Compact laser modulation system for a transportable atomic gravimeter.

Nowadays, atom-based quantum sensors are leaving the laboratory towards field applications requiring compact and robust laser systems. Here we describe the realization of a compact laser system for atomic gravimetry. Starting with a single diode laser operating at 780 nm and adding only one fiber electro-optical modulator, one acousto-optical modulator and one laser amplifier we produce laser beams at all the frequencies required for a Rb-87 atomic gravimeter. Furthermore, we demonstrate that an atomic fountain configuration can also be implemented with our laser system. The modulated system reported here represents a substantial advance in the simplification of the laser source for transportable atom-based quantum sensors that can be adapted to other sensors such as atomic clocks, accelerometers, gyroscopes or magnetometers with minor modifications.

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

Many-body systems at low temperatures generally organize themselves into ordered phases, whose nature and symmetries are captured by an order parameter. This order parameter is spatially uniform in the simplest cases, for example the macroscopic magnetization of a ferromagnetic material. Non-uniform situations also exist in nature, for instance in antiferromagnetic materials, where the magnetization alternates in space, or 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. Here 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, that is purely because of the antiferromagnetic interactions between the atoms and in the absence of external magnetic forces, after a phase separation transition. Furthermore, we explore how the equilibrium domain configuration emerges from an initial state prepared far from equilibrium.

Stepwise Bose-Einstein Condensation in a Spinor Gas.

We observe multistep condensation of sodium atoms with spin F=1, where the different Zeeman components m_{F}=0,±1 condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization m_{z} and on the quadratic Zeeman energy q (QZE) in an applied magnetic field. For large QZE, the overall structure of the phase diagram is the same as for an ideal spin-1 gas, although the precise locations of the phase boundaries are significantly shifted by interactions. For small QZE, antiferromagnetic interactions qualitatively change the phase diagram with respect to the ideal case, leading, for instance, to condensation in m_{F}=±1, a phenomenon that cannot occur for an ideal gas with q>0.

Tunable spin-orbit coupling via strong driving in ultracold-atom systems.

Spin-orbit coupling is an essential ingredient in topological materials, conventional and quantum-gas-based alike. Engineered spin-orbit coupling in ultracold-atom systems-unique in their experimental control and measurement opportunities-provides a major opportunity to investigate and understand topological phenomena. Here we experimentally demonstrate and theoretically analyze a technique for controlling spin-orbit coupling in a two-component Bose-Einstein condensate using amplitude-modulated Raman coupling.

Raman-induced interactions in a single-component Fermi gas near an s-wave Feshbach resonance.

Ultracold gases of interacting spin-orbit-coupled fermions are predicted to display exotic phenomena such as topological superfluidity and its associated Majorana fermions. Here, we experimentally demonstrate a route to strongly interacting single-component atomic Fermi gases by combining an s-wave Feshbach resonance (giving strong interactions) and spin-orbit coupling (creating an effective p-wave channel). We identify the Feshbach resonance by its associated atomic loss feature and show that, in agreement with our single-channel scattering model, this feature is preserved and shifted as a function of the spin-orbit-coupling parameters.

The spin Hall effect in a quantum gas.

Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces--analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic or inertial sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta-Das spin transistor.

Peierls substitution in an engineered lattice potential.

Artificial gauge fields open the possibility to realize quantum many-body systems with ultracold atoms, by engineering Hamiltonians usually associated with electronic systems. In the presence of a periodic potential, artificial gauge fields may bring ultracold atoms closer to the quantum Hall regime. Here, we describe a one-dimensional lattice derived purely from effective Zeeman shifts resulting from a combination of Raman coupling and radio-frequency magnetic fields. In this lattice, the tunneling matrix element is generally complex. We control both the amplitude and the phase of this tunneling parameter, experimentally realizing the Peierls substitution for ultracold neutral atoms.

Synthetic partial waves in ultracold atomic collisions.

Interactions between particles can be strongly altered by their environment. We demonstrate a technique for modifying interactions between ultracold atoms by dressing the bare atomic states with light, creating an effective interaction of vastly increased range that scatters states of finite relative angular momentum at collision energies where only s-wave scattering would normally be expected. We collided two optically dressed neutral atomic Bose-Einstein condensates with equal, and opposite, momenta and observed that the usual s-wave distribution of scattered atoms was altered by the appearance of d- and g-wave contributions. This technique is expected to enable quantum simulation of exotic systems, including those predicted to support Majorana fermions.

Spin-orbit-coupled Bose-Einstein condensates.

Spin-orbit (SO) coupling--the interaction between a quantum particle's spin and its momentum--is ubiquitous in physical systems. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological insulators; it contributes to the electronic properties of materials such as GaAs, and is important for spintronic devices. Quantum many-body systems of ultracold atoms can be precisely controlled experimentally, and would therefore seem to provide an ideal platform on which to study SO coupling. Although an atom's intrinsic SO coupling affects its electronic structure, it does not lead to coupling between the spin and the centre-of-mass motion of the atom. Here, we engineer SO coupling (with equal Rashba and Dresselhaus strengths) in a neutral atomic Bose-Einstein condensate by dressing two atomic spin states with a pair of lasers. Such coupling has not been realized previously for ultracold atomic gases, or indeed any bosonic system. Furthermore, in the presence of the laser coupling, the interactions between the two dressed atomic spin states are modified, driving a quantum phase transition from a spatially spin-mixed state (lasers off) to a phase-separated state (above a critical laser intensity). We develop a many-body theory that provides quantitative agreement with the observed location of the transition. The engineered SO coupling--equally applicable for bosons and fermions--sets the stage for the realization of topological insulators in fermionic neutral atom systems.

Phases of a two-dimensional bose gas in an optical lattice.

Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of ≈60 harmonically trapped 2D Bose-Hubbard systems from a 87Rb Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol, Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.

Synthetic magnetic fields for ultracold neutral atoms.

Neutral atomic Bose condensates and degenerate Fermi gases have been used to realize important many-body phenomena in their most simple and essential forms, without many of the complexities usually associated with material systems. However, the charge neutrality of these systems presents an apparent limitation-a wide range of intriguing phenomena arise from the Lorentz force for charged particles in a magnetic field, such as the fractional quantum Hall effect in two-dimensional electron systems. The limitation can be circumvented by exploiting the equivalence of the Lorentz force and the Coriolis force to create synthetic magnetic fields in rotating neutral systems. This was demonstrated by the appearance of quantized vortices in pioneering experiments on rotating quantum gases, a hallmark of superfluids or superconductors in a magnetic field. However, because of technical issues limiting the maximum rotation velocity, the metastable nature of the rotating state and the difficulty of applying stable rotating optical lattices, rotational approaches are not able to reach the large fields required for quantum Hall physics. Here we experimentally realize an optically synthesized magnetic field for ultracold neutral atoms, which is evident from the appearance of vortices in our Bose-Einstein condensate. Our approach uses a spatially dependent optical coupling between internal states of the atoms, yielding a Berry's phase sufficient to create large synthetic magnetic fields, and is not subject to the limitations of rotating systems. With a suitable lattice configuration, it should be possible to reach the quantum Hall regime, potentially enabling studies of topological quantum computation.