Josephson effects in dilute bose-einstein condensates

We propose an experiment that would demonstrate the dc and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a "driven-pendulum" equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the dc and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, in an experimentally realistic situation.     

Vortex pair excitation in a Bose-Einstein condensate by moving potential barriers

The subsonic motion regime of a potential barrier in a Bose-Einstein condensate is considered. It is characterized by a critical velocity above which vortex pairs appear with opposite topological charges (“vortex-antivortex” pairs). The theoretical picture developed is confirmed by the results of numerical simulations within the framework of the Gross-Pitaevskii equation.     

Dynamical properties of a condensate in a moving random potential

We study the dynamics of an inhomogeneous Bose-Einstein condensate subject to a one-dimensional harmonic trap and a moving random potential of finite extent. Above the critical velocity, a part of a condensate glues to the moving random potential with a consequent displacement of the condensate center-of-mass along the harmonic trap. We show that the center-of-mass turning point provides a direct measure of the average drag force acting on the condensate.     

Realization of a sonic black hole analog in a Bose-Einstein condensate

We have created an analog of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. A steplike potential accelerates the flow of the condensate to velocities which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow velocity equals the speed of sound is the sonic event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound. A simulation finds negative energy excitations, by means of Bragg spectroscopy.     

自旋-轨道耦合作用下玻色-爱因斯坦凝聚在量子相变附近的朗道临界速度

各向异性超流体中的朗道临界速度并非简单地由运动方向的元激发能谱决定.在自旋-轨道耦合作用下的双分量玻色-爱因斯坦凝聚中,当系统跨过平面波相与零动量相之间的量子相变时,尽管超流声速连续变化,但垂直于自旋-轨道耦合方向的朗道临界速度会出现跳变,跳变幅度随自旋相互作用强度单调增加.根据线性响应理论,计算了凝聚体中运动杂质在不同速度下的能量耗散率,提出可以通过能量耗散观测临界速度在量子相变处的不连续性.     

Stationary and nonstationary fluid flow of a bose-einstein condensate through a penetrable barrier

We experimentally study the fluid flow induced by a broad, penetrable barrier moving through an elongated dilute gaseous Bose-Einstein condensate. The barrier is created by a laser beam swept through the condensate, and the resulting dipole potential can be either attractive or repulsive. We examine both cases and find regimes of stable and unstable fluid flow: At slow speeds of the barrier, the fluid flow is steady due to the superfluidity of the condensate. At intermediate speeds, we observe an unsteady regime in which the condensate gets filled with dark solitons. At faster speeds, soliton formation completely ceases, and a remarkable absence of excitation in the condensate is seen again.     

Josephson effect throughout the BCS-BEC crossover

We study the stationary Josephson effect for neutral fermions across the BCS-BEC (Bose-Einstein condensate) crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.     

Motion of a Bose-Einstein Condensate Bright Soliton Incident on a Step-Like Potential

The motion characteristics of a Bose-Einstein condensate bright soliton incident on a local step-like potential barrier are investigated analytically by means of the variational approach. The dynamics of the soliton-potential interaction is studied as well. Then the results are verified by direct numerical simulations of the Gross-Pitaevskii equation. It is found that a moving bright soliton can be reflected from or pass over a step-like potentiaI in a controllable fashion, the critical velocity depends on the width of the soliton and the parameters of the step, and the motion trajectory of the soliton does not depend on its phase. The atom density envelope of the soliton is changed as the result of the interaction between the soliton and the step-like potential.     

Critical trap aspect ratios for dipolar BEC

We show that there exists critical trap aspect ratios for a trapped Bose-Einstein condensate with dipole-dipole interactions. We discuss the role of critical trap aspect ratios on both the critical angular velocity above which a vortex is energetically favorable and the precession velocity of an off-axis vortex.     

一个玻色-爱因斯坦凝聚体超流临界速度值的修正

超流最关键的物理量就是临界速度,美国MIT(麻省理工学院)实验组用激光来回扫描凝聚体的方法测出BEC超流体的临界速度,但是与Bogolyubov的理论得出来的值相比小得多,P.O.Fedichev考虑凝聚体处在外势中和各相异性的特点,理论计算的结果与MIT(麻省理工学院)实验组测量的实验值接近,但还是有一定的差距。考虑到非凝聚粒子的影响,发现MIT组测得的实验值并不是临界速度,而是准粒子的速度,实际临界速度比测得的速度要大。估算了准粒子的有效质量,并用碰撞模型对MIT组测得的实验值进行了修正。Jun Suzuki考虑了非凝聚态粒子的影响,计算出的临界速度的理论值与修正后的MIT组的实验结果相符。     

Dynamical superfluid-insulator transition in a chain of weakly coupled bose-Einstein condensates

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the condensates coherently oscillate in the array. For large displacements, the condensates remain localized on the side of the harmonic trap with a randomization of the relative phases. The superfluid-insulator transition is due to a discrete modulational instability, occurring when the condensate center of mass velocity is larger than a critical value.     

