We present theoretical and experimental studies of the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. For low atom densities and inertial forces, the condensate performs regular Bloch oscillations, and its center-of-mass motion closely follows semiclassical single-particle trajectories, shaped by the lowest-energy band. But in other regimes, the center-of-mass motion disrupts the internal structure of the condensate by generating solitons and vortex rings, which can trigger explosive expansion of the atom cloud. We use images of the atom cloud to provide experimental evidence for this internal disruption, and find that the process occurs most readily in high-density condensates undergoing slow Bloch oscillations

Classically it is impossible to have transport without transit, i.e., if the points one, two and three lie sequentially along a path then an object moving from one to three must, at some point in time, be located at two. However, for a quantum particle in a three-well system it is possible to transport the particle between wells one and three such that the probability of finding it at any time in the classically accessible state in well two is negligible. We consider theoretically the analogous scenario for a Bose-Einstein condensate confined within a three well system. In particular, we predict the adiabatic transportation of an interacting Bose-Einstein condensate of 2000 7 Li atoms from well one to well three without transiting the allowed intermediate region. To an observer of this macroscopic quantum effect it would appear that, over a timescale of the order of 1s, the condensate had transported, but not transited, a macroscopic distance of ∼ 20µm between wells one and three.The system under consideration is schematically shown in Fig. 1(a), where a three-dimensional harmonic trap is split into three regions via the addition of two parallel repulsive Gaussian potentials. With the Bose-Einstein condensate (BEC) [blue object in Fig. 1(a)], initially in well 1, we show how it is possible, through adiabatic changes to the tunneling rates between the wells, to transport it into well 3 with minimal (ideally zero) occupation of the intervening well. This effect as a function of time is shown in Fig. 1(b), where an interacting BEC of 2000 7 Li atoms is transported from well 1 to well 3 over a timescale of ∼ 1s, with less than 1% atoms occupying well 2 at any particular time. As such it appears that the BEC is transported from well 1 to well 3 without transiting through well 2.This effect of transport without transit (TWT) can be likened to the lay concept of teleportation. However, although TWT relies on quantum control of the global BEC state and associated tunneling matrix elements, it is quite distinct from the quantum definition of teleportation [1]. In the TWT of a BEC we describe the many body system in a time dependent mean-field approximation. As such the wavefunction used to describe the condensed state is a classical field and can not describe such properties as entanglement and hence quantum teleportation.The ideas underpinning the protocol for TWT stem from Stimulated Raman Adiabatic Passage (STIRAP) [2,3,4,5]. STIRAP is a robust optical technique for transferring population between two atomic states, |1 and |3 , via an intermediate excited state, |2 . Using off-resonant pulses to couple states |1 to |2 and |2 to |3 , characterised by coupling parameters K 12 and K 23 , and such that K 23 precedes and overlaps K 12 , the population can be adiabatically transferred from state |1 to |3 . Population transfer is achieved via a superposition of states |1 and |3 with the occupation of state |2 strongly suppressed. These techniques are used in quantum optics for coherent internal state transfer [5,6,7,8] and h...

The collisions of three-dimensional bright solitary matter waves formed from atomic Bose-Einstein condensates are shown to exhibit rich behaviour. Collisions range from being elastic to completely destructive due to the onset of collapse during the interaction. Through a detailed quantitative analysis we map out the role of relative phase, impact speed and interaction strength. In particular, we identify the importance of the collapse time in the onset of unstable collisions and show how the relative phase controls a population transfer between the waves. Our analysis enables us to interpret recent experimental observations of bright solitary matter waves. ‡ Current address:

We present a comprehensive theoretical study of vortex lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap. We consider rotating solutions of the classical hydrodynamic equations, their response to perturbations, as well as time-dependent simulations. We discriminate three distinct, experimentally testable, regimes of instability: ripple, interbranch, and catastrophic. Under symmetry-breaking perturbations these instabilities lead to lattice formation even at zero temperature. While our results are consistent with previous theoretical and experimental results, they shed new light on lattice formation.

We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the ThomasFermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the non-adiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyse the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.PACS numbers: 03.75. Kk, 75.80.+q Wavepacket collapse is a phenomenon seen in diverse physical systems whose common feature is that they obey non-linear wave equations [1], e.g., in nonlinear optics [2], plasmas [3] and trapped atomic Bose-Einstein condensates (BECs) [4,5,6,7,8,9]. In the latter case, collapse occurs when the atomic interactions are sufficiently attractive. For the usual case of isotropic s-wave interactions experiments have demonstrated both global [5] and local collapse [7] depending upon, respectively, whether the imaginary healing length is of similar size or much smaller than the BEC [10]. During global collapse the monopole mode becomes dynamically unstable and the BEC evolves towards a point singularity, with the threshold for collapse generally exhibiting a weak dependence on trap geometry [11,12]. Local collapse occurs when a phonon mode is dynamically unstable such that the collapse length scale is considerably smaller than the BEC.Recently, the Stuttgart group demonstrated collapse in a BEC with dipole-dipole interactions, where the atomic dipoles were polarized in a common direction by an external field [8,9]. The long-range nature of dipolar interactions means that the Gross-Pitaevskii wave equation that governs the BEC is not only non-linear but also non-local [13,14,15,16]. On top of being long-range, dipolar interactions are also anisotropic, being attractive in certain directions and repulsive in others. This anisotropy has manifested itself experimentally in the stability of the ground state, which is strongly dependent on the trap geometry [8], and in the anisotropic collapse of the condensate [9]. Some uncertainty exists over the mechanism of collapse in these systems. In the latter experiment, striking images indicate that the condensate underwent global collapse, which is likely to have occurred through a quadrupole mode [16,17,18]. In the former experiment, however, recent theoretical results suggest that local collapse played a dominant role [19].A unique feature of trapped dipolar BECs in comparison to s-wave BECs is that they are predicted to exhibit minima in their excitation spec...