Interference of Bose-Einstein condensates and entangled single-atom state in a spin-dependent optical lattice

We present a theoretical model to investigate the interference of an array of Bose-Einstein condensates loaded in a one-dimensional spin-dependent optical lattice, which is based on an assumption that for the atoms in the entangled single-atom state between the internal and the external degrees of freedom each atom interferes only with itself. Our theoretical results agree well with the interference patterns observed in a recent experiment by Mandel et al. [Phys. Rev. Lett. 91, 010407 (2003)]. In addition, an experimental suggestion of nonuniform phase distribution is proposed to test further our theoretical model and prediction. The present work shows that the entanglement of a single atom is sufficient for the interference of the condensates confined in a spin-dependent optical lattice and this interference is irrelevant with the phases of individual condensates, i.e., this interference arises only between each condensate and itself and there is no interference effect between two arbitrary different condensates.     

Generating periodic interference in Bose–Einstein condensates

The interference between two condensates with repulsive interaction is investigated numerically by solving the onedimensional time-dependent Gross–Pitaevskii equation.The periodic interference pattern forms in two condensates,which are prepared in a double-well potential consisting of two truncated harmonic wells centered at different positions.Dark solitons are observed when two condensates overlap.Due to the existence of atom–atom interactions,atoms are transferred among the ground state and the excited states,which coincides with the condensate energy change.     

Nonlinear effects in interference of bose-einstein condensates

Nonlinear effects in the interference of Bose-Einstein condensates are studied using exact solutions of the one-dimensional nonlinear Schrodinger equation, which is applicable when the lateral motion is confined or negligible. With the inverse scattering method, the interference pattern is studied as a scattering problem with the linear Schrodinger equation, whose potential is profiled by the initial density distribution of the condensates. Our theory not only provides an analytical framework for quantitative predictions for the one-dimensional case, it also gives an intuitive understanding of some mysterious features of the interference patterns observed in experiments and numerical simulations.     

Atom interferometry with Bose-Einstein condensates in a double-well potential

A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by 13 microm for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.     

Observation of phase defects in quasi-two-dimensional Bose-Einstein condensates

We have observed phase defects in quasi-2D Bose-Einstein condensates close to the condensation temperature. Either a single or several equally spaced condensates are produced by selectively evaporating the sites of a 1D optical lattice. When several clouds are released from the lattice and allowed to overlap, dislocation lines in the interference patterns reveal nontrivial phase defects.     

玻色-爱因斯坦凝聚体间相互作用的动力学性质研究

采用辛算法数值求解一维含时Gross-Pitaevskii方程.数值模拟玻色爱因斯坦凝聚体的"Breathing"特征,研究撤掉简谐势阱时两个凝聚体相互作用产生的干涉现象及两个凝聚体相位差发生变化时凝聚体的动力学性质.     

Observation of vortex phase singularities in Bose-Einstein condensates

We have observed phase singularities due to vortex excitation in Bose-Einstein condensates. Vortices were created by moving a laser beam through a condensate. They were observed as dislocations in the interference fringes formed by the stirred condensate and a second unperturbed condensate. The velocity dependence for vortex excitation and the time scale for re-establishing a uniform phase across the condensate were determined.     

Temperature Dependence of Two- and Three-Gluon Condensates in the Instanton Vacuum

The two-gluon and three-gluon condensates at finite temperature are calculated in the framework of the grand partition function for a weak-interacting instanton medium of a disordered phase. The interference parts of both chromomagnetic and chromoelectric two-gluon condensates are found to be small but still significant for a quantitative determination of the value of the condensates at very low temperature, and negligible at the temperature above 1.5Λ_MS, with respect to their non-interference ones. The interference parts of the threegluon condensates are found to be quite small even at very low temperature. With the QCD scale parameter fixed by the value of the Lorentz invariant two-gluon condensate at zero temperature, the value of the three-gluon condensate at zero temperature is found to be coincident with the phenomenological estimate. The values of the gluon condensates decrease when temperature increases, and are negligible when the temperature goes beyond 2.5Λ_MS in the case of the SU_C(3) pure gauge theory.     

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.     

Observations on sound propagation in rapidly rotating Bose-Einstein condensates

Repulsive laser potential pulses applied to vortex lattices of rapidly rotating Bose-Einstein condensates create propagating density waves which we have observed experimentally and modeled computationally to high accuracy. We have observed a rich variety of dynamical phenomena ranging from interference effects and shock-wave formation to anisotropic sound propagation.     

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.     

玻色爱因斯坦凝聚体一维轴向干涉中的非线性现象

利用含时的Ｇｒｏｓｓ－Ｐｉｔａｅｖｓｋｉｉ方程,研究了轴对称的高密度玻色爱因斯坦凝聚体在干涉过程中因原子间相互人用而产生的非线性现象。发现玻色爱因斯坦凝聚体的一维轴向干涉条纹的密度分布是一种驻波状结构。通过原子波之间非线性耦合相互作用,这种结构可以表现为物质波光栅,对其周期的原子波产生衍射现象。     

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.     

改进打靶法求解Gross-Pitaevskii方程及三个凝聚体的干涉

用改进的打靶法求解零温简谐势阱中中性原子玻色-爱因斯坦凝聚的一维Gross-Pitaevskii方程,给出不同非线性参数时凝聚体基态的本征值.用辛算法研究三个凝聚体在撤掉陷俘势后产生的干涉,和三个凝聚体处于同-陷俘势中的干涉及周期性演化,讨论不同的相对相位对凝聚体干涉的影响.     

Influence of Decoherence on Interference Between Two Bose-Einstein Condensates

The influence of decoherence on interference between two trapped Bose-Einstein condensates with arbitrary initial states is studied. Analytic expressions of the intensity and visibility of the interference pattern are found. It is shown that the decoherence weakens the interference intensity and decreases the visibility of the interference pattern.     

Tunneling of Boseben-Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

The tunneling effect of Bose-Einstein condensate (BEC) in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.     

Time Evolution for Relative Phase of Two Bose-Einstein Condensates

Considering the collisions between the two condensates and the tunneling effects, we study the time evolution of the relative phase of two Bose-Einstein condensates (BECs). The phase amplitude is given in coherent picture for many cases, which furnishes us a new method to study the interference of two BECs.     

Atom interferometer based on phase coherent splitting of Bose-Einstein condensates with an integrated magnetic grating

We report the phase coherent splitting of Bose-Einstein condensates by means of a phase grating produced near the surface of a microelectronic chip. A lattice potential with a period of 4 mum is generated by the superposition of static and oscillating magnetic fields. Precise control of the diffraction is achieved by controlling the currents in the integrated conductors. The interference of overlapping diffraction orders is observed after 8 ms of propagation in a harmonic trap and subsequent ballistic expansion of the atomic ensemble. By analyzing the interference pattern we show a reproducible phase relation between the diffraction orders with an uncertainty limited by the resolution of the diffraction grating.     

Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons

We show that the time-dependent nonlinear Schrodinger equation of mean-field theory has limited utility for a one-dimensional condensate of impenetrable bosons. Mean-field theory with its associated order parameter predicts interference between split condensates that are recombined, whereas an exact many-body treatment shows minimal interference.     

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.