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The characterization of quantum magnetism in a large spin ($geq 1$) system naturally involves both spin-vectors and -tensors. While certain types of spin-vector (e.g., ferromagnetic, spiral) and spin-tensor (e.g., nematic in frustrated lattices) orders have been investigated separately, the coexistence and correlation between them have not been well explored. Here we propose a novel quantum spiral spin-tensor order on a spin-1 Heisenberg chain subject to a spiral spin-tensor Zeeman field, which can be experimentally realized using a Raman-dressed cold atom optical lattice. We develop a method to fully characterize quantum phases of such spiral tensor magnetism with the coexistence of spin-vector and spin-tensor orders as well as their correlations using eight geometric parameters. Our method provides a powerful tool for characterizing spin-1 quantum magnetism and opens an avenue for exploring novel magnetic orders and spin-tensor electronics/atomtronics in large-spin systems.
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We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with true spin-orbit coupling, involving spin-changing hoppings.
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Quantum magnetism describes the properties of many materials such as transition metal oxides and cuprate superconductors. One of its elementary processes is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the full spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, a post-selection of the data allows to reduce the effect of temperature, giving access to a space- and time-resolved measurement of the quantum-coherent propagation of a magnetic excitation in the Heisenberg model. Extending the study to the baths superfluid regime, we determine quantitatively how the bath strongly affects the motion of the impurity. The experimental data shows a remarkable agreement with theoretical predictions allowing us to determine the effect of temperature on the coherence and velocity of impurity motion. Our results pave the way for a new approach to study quantum magnetism, mobile impurities in quantum fluids, and polarons in lattice systems.
Phases of matter are conventionally characterized by order parameters describing the type and degree of order in a system. For example, crystals consist of spatially ordered arrays of atoms, an order that is lost as the crystal melts. Like- wise in ferromagnets, the magnetic moments of the constituent particles align only below the Curie temperature, TC. These two examples reflect two classes of phase transitions: the melting of a crystal is a first-order phase transition (the crystalline order vanishes abruptly) and the onset of magnetism is a second- order phase transition (the magnetization increases continuously from zero as the temperature falls below TC). Such magnetism is robust in systems with localized magnetic particles, and yet rare in model itinerant systems where the particles are free to move about. Here for the first time, we explore the itinerant magnetic phases present in a spin-1 spin-orbit coupled atomic Bose gas; in this system, itinerant ferromagnetic order is stabilized by the spin-orbit coupling, vanishing in its absence. We first located a second-order phase transition that continuously stiffens until, at a tricritical point, it transforms into a first- order transition (with observed width as small as h x 4 Hz). We then studied the long-lived metastable states associated with the first-order transition. These measurements are all in agreement with theory.
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