Out-of-equilibrium quantum magnetism and thermalization in a spin-3 many-body dipolar lattice system.

Understanding quantum thermalization through entanglement build up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Spin systems made of long-range interacting atoms offer an ideal experimental platform to investigate this question. Here, we study the spin dynamics and approach towards local thermal equilibrium of a macroscopic ensemble of S = 3 chromium atoms pinned in a three dimensional optical lattice and prepared in a pure coherent spin state, under the effect of magnetic dipole-dipole interactions. Our isolated system thermalizes under its own dynamics, reaching a steady state consistent with a thermal ensemble with a temperature dictated from the system's energy. The build up of quantum correlations during the dynamics is supported by comparison with an improved numerical quantum phase-space method. Our observations are consistent with a scenario of quantum thermalization linked to the growth of entanglement entropy.

Collective Spin Modes of a Trapped Quantum Ferrofluid.

We report on the observation of a collective spin mode in a spinor Bose-Einstein condensate. Initially, all spins point perpendicular to the external magnetic field. The lowest energy mode consists of a sinusoidal oscillation of the local spin around its original axis, with an oscillation amplitude that linearly depends on the spatial coordinates. The frequency of the oscillation is set by the zero-point kinetic energy of the BEC. The observations are in excellent agreement with hydrodynamic equations. The observed spin mode has a universal character, independent of the atomic spin and spin-dependent contact interactions.

Competition between Bose-Einstein Condensation and Spin Dynamics.

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation by rapidly cooling a chromium multicomponent Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin-excited states. Small metastable spinor condensates are, nevertheless, produced, and they manifest in strong spin fluctuations.

Cooling of a Bose-Einstein Condensate by Spin Distillation.

We propose and experimentally demonstrate a new cooling mechanism leading to purification of a Bose-Einstein condensate (BEC). Our scheme starts with a BEC polarized in the lowest energy spin state. Spin excited states are thermally populated by lowering the single particle energy gap set by the magnetic field. Then, these spin-excited thermal components are filtered out, which leads to an increase of the BEC fraction. We experimentally demonstrate such cooling for a spin 3 ^{52}Cr dipolar BEC. Our scheme should be applicable to Na or Rb, with the perspective to reach temperatures below 1 nK.

Nonequilibrium quantum magnetism in a dipolar lattice gas.

We report on the realization of quantum magnetism using a degenerate dipolar gas in an optical lattice. Our system implements a lattice model resembling the celebrated t-J model. It is characterized by a nonequilibrium spinor dynamics resulting from intersite Heisenberg-like spin-spin interactions provided by nonlocal dipole-dipole interactions. Moreover, due to its large spin, our chromium lattice gases constitute an excellent environment for the study of quantum magnetism of high-spin systems, as illustrated by the complex spin dynamics observed for doubly occupied sites.

Anisotropic excitation spectrum of a dipolar quantum Bose gas.

We measure the excitation spectrum of a dipolar chromium Bose-Einstein condensate with Raman-Bragg spectroscopy. The energy spectrum depends on the orientation of the dipoles with respect to the excitation momentum, demonstrating an anisotropy that originates from the dipole-dipole interactions between the atoms. We compare our results with the Bogoliubov theory based on the local density approximation and, at large excitation wavelengths, with the numerical simulations of the time-dependent Gross-Pitaevskii equation. Our results show an anisotropy of the speed of sound.

Thermodynamics of a Bose-Einstein condensate with free magnetization.

We study thermodynamic properties of a gas of spin 3(52)Cr atoms across Bose-Einstein condensation. Magnetization is free, due to dipole-dipole interactions. We show that the critical temperature for condensation is lowered at extremely low magnetic fields, when the spin degree of freedom is thermally activated. The depolarized gas condenses in only one spin component, unless the magnetic field is set below a critical value, below which a nonferromagnetic phase is favored. Finally, we present a spin thermometry efficient even below the degeneracy temperature.

Spontaneous demagnetization of a dipolar spinor Bose gas in an ultralow magnetic field.

We study the spinor properties of S = 3 (52)Cr condensates, in which dipole-dipole interactions allow changes in magnetization. We observe a demagnetization of the Bose-Einstein condensate (BEC) when the magnetic field is quenched below a critical value corresponding to a phase transition between a ferromagnetic and a nonpolarized ground state, which occurs when spin-dependent contact interactions overwhelm the linear Zeeman effect. The critical field is increased when the density is raised by loading the BEC in a deep 2D optical lattice. The magnetization dynamics is set by dipole-dipole interactions.

Spin relaxation and band excitation of a dipolar Bose-Einstein condensate in 2D optical lattices.

We observe interband transitions mediated by dipole-dipole interactions for an array of 1D quantum gases of chromium atoms, trapped in a 2D optical lattice. Interband transitions occur when dipolar relaxation releases an energy larger than the lattice band gap. For symmetric lattice sites, and a magnetic field parallel to the lattice axis, we compare the measured dipolar relaxation rate with a Fermi golden rule calculation. Below a magnetic field threshold, we obtain an almost complete suppression of dipolar relaxation, leading to metastable 1D gases in the highest Zeeman state.

Collective excitations of a dipolar Bose-Einstein condensate.

We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas-Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a Gaussian ansatz.

Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas.

We investigate the correlation properties of a one-dimensional interacting Bose gas by loading a magnetically trapped 87Rb Bose-Einstein condensate (BEC) into a deep two-dimensional optical lattice. We measure the three-body recombination rate for both the BEC in the magnetic trap and the BEC loaded into the optical lattice. The recombination rate coefficient is a factor of 7 smaller in the lattice, which we interpret as a reduction in the local three-body correlation function in the 1D case. This is a signature of correlation intermediate between that of the uncorrelated, phase coherent, 1D, mean-field regime and the strongly correlated Tonks-Girardeau regime.

Quantum information with neutral atoms as qubits.

One of the essential features of a quantum computer is a quantum 'register' of well-characterized qubits. Neutral atoms in optical lattices are a natural candidate for such a register. We have demonstrated a patterned-loading technique that can be used to load atoms into large arrays of tightly confined but optically resolvable lattice sites. We have also seen preliminary indications of the Mott-insulator transition, which provides a route for single-atom initialization of the individual sites. Combining the two experiments should allow for large arrays of individually addressable single atoms, a system which provides a starting point for further quantum computation studies.

Resonant coupling in the formation of ultracold ground state molecules via photoassociation.

We demonstrate the existence of a new mechanism for the formation of ultracold molecules via photoassociation of cold cesium atoms. The experimental results, interpreted with numerical calculations, suggest that a resonant coupling between vibrational levels of the 0+u (6s+6p1/2) and (6s+6p3/2) states enables formation of ultracold molecules in vibrational levels of the ground state well below the 6s+6s dissociation limit. Such a scheme should be observable with many other electronic states and atomic species.

Photoassociative spectroscopy as a self-sufficient tool for the determination of the Cs triplet scattering length

In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the s-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel f = 4, m(f) = 4. We analyzed the intensities of the lines associated with the Cs2 0(-)(g) state dissociating to the 6s(1/2)+6p(3/2) asymptote. This yields a value of the Cs triplet state scattering length, a(T) = -530a(0), while consistency requirements impose a value of the multipole ground state molecular coefficient, C6 = 6510 a.u.