We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.
We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.
We study the dynamics of vortex nucleation and lattice formation in a Bose--Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross--Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by R. A. Williams et al. [Phys. Rev. Lett. 104, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.
Vortex nucleation in a rotating optical lattice of ultracold atoms Ross Williams, Brasenose College, Oxford D.Phil thesis, Michaelmas 2009 This thesis describes the design and implementation of a two-dimensional rotating optical lattice for ultracold atoms. Rotating optical lattices for ultracold atoms have generated a great deal of theoretical interest due to the close analogy between electrons under a magnetic field and rotating neutral atoms. However, such is the difficulty associated with creating rotating lattice potentials which do not cause significant heating of the atoms there has been only one previous experimental realisation of a practical device, [Phys. Rev. Lett. 97, 240402 (2006)]. There S. Tung et al. reported that heating due to rotation limited the optical lattice to depths of less than 30% of the condensate’s chemical potential. We describe a new method for generating a rotating optical lattice, based on acousto-optic deflection and forming the lattice in the focal plane of a high numerical aperture lens. The intrinsically smooth rotation and excellent degree of control over the rotation frequency enabled a new breed of experiments to be performed, allowing the weak-lattice regime to be surpassed for the first time. In particular we report on the first experiments with a rotating optical lattice where lattice depths were reached such that a two-dimensional array of weakly-linked condensates was created, realising a bosonic Josephson-junction array under an effective magnetic field. We observe a new method of vortex nucleation, whereby rotation-induced phase differences between neighbouring condensates are converted to vortices upon ramping down the lattice. The arrangement for generating a rotating optical lattice also allowed the first realisation of a two-dimensional optical lattice with variable periodicity, known as an accordion lattice. Calibration of the accordion lattice is described, together with a discussion on the crossover from quantum to classical dynamics in large periodicity optical lattices.
This thesis manuscript presents experimental results on Bose-Einstein condensates in optical lattices and in the regime of fast rotation. In an optical lattice an array of inde-pendent 2-dimensional Bose-Einstein condensates is produced from an initially 3-dimen-sional cloud. The number of 2D BECs in this array can be controlled by superimposing a magnetic field gradient along the axis of the lattice and then selectively evaporating the sites. When producing a small number of sites and letting them interfere, dislocations in the interference pattern were observed, which must be due to nontrivial phase defects, as for example free vortices. Such vortices and vortex-antivortex pairs play an important role in the superfluid to normal phase transition in a 2-dimensional gas, the Kosterlitz-Thouless transition. With 3-dimensional condensates the limit of fast rotation is studied in a hybrid potential contain-ing a small quartic term. In this trap rotation frequencies larger than the harmonic trapping fre-quency can be reached. These experiments are a first step to a possible observation of strongly correlated states close to the regime of the fractional quantum Hall effect.
We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. The vortex cores were observed using time-of-flight absorption imaging. Depending on the stirrer size, either discrete resonances or a broad response was visible as the stir frequency was varied. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices.
The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.
Bose-Einstein condensate (BEC) is essentially a macroscopic quantum effect with quantum volatility, macroscopic quantum coherence and artificial controllability. Owing to its unique controllability, it becomes a new ideal platform for quantum simulations and studies of interacting quantum systems. In this paper, the generation of vortices and the formation of vortex chains, as well as characteristics of vortex chains in rotating two-dimensional BEC in a potential composed of harmonic potential and optical lattice are studied numerically. Firstly, the generation of vortices, the formation and distribution of vortex chains and the effects of different physical parameters on the vortex chains in two-dimensional BEC are investigated by using the multigrid preconditioned conjugate gradient method. Secondly, the evolution of the vortex chains with time is studied by using the time-splitting spectral method. The results show that the generation of vortices in BEC trapped in the compound potential corresponds to the minimum value of the potential. When the depth of the optical lattice increases to a certain value, vortex chains are formed in the BEC. With the further increase of the depth of the optical lattice, the vortex depth in the vortex chain in the BEC decreases continuously, and finally the vortex chain disappears completely. When the interaction strength between atoms increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the interaction strength between atoms increases to a certain value, the symmetry of the vortex chains is broken. As the rotation frequency of the condensate increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the rotation frequency is close to the external trapping potential frequency, the linear alignment of the vortex chains is disrupted. It is also found that there are three stages in the evolution of the vortex chains in the BEC: in the first stage, vortex chains rotate together with the condensate, and the original chain distribution keeps unchanged; in the second stage, the phenomenon of vortex space extrusion appears, and the vortex chain is destroyed; in the third stage, the phenomenon of vortex space expansion occurs, and finally the vortex chains disappear. The results above show that the depth of the optical lattice, the interaction strength between atoms, and the rotation frequency of the condensate have important effects on the vortices and vortex chains in the condensate. By adjusting these physical quantities, the number of vortices and the shape of vortex chains in the BEC can be effectively manipulated. This may provide some theoretical reference and guidance for future experiments and applications.