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.     

Dynamics of Bose-Einstein condensates in a one-dimensional optical lattice with double-well potential

We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π-mode self-trapping regime.     

Adiabatic tunneling of Bose–Einstein condensates with modulated atom interaction in a double-well potential

We study the adiabatic tunneling of Bose–Einstein condensates in a symmetric double-well potential when the interaction strength between the atoms is modulated linearly or in a cosine periodic form. It is shown that the system evolves along a nonlinear eigenstate path. In the case of linear modulation under the adiabatic approximation conditions, the tunneling probability of the condensate atoms to the other potential well is half. However, when the system is periodically scanned in the adiabatic process, we find an interesting phenomenon. A small change in the cycle period can lead to the condensate atoms returning to the right well or tunneling to the left well. The system comes from a linear eigenstate back to a nonlinear one, which is completely different from the linear eigenstate evolution. We explain the results by using the energy level and the phase diagram.     

Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials

In this work, we consider quasi-one-dimensional Bose-Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double-well potentials. In particular, we study a setup in which such a “collisionally inhomogeneous” BEC has the same (attractive-attractive or repulsive-repulsive) or different (attractive-repulsive) types of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the non-interacting (linear) limit into their nonlinear counterparts. The collisional inhomogeneity produces a saddle-node bifurcation scenario between two additional solution branches; as the inhomogeneity becomes stronger, the turning point of the saddle-node tends to infinity and eventually only the two original branches remain, which is completely different from the standard double-well phenomenology. Finally, one of these branches changes its monotonicity as a function of the chemical potential, a feature especially prominent, when the sign of the nonlinearity changes between the two wells. Our theoretical predictions, are in excellent agreement with the numerical results.     

Demonstrating mesoscopic superpositions in double-well Bose-Einstein condensates

The availability of Bose-Einstein condensates as mesoscopic or macroscopic quantum objects has aroused new interest in the possibility of making and detecting coherent superpositions involving many atoms. We consider the important problem of distinguishing whether a coherent superposition or a statistical mixture is generated by a given experimental procedure, using the specific example of a double-well condensate. In this system, such a superposition state can be generated by using a Feshbach resonance to tune the inter-atomic interactions. We find that unambiguously distinguishing even a perfect ‘NOON’ state from a statistical mixture using standard detection methods will present experimental difficulties.     

Atom optics with rotating Bose-Einstein condensates

The atom optics of Bose-Einstein condensates containing a vortex of circulation one is discussed. We first analyze in detail the reflection of such a condensate falling on an atomic mirror. In a second part, we consider a rotating condensate in the case of attractive interactions. We show that for sufficiently large nonlinearity the rotational symmetry of the rotating condensate is broken. Received 16 September 2002 / Received in final form 17 November 2002 Published online 11 February 2003     

Atom interferometry with a weakly interacting Bose-Einstein condensate

We demonstrate the operation of an atom interferometer based on a weakly interacting Bose-Einstein condensate. We strongly reduce the interaction induced decoherence that usually limits interferometers based on trapped condensates by tuning the s-wave scattering length almost to zero via a magnetic Feshbach resonance. We employ a 39K condensate trapped in an optical lattice, where Bloch oscillations are forced by gravity. The fine-tuning of the scattering length down to 0.1 a_(0) and the micrometric sizes of the atomic sample make our system a very promising candidate for measuring forces with high spatial resolution. Our technique can be in principle extended to other measurement schemes opening new possibilities in the field of trapped atom interferometry.     

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 phase transition and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a double-well potential

We investigate the quantum phase transition (QPT) and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a symmetric double well under the mean-field approximation. We find the system undergoes a new QPT towards phase-locking state when atom-pair tunnelling is strong enough, and the critical point of self-trapping QPT is shifted by atom-pair tunnelling. As for the dynamics, the system displays localized dynamical behaviour: phase-locking motion and self-trapping motion. We further study the correlation between this localized dynamics and QPT, and find that the area of the localized trajectories in the phase space can serve as an order parameter for both QPTs. The critical exponent of this order parameter is also discussed.     

Distillation of bose-einstein condensates in a double-well potential

Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the two wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations.     

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     

有效质量法调控原子玻色-爱因斯坦凝聚体的双阱动力学

操控原子玻色-爱因斯坦凝聚体在双势阱中的动力学通常是通过改变势阱深度来实现,本文提出了一种基于调节原子有效质量的控制方案,可以在不改变双阱势的前提下操控凝聚体的双阱动力学.利用双模近似,本文解析地导出了超冷原子在双阱势中的隧穿强度和相互作用强度对有效质量的依赖关系,并基于平均场近似数值模拟了在有效质量调节下的凝聚体动力学演化,展示了隧穿振荡和自束缚等典型的双阱动力学行为.此外,本文的研究还发现,借助负有效质量效应,这一方案甚至可以等效地实现对负散射长度原子凝聚体双阱动力学行为的操控.     

Magic numbers and erratic level crossings of double-well Bose-Einstein condensates

By developing an approach by which we are able to quickly obtain spectra and eigenstates, we reveal for what is believed to be the first time the two novel phenomena of magic numbers and erratic level crossings in double-well Bose-Einstein condensates of N atoms. For N < or = 27 and values of U/J that are not too small (U is the two-body interaction strength, and J is the hopping parameter), systems with even atoms are shown to be much more stable than those with odd atoms, and hence even integers play a role in such systems as if they were the magic numbers of nuclei. For N > or = 30, erratic level crossings occur as NU > J.     

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     

Adiabatic transport of Bose-Einstein condensates in a double-well trap: Case of weak nonlinearity

A complete adiabatic transport of Bose-Einstein condensate in a double-well trap is investigated within the Landau-Zener (LZ), and Gaussian Landau-Zener (GLZ) schemes for the case of a small non-linearity, when the atomic interaction is weaker than the coupling. The schemes use the constant (LZ) and time-dependent Gaussian (GLZ) couplings. The mean field calculations show that LZ and GLZ suggest essentially different transport dynamics. Significant deviations from the case of a strong coupling are discussed.     

双势阱中玻色-爱因斯坦凝聚的绝热隧穿

研究了玻色-爱因斯坦凝聚体在双势阱中随着能级差绝热循环变化而发生的绝热隧穿.发现当相互作用较强且初态选择为凝聚体全部置于较浅势阱时,演化过程破坏绝热定理,而演化结果有可能回到初态,也有可能不回到初态,取决于演化周期的选择;另外还发现演化过程表现出对初态选择的依赖,具有不对称的特征.利用能级图和相图,对上述现象给出了解释. 关键词： 玻色-爱因斯坦凝聚 Landau-Zener模型 绝热隧穿     

三势阱中玻色-爱因斯坦凝聚的开关特性

应用平均场近似的方法,研究了弱耦合的三势阱中玻色-爱因斯坦凝聚的开关效应.当粒子置于左阱时,可以通过在中间势阱中加入少量粒子控制左阱粒子向右阱的隧穿,从而呈现出明显的导通与截止行为.对中间势阱的深度和相对相位的影响也进行了讨论,并指出了该理论模型的一些潜在应用前景. 关键词： 玻色-爱因斯坦凝聚 开关效应 三势阱 平均场近似     

Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

Excitations of one-dimensional Bose-Einstein condensates in a random potential

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as l(omega) approximately 1/omega(alpha). We show that the well-known result alpha=2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, alpha starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, alpha=1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.