Abstract. We have performed a number of experiments with a Bose-Einstein condensate (BEC) in a one dimensional optical lattice. Making use of the small momentum spread of a BEC and standard atom optics techniques a high level of coherent control over an artificial solid state system is demonstrated. We are able to load the BEC into the lattice ground state with a very high efficiency by adiabatically turning on the optical lattice. We coherently transfer population between lattice states and observe their evolution. Methods are developed and used to perform band spectroscopy. We use these techniques to build a BEC accelerator and a novel, coherent, large-momentum-transfer beamsplitter.PACS numbers: 03.75. Fi, 32.80.Qk An optical lattice is a practically perfect periodic potential for atoms, produced by the interference of two or more laser beams. A Bose-Einstein condensate (BEC) [1,2] is the ultimate coherent atom source, a collection of atoms, all in the same state, with an extremely narrow momentum spread. Combining a BEC with an optical lattice provides an opportunity for exploring a quantum system analogous to electrons in a solid state crystal but with unprecedented control over both the lattice and the particles.Periodic optical potentials have been widely used in atomic physics (For reviews see [3,4,5]). Recent experiments and theory have studied BECs in optical lattices [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18][19, 20, 21, 22, 23, 24, 25]. Here we present a series of new experiments in which we precisely manipulate the BEC/lattice system and interpret the results in terms of a single-particle band structure theory.We describe 1D lattice experiments with a sodium BEC in a regime where interactions between atoms are negligible. This paper is organised as follows: we begin with a description of the experimental arrangement (Sec. 1) and a brief summary of band theory (Sec. 2). We explore diabatic and adiabatic loading of a BEC into a lattice in Sec. 3. Using momentum state analysis we measure coherent superpositions between bands and determine that we can adiabatically load more than 99% of the atoms into a well-defined Bloch state. In Sec. 4 we manipulate the lattice potential to transfer population between Bloch states, mapping the band structure of the lattice eigenstates. We follow the work of [26,27,28] in Sec. 5 in the deep lattice regime to † Present address:

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling between two regions of classically stable motion. An archetype of such non-classical motion is tunnelling through an energy barrier. In the 1980s, a new process, 'dynamical' tunnelling, was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom. Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose-Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180 degrees out of phase with the initial state.

We form ultracold Na2 molecules by single-photon photoassociation of a Bose-Einstein condensate, measuring the photoassociation rate, linewidth, and light shift of the J = 1, v = 135 vibrational level of the A1 Sigma (+)(u) molecular state. The photoassociation rate constant increases linearly with intensity, even where it is predicted that many-body effects might limit the rate. Our observations are in good agreement with a two-body theory having no free parameters.

We have performed experiments using a 3D-Bose-Einstein condensate of sodium atoms in a 1D optical lattice to explore some unusual properties of band-structure. In particular, we investigate the loading of a condensate into a moving lattice and find non-intuitive behavior. We also revisit the behavior of atoms, prepared in a single quasimomentum state, in an accelerating lattice. We generalize this study to a cloud whose atoms have a large quasimomentum spread, and show that the cloud behaves differently from atoms in a single Bloch state. Finally, we compare our findings with recent experiments performed with fermions in an optical lattice.PACS numbers: 03.75. Lm, 32.80.Qk An optical lattice is a practically perfect periodic potential for atoms, produced by the interference of two or more laser beams. An atomic-gas Bose-Einstein condensate (BEC)[1, 2] is a coherent source of matter waves, a collection of atoms, all in the same state, with an extremely narrow momentum spread. Putting such atoms into such a potential provides an opportunity for exploring a quantum system with many similarities to electrons in a solid state crystal but with unprecedented control over both the lattice and the particles. In particular we can easily control the velocity and acceleration of the lattice as well as its strength, making it a variable "quantum conveyor belt". This allows us to explore situations that are difficult or impossible to achieve in solid state systems. The results are often remarkable and counterintuitive. For example atoms that are being carried along by a moving optical lattice are left stationary when the still-moving lattice is turned off, in apparent violation of the law of inertia.A few experiments have studied quantum degenerate atoms in moving optical lattices [3,4,5,6]. Bragg diffraction of a Bose condensate is a special case of quantum degenerate atoms in a moving lattice [7]. Here, using a Bose-Einstein condensate and a moving lattice, we achieve full control over the system, in particular its initial quasimomentum and band index as well as its subsequent evolution. We also show the difference in behavior when the atom sample has a large spread of quasimomenta, as compared with the narrow quasimomentum distribution of a coherent BEC.Our lattice is one-dimensional along the x axis, produced by the interference of two counter-propagating laser beams, each of wave-vector k = 2π/λ (λ ≈ 589 nm is the wavelength of the laser beams). This results in a sinusoidal potential, V sin 2 kx, with a spatial period We will use Bloch theory, emphasizing the single particle character of the problem. An overview of Bloch theory, as it applies to this one dimensional system, is supplied in reference [3]. Briefly, the wave function of the atoms in the lattice can be decomposed into the Bloch eigenstates u n,q (x)e iqx characterized by a band index n and a quasimomentum q, defined in the rest frame of the lattice. The eigenenergies of the system, E n (q), as well as the eigenstates are periodic in q with a periodicity 2h...

Two distinct mechanisms are investigated for transferring a pure 87 Rb Bose-Einstein condensate in the |F = 2, m F = 2〉 state into a mixture of condensates in all the m F states within the F = 2 manifold. Some of these condensates remain trapped whilst others are output coupled in the form of an elementary pulsed atom laser. Here we present details of the condensate preparation and results of the two condensate output coupling schemes. The first scheme is a radio frequency technique which allows controllable transfer into available m F states, and the second makes use of Majorana spin flips to equally populate all the manifold sub-states. More recently, the production of multi-component condensates has revealed intriguing quantum fluid dynamics, and enabled precise measurement of relative quantum phase [9]. Experiments at JILA have focused on mixtures involving atoms in different ground state hyperfine levels (quantum number F), and coupling with a two photon (microwave plus radio frequency) transition. Experiments at MIT have used an optical dipole trap to confine a condensate occupying all magnetic sub-states (quantum number m F ) of the same hyperfine level [10]. Spin exchange processes result in domain formation which exhibits an anti-ferromagnetic interaction [11]. An important aspect of that work is the confinement of condensed atoms in sub-states which cannot be magnetically trapped.In this paper we present the results of two techniques for transforming a single state |F = 2, m F = 2〉 87 Rb Bose condensate into a mixture of all five magnetic sub-states of the F = 2 hyperfine level. Two of these states are magnetically confined (|2, 2〉 and |2, 1〉), with magnetic moments differing by a factor of 2, and the other states are unconfined.Applying an RF field similar to that used in the evaporative cooling stage of the experiment we can couple atoms between adjacent m F states. It is possible to control the number of atoms which are coupled from the |2, 2〉 state into the other m F states: condensates with predetermined sub-state populations can be constructed. For example, we can limit the transfer into untrapped states.