Excitation spectrum and structure factor of a two-component Bose-Einstein condensate in different hyperfine states

The elementary excitation spectrum of a two-component Bose-Einstein condensate in different hyperfine states is obtained by Green＇s function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green＇s functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.     

Ground State and Single Vortex for Bose-Einstein Condensates in Anisotropic Traps

For Bose-Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose-Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large-N limit of the vortex critical angular velocity for a 〉0, and the critical number for condensate population approaches the point of collapse for a 〈 0, by using approximate variational method.     

Stability of Bose-Einstein condensates in a double-well potential

We investigate the stability of the first excited state, the so-called “π-state,” of Bose-Einstein condensates in a double-well potential. From the condition of complex excitation energies, we determine the critical barrier height, above which the π-state is dynamically unstable. We find that the critical barrier height decreases monotonically as the number of condensate atoms increases. We also simulate the dynamics of the π-state by solving the time-dependent Gross-Pitaevskii equation. Our simulation results show that the π-state in the dynamically unstable region exhibits distinctively different behavior from that in the dynamically stable region.     

Misinterpretation yields supervelocities during transmission of wave packets through a barrier

This paper is concerned with the transmission time of an incident Gaussian wave packet through a symmetric rectangular barrier. Following Hartman (J. Appl. Phys. 33, 3427 (1962)), the transmission time is usually taken as the difference between the time at which the peak of the transmitted packet leaves the barrier of thickness and the time at which the peak of the incident Gaussian wave packet arrives at the barrier. This yields a corresponding transmission velocity which appears under certain conditions as a supervelocity, i.e. becomes larger than the corresponding propagation velocity in free space which is the group velocity for electrons or the velocity of light for photons, respectively. By analysing the propagation of a broadband wave packet (which leads in free space to an extremely concentrated wave packet at a certain time) we obtain the pulse response function of the barrier and show that the insertion of the barrier is physically unable to produce a supervelocity. Therefore, the peak of an incident Gaussian wave packet and the peak of the transmitted wave packet are in no causal relationship. The shape of the transmitted wave packet is produced from the incident wave by convolution with the pulse response of the barrier. This yields a distortion of the shape of the wave packet which includes also the observed negative time shift of the peak. We demonstrate further that the phenomenon of Hartman's supervelocities is not restricted to barriers with their exponentially decaying fields but occurs for instance also in transmission lines with an inserted LCR circuit. Received 7 January 1999 and Received in final form 22 April 1999     

Stabilization of solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle

The stability of dark solitons generated by supersonic flow of a Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to the decay of disturbances of solitons at a fixed distance from the obstacle and the formation of effectively stable dark solitons. This phenomenon explains the surprising stability of the flow picture that has been observed in numerical simulations.     

Stability of supercurrents and condensates in type I superconductors

Excitations of Cooper pairs into non-condensed bound pairs are similar to excitations oftrue bosons out of the Bose-Einstein condensate. Using the Landau criterion ofsuperfluidity we evaluate the critical current above which these pair-excitations wouldlead to a finite resistivity. The predicted value strongly depends on the chosenapproximation. The Thouless approach based on the Galitskii T-matrix and theKadanoff-Martin theory which is in many aspects equivalent to the BCS theory, both lead tozero critical velocity, what is in conflict with the mere existence of supercurrents. Incontrast, the T-matrix with multiple scattering corrections provides the critical velocityof pair excitation which is √3-times larger than the critical velocity of pairbreaking. This agrees with the experimentally well established fact that supercurrents intype I superconductors are limited by pair breaking, not by pair excitation.     

偶极玻色-爱因斯坦凝聚体中的各向异性耗散

针对偶极相互作用的玻色-爱因斯坦凝聚体,解析计算了点状杂质沿平行极化轴和垂直极化轴运动的能量耗散率,证明了在超流临界速度更大的方向上耗散率也更高.该结论为最近在162Dy原子气体中观测到的实验现象提供了理论支持.对于一般的运动方向,给出了耗散率在高速极限下以及临界速度附近的渐近形式.结合数值计算的结果,论证了耗散率随方向角的变化总是表现出与临界速度一致的各向异性.     

Instability of Bose-Einstein condensates moving in optical lattices

We investigate the Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at a finite temperature. Using a 1D tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence reveals the microscopic mechanism of the Landau instability.     

Dissipative flow and vortex shedding in the Painlevé boundary layer of a Bose-Einstein condensate

This paper addresses the drag force and formation of vortices in the boundary layer of a Bose-Einstein condensate stirred by a laser beam following the experiments of Phys. Rev. Lett. 83, 2502 (1999)]. We make our analysis in the frame moving at constant speed where the beam is fixed. We find that there is always a drag around the laser beam. We also analyze the mechanism of vortex nucleation. At low velocity, there are no vortices and the drag has its origin in a wakelike phenomenon: This is a particularity of trapped systems since the density gets small in an extended region. The shedding of vortices starts only at a threshold velocity and is responsible for a large increase in drag. This critical velocity for vortex nucleation is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud.