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.

We analyze the spin dynamics of an out-of-equilibrium large spin dipolar atomic Bose gas in an optical lattice. We observe a smooth crossover from a complex oscillatory behavior to an exponential behavior throughout the Mott-to-superfluid transition. While both of these regimes are well described by our theoretical models, we provide data in the intermediate regime where dipolar interactions, contact interactions, and superexchange mechanisms compete. In this strongly correlated regime, spin dynamics and transport are coupled, which challenges theoretical models for quantum magnetism. DOI: 10.1103/PhysRevA.93.021603 Dipolar atoms and molecules loaded in optical lattices are a promising platform to study quantum many-body physics [1,2], and, in particular, quantum magnetism [3][4][5][6][7][8]. In dipolar systems, direct spin-spin interactions are provided by the dipole-dipole interaction (DDI) without relying on a superexchange mechanism [9]. Although magnetization changing collisions associated with the anisotropic character of dipolar interactions may introduce interesting exotic quantum phases [10][11][12][13], these off-resonant processes are often negligible. Then, dipolar interactions reduce to the following Hamiltonian,where2 (μ 0 being the magnetic permeability of vacuum, g the Landé factor, and μ B the Bohr magneton), r is the distance between atoms, θ 1,2 the angle between the magnetic field and the interatomic axis, and S ±,z i are the spin operators acting on atom i. This Hamiltonian, known as the secular dipolar Hamiltonian in the context of nuclear magnetic resonance [14], bears strong similarities to the XXZ model of quantum magnetism [9].Experimental investigations of such spin Hamiltonians have recently started, with dipolar molecules [15], and magnetic [16] and Rydberg [17] atoms, which have raised great interest [8,[10][11][12][13]18]. While these studies have focused on a localized regime where the particles are pinned to a well-defined position, in this Rapid Communication we investigate the case where magnetic atoms are free to move in an optical lattice. Thus spin dynamics and transport are coupled due to an interplay between superexchange mechanisms and dipolar spin exchange. Our experiment provides data in this regime which challenges theoretical descriptions.We study the spin-exchange dynamics of magnetic chromium 52 Cr bosonic atoms loaded in a three-dimensional (3D) optical lattice, across the Mott-to-superfluid transition [19]. We observe, as a function of the lattice depth, a crossover between two distinct behaviors. In the Mott phase, the spin dynamics displays a complex oscillatory behavior, as already studied in Ref. [16]. Although the physics is inherently many body due to strong correlations and the long-range nature of the dipolar interactions, we provide a quantitative interpretation of the oscillations due to intersite DDIs, using a simple model based on perturbation theory. In the superfluid regime, the spin dynamics shows an exponential behavior. Our data are then in go...

We study dipolar relaxation of a chromium Bose-Einstein condensate loaded into a three-dimensional (3D) optical lattice. We observe dipolar relaxation resonances when the magnetic energy released during the inelastic collision matches an excitation towards higher-energy bands. Spectroscopy of these resonances for two orientations of the magnetic field provides a 3D band spectroscopy of the lattice. The narrowest resonance is registered for the lowest excitation energy. Its line shape is sensitive to the on-site interaction energy. We use such sensitivity to probe number squeezing in a Mott insulator. Quantum dipolar gases have attracted much attention in recent years [1][2][3]. Following the seminal studies of Cr BoseEinstein condensates (BECs) [4][5][6][7] and the recent production of Er [8] and Dy [9,10] quantum gases, it is natural to study dipolar gases confined in optical lattices. Dipolar gases in lattices provide an ideal playground for studying quantum phase transitions in a system with long-range interactions. The unique properties of dipole-dipole interactions (DDIs) present direct similarities with the Heisenberg model of quantum magnetism [11][12][13][14] and lead to novel quantum phases displaying possible long-range ordering in lattices [15][16][17]. The nonlinear coupling between spin and orbital degrees of freedom provided by dipolar interactions [18][19][20][21][22][23] is particularly interesting. Although at large magnetic field, this coupling leads to fast dipolar relaxation losses for atoms in excited spin states [24], we have recently demonstrated that working at low magnetic field enables the study of multicomponent quantum gases with free magnetization [25,26]. Here we extend this research to include dipolar particles trapped in optical lattices and directly observe discrete, atom-number-dependent coupling between spin and orbital degrees of freedom.We study the magnetization dynamics of 52 Cr atoms loaded in a deep three-dimensional (3D) optical lattice. Under our experimental conditions, we produce a Mott insulator state with a core of two particles per site [27,28]. Compared to our previous results in two-dimensional (2D) optical lattices [23], the 3D confinement allows us to reach a new regime, where on-site dipolar relaxation is inhibited unless the released magnetic energy matches a lattice band excitation: dipolar relaxation is a resonant process. The interplay between the anisotropies of dipolar interaction and of lattice sites leads to a resonance spectrum which depends on the magnetic-field orientation. Measuring demagnetization as a function of the magnetic field for two orientations allows for spectroscopy of the 3D lattice band structure. We operate in an asymmetric 3D lattice such that the narrowest resonance is found to be sensitive to the on-site atom-number distribution and reveals the number-squeezed distribution of the Mott state. Changing our experimental conditions, we prepare sites containing three atoms. Spin-orbit coupling DDI then produces three-body states that a...

We experimentally study the spin dynamics of mesoscopic ensembles of ultracold magnetic spin-3 atoms located in two separated wells of an optical dipole trap. We use a radio-frequency sweep to selectively flip the spin of the atoms in one of the wells, which produces two separated spin domains of opposite polarization. We observe that these engineered spin domains are metastable with respect to the long-range magnetic dipolar interactions between the two ensembles. The absence of inter-cloud dipolar spin-exchange processes reveals a classical behavior, in contrast to previous results with atoms loaded in an optical lattice. When we merge the two subsystems, we observe spin-exchange dynamics due to contact interactions which enable the first determination of the s-wave scattering length of 52Cr atoms in the S=0 molecular channel a_0=13.5^{+11}_{-10.5}a_B (where a_B is the Bohr radius).Comment: 9 pages, 7 figure

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