Observation of fragmentation of a spinor Bose-Einstein condensate.

Weakly interacting Bose gases usually form Bose-Einstein condensates in which most particles occupy the same single-particle state. However, when this state cannot realize a continuous symmetry of the many-body Hamiltonian, a fragmented condensate exhibiting the expected symmetry may emerge. Here, we produced a three-fragment condensate for a mesoscopic spin-1 gas of about 100 atoms, with anti-ferromagnetic interactions and vanishing collective spin. Using a spin-resolved detection approaching single-atom resolution, we show that the reconstructed state is close to the expected many-body ground state, whereas one-body observables are the same as for a completely mixed state. Our results highlight how the interplay between symmetry and interactions generates entanglement in a mesoscopic quantum system.

From Many-Body Oscillations to Thermalization in an Isolated Spinor Gas.

The dynamics of a many-body system can take many forms, from a purely reversible evolution to fast thermalization. Here we show experimentally and numerically that an assembly of spin-1 atoms all in the same spatial mode allows one to explore this wide variety of behaviors. When the system can be described by a Bogoliubov analysis, the relevant energy spectrum is linear and leads to undamped oscillations of many-body observables. Outside this regime, the nonlinearity of the spectrum leads to irreversibility, characterized by a universal behavior. When the integrability of the Hamiltonian is broken, a chaotic dynamics emerges and leads to thermalization, in agreement with the eigenstate thermalization hypothesis paradigm.

Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level.

Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.

Direct imaging of topological edge states in cold-atom systems.

Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes--guaranteed by the existence of nontrivial topological invariants--have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas and imaging its time evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.

Detecting chiral edge states in the Hofstadter optical lattice.

We propose a realistic scheme to detect topological edge states in an optical lattice subjected to a synthetic magnetic field, based on a generalization of Bragg spectroscopy sensitive to angular momentum. We demonstrate that using a well-designed laser probe, the Bragg spectra provide an unambiguous signature of the topological edge states that establishes their chiral nature. This signature is present for a variety of boundaries, from a hard wall to a smooth harmonic potential added on top of the optical lattice. Experimentally, the Bragg signal should be very weak. To make it detectable, we introduce a "shelving method," based on Raman transitions, which transfers angular momentum and changes the internal atomic state simultaneously. This scheme allows us to detect the weak signal from the selected edge states on a dark background, and drastically improves the detectivity. It also leads to the possibility to directly visualize the topological edge states, using in situ imaging, offering a unique and instructive view on topological insulating phases.

Quantum spin dynamics of mode-squeezed Luttinger liquids in two-component atomic gases.

We report on the observation of many-body spin dynamics of interacting, one-dimensional (1D) ultracold bosonic gases with two spin states. By controlling the nonlinear atomic interactions close to a Feshbach resonance we are able to induce a phase diffusive many-body spin dynamics of the relative phase between the two components. We monitor this dynamical evolution by Ramsey interferometry, supplemented by a novel, many-body echo technique, which unveils the role of quantum fluctuations in 1D. We find that the time evolution of the system is well described by a Luttinger liquid initially prepared in a multimode squeezed state. Our approach allows us to probe the nonequilibrium evolution of one-dimensional many-body quantum systems.

Sum-frequency generation of 589 nm light with near-unit efficiency.

We report on a laser source at 589 nm based on sum-frequency generation of two infrared laser at 1064 nm and 1319 nm. Output power as high as 800 mW is achieved starting from 370 mW at 1319 nm and 770 mW at 1064 nm, corresponding to converting roughly 90% of the 1319 nm photons entering the cavity. The power and frequency stability of this source are ideally suited for cooling and trapping of sodium atoms.

Boson Mott insulators at finite temperatures.

We discuss the finite temperature properties of ultracold bosons in optical lattices in the presence of an additional, smoothly varying potential, as in current experiments. Three regimes emerge in the phase diagram: a low-temperature Mott regime similar to the zero-temperature quantum phase, an intermediate regime where Mott insulator features persist, but where superfluidity is absent, and a thermal regime where features of the Mott insulator state have disappeared. We obtain the thermodynamic functions of the Mott phase in the latter cases. The results are used to estimate the temperatures achieved by adiabatic loading in current experiments. We point out the crucial role of the trapping potential in determining the final temperature, and suggest a scheme for further cooling by adiabatic decompression.

Formation of spatial shell structure in the superfluid to Mott insulator transition.

We report on the direct observation of the transition from a compressible superfluid to an incompressible Mott insulator by recording the in-trap density distribution of a Bosonic quantum gas in an optical lattice. Using spatially selective microwave transitions and spin-changing collisions, we are able to locally modify the spin state of the trapped quantum gas and record the spatial distribution of lattice sites with different filling factors. As the system evolves from a superfluid to a Mott insulator, we observe the formation of a distinct shell structure, in good agreement with theory.

Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition.

The evolution of on-site number fluctuations of ultracold atoms in optical lattices is experimentally investigated by monitoring the suppression of spin-changing collisions across the superfluid-Mott insulator transition. For low atom numbers, corresponding to an average filling factor close to unity, large on-site number fluctuations are necessary for spin-changing collisions to occur. The continuous suppression of spin-changing collisions is thus direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed until a threshold atom number, consistent with the number where a Mott plateau with doubly occupied sites is expected to form.

Coherent collisional spin dynamics in optical lattices.

We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin-changing collisions. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.

Phase coherence of an atomic Mott insulator.

We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.

Spatial quantum noise interferometry in expanding ultracold atom clouds.

In a pioneering experiment, Hanbury Brown and Twiss (HBT) demonstrated that noise correlations could be used to probe the properties of a (bosonic) particle source through quantum statistics; the effect relies on quantum interference between possible detection paths for two indistinguishable particles. HBT correlations--together with their fermionic counterparts--find numerous applications, ranging from quantum optics to nuclear and elementary particle physics. Spatial HBT interferometry has been suggested as a means to probe hidden order in strongly correlated phases of ultracold atoms. Here we report such a measurement on the Mott insulator phase of a rubidium Bose gas as it is released from an optical lattice trap. We show that strong periodic quantum correlations exist between density fluctuations in the expanding atom cloud. These spatial correlations reflect the underlying ordering in the lattice, and find a natural interpretation in terms of a multiple-wave HBT interference effect. The method should provide a useful tool for identifying complex quantum phases of ultracold bosonic and fermionic atoms.