There is a pressing need for robust and straightforward methods to create potentials for trapping Bose-Einstein condensates which are simultaneously dynamic, fully arbitrary, and sufficiently stable to not heat the ultracold gas. We show here how to accomplish these goals, using a rapidly-moving laser beam that "paints" a timeaveraged optical dipole potential in which we create BECs in a variety of geometries, including toroids, ring lattices, and square lattices. Matter wave interference patterns confirm that the trapped gas is a condensate. As a simple illustration of dynamics, we show that the technique can transform a toroidal condensate into a ring lattice and back into a toroid. The technique is general and should work with any sufficiently polarizable low-energy particles.

We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, limited only by experimental factors such as drift and trap lifetime. The quantized rotation was initiated by transferring one unit variant Planck's over 2pi of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply connected, and was observed with a Bose-Einstein condensate fraction as small as 20%. We also created flow with two units of angular momentum and observed its splitting into two singly charged vortices when the trap geometry was changed from multiply to simply connected.

State-selected rubidium-87 molecules were created at rest in a dilute Bose-Einstein condensate of rubidium-87 atoms with coherent free-bound stimulated Raman transitions. The transition rate exhibited a resonance line shape with an extremely narrow width as small as 1.5 kilohertz. The precise shape and position of the resonance are sensitive to the mean-field interactions between the molecules and the atomic condensate. As a result, we were able to measure the molecule-condensate interactions. This method allows molecular binding energies to be determined with unprecedented accuracy and is of interest as a mechanism for the generation of a molecular Bose-Einstein condensate.

We demonstrate the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of , using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. Furthermore, we create vortices of charge 2 by transferring to each atom the orbital angular momentum of two photons.PACS numbers: 03.75. Lm, 42.50.Vk Light can carry two kinds of angular momentum: Internal or spin angular momentum (SAM) associated with its polarization and external or orbital angular momentum (OAM) associated with its spatial mode [1]. A light beam with a phase singularity, e.g., a Laguerre-Gaussian (LG) beam, has a well-defined OAM along its propagation axis [2]. Beams with phase singularities have only recently been generated [3,4,5], and are now routinely created so as to carry specific values of OAM [6,7].Interaction of light with matter inevitably involves the exchange of momentum. For linear momentum (LM), the mechanical effects of light range from comet tails to laser cooling of atoms. The transfer of optical SAM to atoms has been studied for over a century [8], and the mechanical effect of SAM on macroscopic matter was first demonstrated 70 years ago in an experiment where circularly polarized light rotated a birefringent plate [9]. More recently, the mechanical effects of optical OAM on microscopic particles and atoms have been investigated [6]. SAM and OAM of light has been used to rotate micron-sized particles held in optical tweezers [10,11,12]. The forces on atoms due to optical OAM [13] An atomic gas Bose-Einstein condensate (BEC) allows the study of macroscopic quantum states. For example, BEC superfluid properties can be explored using vortex states (macroscopic rotational atomic states with angular momentum per atom quantized in units of ). The many-body wavefunction of the BEC is very well approximated by the product of identical single-particle wavefunctions, so for a BEC in a vortex state, each particle carries quantized OAM. The first generation of a vortex in a BEC used a "phase engineering" scheme involving a rapidly rotating G laser beam coupling the external motion to internal state Rabi oscillations [17,18]. Later schemes included mechanically stirring the BEC with a focused laser beam [19] and "phase imprinting" by adiabatic passage [16,20]. However, transfer of OAM from the rotating light beams in these earlier schemes is not well-defined.Here, we report the direct observation of the quantized transfer of well-defined OAM of photons to atoms. Using a 2-photon stimulated Raman process, similar to Bragg diffraction [21], but with a LG beam carrying OAM of per photon, we generate an atomic vortex state in a BEC. Over the past decade, numerous papers [22,23] proposed generating vortices in a BEC using stimulate...

We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz and Thouless (BKT) transition temperature. By measuring the density profile, in situ and after time of flight, and the coherence length, we identify different states of the gas. In particular, we observe that the gas develops a bimodal distribution without long range order. In this state, the gas presents a longer coherence length than the thermal cloud; it is quasi-condensed but is not superfluid. Experimental evidence indicates that we observe the superfluid transition (BKT transition).PACS numbers: 03.75. Lm, 64.70.Tg One of the most fascinating aspects of a Bose gas in the degenerate regime is the role of dimensionality. A 2D interacting Bose gas is superfluid at low enough temperature [1,2]. However, by contrast to the 3D case, there is no long range coherence and the coherence decays as a power law [1,2]. At temperatures above the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, the gas is not superfluid. Due to proliferation of free vortices, the quasi-condensate (QC) is fractured into small regions of nearly uniform phase, whose size, which corresponds to the typical length of the exponential decay of the coherence, is larger than the thermal de Broglie wavelength (λ = 2π 2 /M k B T , where T is the temperature and M the atomic mass). For higher T, this size becomes smaller and approaches λ, as the gas crosses over to the thermal phase.Experiments on 2D bosonic systems, such as twodimensional 4 He films [3] and trapped Bose gases [4,5], are able to show signatures of the BKT transition. Other systems, such as the superconducting transition in arrays of Josephson junctions [6] and a two dimensional lattice of (3D) Bose-Einstein condensates [7], also exhibit a similar transition. Another interesting observation was in two dimensional spin polarized atomic hydrogen on liquid 4 He [8] where a reduction in three-body dipolar recombination (which is usually associated with condensation) was observed well above the BKT transition temperature. This observation results from a reduction of density fluctuations, which corresponds to quasi-condensation [9] [10].In this letter, we present evidence of transitions in a quasi-2D Bose gas from thermal (normal gas), to quasicondensate without superfluidity, to superfluid quasicondensate (BKT transition). We explicitly identify the theoretically expected non-superfluid quasi-condensate, a feature not clearly seen in other experiments on a 2D trapped Bose gases [4,5]. We use an interferometric method to study the coherence of the gas down to distances smaller than the thermal de Broglie wavelength. Our results can be understood using the local density approximation (LDA) on a model [11] of a homogeneous system. More recently, calculations for a trapped system have been carried out using classical-quantum field methods [12] and quantum Monte Carlo methods [13].The BKT transition occurs at a universal value of the superfluid density n s = 4/λ 2 . However, the ...

We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.

We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.

An integrated coherent matter wave circuit is a single device, analogous to an integrated optical circuit, in which coherent de Broglie waves are created and then launched into waveguides where they can be switched, divided, recombined, and detected as they propagate. Applications of such circuits include guided atom interferometers, atomtronic circuits, and precisely controlled delivery of atoms. Here we report experiments demonstrating integrated circuits for guided coherent matter waves. The circuit elements are created with the painted potential technique, a form of time-averaged optical dipole potential in which a rapidly moving, tightly focused laser beam exerts forces on atoms through their electric polarizability. The source of coherent matter waves is a Bose-Einstein condensate (BEC). We launch BECs into painted waveguides that guide them around bends and form switches, phase coherent beamsplitters, and closed circuits. These are the basic elements that are needed to engineer arbitrarily complex matter wave circuitry.