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 f
erromagnets, 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.
We explore the time evolution of quasi-1D two component Bose-Einstein condensates (BECs) following a quench from one component BECs with a ${rm U}(1)$ order parameter into two component condensates with a ${rm U}(1)shorttimes{rm Z}_2$ order parameter
. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifing any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin polarized domains, which are far from the systems ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is fully consistent with our stochastic-projected Gross-Pitaevskii calculation.
We study laser induced spin-orbit (SO) coupling in cold atom systems where lasers couple three internal states to a pair of excited states, in a double tripod topology. Proper choice of laser amplitudes and phases produces a Hamiltonian with a doubly
degenerate ground state separated from the remaining excited eigenstates by gaps determined by the Rabi frequencies of the atom-light coupling. After eliminating the excited states with a Born- Oppenheimer approximation, the Hamiltonian of the remaining two states includes Dresselhaus (or equivalently Rashba) SO coupling. Unlike earlier proposals, here the SO coupled states are the two lowest energy dressed spin states and are thus immune to collisional relaxation. Finally, we discuss a specific implementation of our system using Raman transitions between different hyperfine states within the electronic ground state manifold of nuclear spin I = 3/2 alkali atoms.
