Observation of Vortex Nucleation in a Rotating Two-Dimensional Lattice of Bose-Einstein Condensates

Abstract

We report the observation of vortex nucleation in a rotating optical lattice. A 87 Rb 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 neighbouring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.PACS numbers: 03.75. Lm, 67.85.Hj, 74.50.+r, 74.81.Fa Ultracold quantum gases in rotating optical lattices find themselves at the intersection of two fields which have generated an impressive body of experimental and theoretical work. The versatile and clean potentials offered by optical lattices have proved to be an incredibly adept system for exploring a wide range of fundamental problems in condensed matter physics such as the Mott-insulator transition [1], Anderson localization [2,3] and Tonks-Girardeau gases [4]. Similarly rotating quantum gases have provided an array of striking results, from the nucleation of vortex lattices in Bose gases [5,6] to rotating Fermi gases at the BCS-BEC crossover [7]. The close analogy between the physics of rapidly rotating neutral atoms and electrons under a magnetic field has led to considerable interest in the possibility of achieving strongly-correlated quantum Hall states in a rapidly rotating atomic gas [8,9].Rotating optical lattices for cold atoms have generated a large amount of interest in their own right, which can broadly be divided into three main areas: (i) Weak rotating lattices have been used to pin vortices [10] and theoretical work has shown that rich vortex lattices structures, including lattices of doubly quantized vortices, are predicted to emerge [11,12]; (ii) Stronger optical lattice potentials with a large number of atoms per site (100-1000) realize the physics of Josephson junction arrays (JJA) under magnetic fields [13,14]; (iii) Arguably the most interesting regime is for a dilute gas in the tight binding regime in a rotating lattice where fractional quantum Hall physics is predicted to occur [15][16][17]. In all three regimes rich structures emerge that depend on the relative density of vortices and lattice sites.We report on the first experiments with a rotating optical lattice in the 'deep' lattice regime where lattices depths were reached such that a 2D array of weakly linked condensates was created, forming a Josephson junction array. Under rotation this system realizes the uniformly frustrated JJA [13,18]. We have investigated the nucleation of vortices in a rotating lattice, start...

Non-Abelian Braiding of Lattice Bosons

“…This model describes Cooper pairs hopping on a Josephson junction array in a magnetic field [25][26][27] when the charging energy is large compared to the hopping energy. It also describes cold atoms in a deep optical lattice [28] with an artificial gauge field [29][30][31][32][33]. Recent developments in cold atom physics [33] suggest that the fractional quantum Hall regime will be attained in the near future.…”

Condensed ground states of frustrated Bose-Hubbard models

“…This "frustrated" Bose-Hubbard model can show very interesting physics, far beyond the physics of the usual BoseHubbard model. 6 Atomic systems well-described by this frustrated Bose-Hubbard have been studied experimentally by using rotating optical lattices, 7,8 albeit so far limited to situations of large lattice constants and large numbers of particles per lattice site which are outside the strongly correlated regime. However, a series of theoretical proposals [9][10][11][12][13][14][15] indicate that it should be possible to imprint strong gauge fields on an optical lattice, and thereby realize a regime where interactions are strong, and with both the particle number per site, n, and vortex number per plaquette, n φ , of order one.…”

Thermodynamic properties of a rotating Bose--Einstein condensation in a deep optical lattice

“…Motivated by the experiments by Tung et al [21] and Williams et al [22,23], the condensate fraction, critical temperature, and heat capacity are calculated. We suggest a modified semiclassical approximation, which is the density of state (DOS) approach.…”