(3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices

We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a rotating optical lattice or, alternatively, in a synthetic magnetic field. This approach has the advantage to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. We also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions

Spontaneous formation and relaxation of spin domains in antiferromagnetic spin-1 quasi-condensates

Quantum systems of many interacting particles at low temperatures generally organize themselves into ordered phases of matter, whose nature and symmetries are captured by an order parameter. In the simplest cases, this order parameter is spatially uniform. For example, a system of localized spins with ferromagnetic interactions align themselves to a common direction and build up a macroscopic magnetization on large distances. However, non-uniform situations also exist in nature, for instance in antiferromagnetism where the magnetization alternates in space. The situation becomes even richer when the spin-carrying particles are mobile, for instance in the so-called stripe phases emerging for itinerant electrons in strongly-correlated materials. Understanding such inhomogeneously ordered states is of central importance in many-body physics. In this work, we study experimentally the magnetic ordering of itinerant spin-1 bosons in inhomegeneous spin domains at nano-Kelvin temperatures. We demonstrate that spin domains form spontaneously after a phase separation transition, \textit{i.e.} in the absence of external magnetic force, purely because of the antiferromagnetic interactions between the atoms. Furthermore, we explore how the equilibrium domain configuration emerges from an initial state prepared far-from-equilibrium.Comment: Supplementary material available as ancillary fil

Optical Flux Lattices for Two-Photon Dressed States

We describe a simple scheme by which "optical flux lattices" can be implemented in ultracold atomic gases using two-photon dressed states. This scheme can be applied, for example, to the ground state hyperfine levels of commonly used atomic species. The resulting flux lattices simulate a magnetic field with high mean flux density, and have low energy bands analogous to the lowest Landau level. We show that in practical cases the atomic motion significantly deviates from the adiabatic following of one dressed state, and that this can lead to significant interactions even for fermions occupying a single band. Our scheme allows experiments on cold atomic gases to explore strong correlation phenomena related to the fractional quantum Hall effect, both for fermions and bosons.Comment: 6 page

Topological superfluids on a lattice with non-Abelian gauge fields

Two-component fermionic superfluids on a lattice with an external non-Abelian gauge field give access to a variety of topological phases in presence of a sufficiently large spin imbalance. We address here the important issue of superfluidity breakdown induced by spin imbalance by a self-consistent calculation of the pairing gap, showing which of the predicted phases will be experimentally accessible. We present the full topological phase diagram, and we analyze the connection between Chern numbers and the existence of topologically protected and non-protected edge modes. The Chern numbers are calculated via a very efficient and simple method.Comment: 6 pages, 5 figures to be published in Europhysics Letter

Flux lattices reformulated

We theoretically explore the optical flux lattices produced for ultra-cold atoms subject to laser fields where both the atom-light coupling and the effective detuning are spatially periodic. We analyze the geometric vector potential and the magnetic flux it generates, as well as the accompanying geometric scalar potential. We show how to understand the gauge-dependent Aharonov-Bohm singularities in the vector potential, and calculate the continuous magnetic flux through the elementary cell in terms of these singularities. The analysis is illustrated with a square optical flux lattice. We conclude with an explicit laser configuration yielding such a lattice using a set of five properly chosen beams with two counterpropagating pairs (one along the x axes and the other y axes), together with a single beam along the z axis. We show that this lattice is not phase-stable, and identify the one phase-difference that affects the magnetic flux. Thus armed with realistic laser setup, we directly compute the Chern number of the lowest Bloch band to identify the region where the non- zero magnetic flux produces a topologically non-trivial band structure.Comment: 22 pages, 7 figure

Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 87Rb atoms

We report on precision measurements of spin-dependent interaction-strengths in the 87Rb spin-1 and spin-2 hyperfine ground states. Our method is based on the recent observation of coherence in the collisionally driven spin-dynamics of ultracold atom pairs trapped in optical lattices. Analysis of the Rabi-type oscillations between two spin states of an atom pair allows a direct determination of the coupling parameters in the interaction hamiltonian. We deduce differences in scattering lengths from our data that can directly be compared to theoretical predictions in order to test interatomic potentials. Our measurements agree with the predictions within 20%. The knowledge of these coupling parameters allows one to determine the nature of the magnetic ground state. Our data imply a ferromagnetic ground state for 87Rb in the f=1 manifold, in agreement with earlier experiments performed without the optical lattice. For 87Rb in the f=2 manifold the data points towards an antiferromagnetic ground state, however our error bars do not exclude a possible cyclic phase.Comment: 11 pages, 5 figure

Geometric Phases generated by the non-trivial spatial topology of static vector fields coupled to a neutral spin-endowed particle. Application to 171Yb atoms trapped in a 2D optical lattice

We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field, interacting with the spin magnetic moment of a neutral particle. Our basic tool is the local unitary transformation which recasts the magnetic spin interaction under a diagonal form. Rewriting the kinetic term in the "rotated" frame requires the introduction of non-Abelian covariant derivatives, involving the gradients of the Euler angles which define the orientation of the local field. Within the rotated frame, we have built a perturbation scheme,assuming that the longitudinal non-Abelian field component dominates the transverse ones, to be evaluated to second-order. The geometry embedded in the longitudinal gauge vector field and its curl, the geometric magnetic field, is described by the associated Aharonov-Bohm phase. As an illustration, we study the physics of cold 171Yb atoms dressed by two sets of circularly polarized beams, forming square or triangular 2D optical lattices. The geometric field is computed explicitly from the Euler angles. The magnitude of 2nd-order corrections due to transverse fields can be reduced to the percent level by a choice of light intensity which keeps the dressed atom loss rate below 5 s^{-1}. An auxiliary optical lattice confines the atoms within 2D domains where the geometric field is pointing upward.Comment: 12 pages, 4 figures. Comments and one figure added about the effect of the additional scalar potential (sec. V.B). To be published in J. Phys. A:Math. Theo

Production of Sodium Bose--Einstein condensates in an optical dimple trap

We report on the realization of a sodium Bose--Einstein condensate (BEC) in a combined red-detuned optical dipole trap, formed by two beams crossing in a horizontal plane and a third, tightly focused dimple trap propagating vertically. We produce a BEC in three main steps: loading of the crossed dipole trap from laser-cooled atoms, an intermediate evaporative cooling stage which results in efficient loading of the auxiliary dimple trap, and a final evaporative cooling stage in the dimple trap. Our protocol is implemented in a compact setup and allows us to reach quantum degeneracy even with relatively modest initial atom numbers and available laser power

Particles in non-Abelian gauge potentials - Landau problem and insertion of non-Abelian flux

We study charged spin-1/2 particles in two dimensions, subject to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical geometry, paying particular attention to the role of the total angular momentum J = L +S. After this we show that the adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state leads to the formation of charged spin-textures, which in the simplest cases can be identified with quantum Hall Skyrmions.Comment: 24 pages, 10 figures (with corrected legends