dark solitons attract, collide and repel periodically in two components as time changes, the time period depends strictly on the initial condition and the potential, and there are obvious self-trapping effects on the two dark solitons.     

Dynamical stabilization of self-trapping of two weakly coupled Bose-Einstein condensates

We investigate the effect of an external periodic driving field on the self-trapping of two weakly coupled Bose-Einstein condensates with dissipation. It is shown that the macroscopic self-trapping can be stabilized against dissipation by a high frequency periodic driving field. The parameter ranges for stabilizing self-trapping are found analytically and confirmed numerically.     

Effect of a localized impurity on soliton dynamics in the Bose-Einstein condensates

By using a multiple-scale method,we analytically study the effect of a localized impurity on the soliton dynamics in the Bose-Einstein condensates.It is shown that a dark soliton can be transmitted through a repulsive (or attractive) impurity,while at the position of the localized impurity the soliton can be quasitrapped by the impurity.Additionally,we find that the strength of the localized impurity has an important effect on the dark soliton dynamics.With increasing strength of the localized impurity,the amplitude of the dark soliton becomes bigger,while its width is narrower,and the soliton propagates slower.     

Generation of generalized coherent states with two coupled Bose-Einstein condensates

We present a scheme to prepare generalized coherent states in a system with two species of Bose-Einstein condensates. First, within the two-mode approximation, we demonstrate that a Schrödinger cat-like state can be dynamically generated and, by controlling the Josephson-like coupling strength, the number of coherent states in the superposition can be varied. Later, we analyze numerically the dynamics of the whole system when interspecies collisions are inhibited. Variables such as fractional population, Mandel parameter and variances of annihilation and number operators are used to show that the evolved state is entangled and exhibits sub-Poisson statistics.