Session N7: Spinor Systems

Magnon Interferometry in a ${}^{87}$Rb Spinor Condensate

Low temperature properties of a many-body system are typically governed by the lowest energy excitations. In many magnetic system, these low energy excitations are magnons, a Goldstone boson created by spontaneous symmetry breaking of the order parameter. We report on performing interferometry with coherent magnon waves to measure the magnon dispersion relation and gap in a spin-1 ferromagnetic rubidium spinor condensate. We find a magnon mass slightly heavier than predicted by mean-field calculations of condensate with contact interactions. We also observe a nonzero gap, consistent with magnetic dipole-dipole interactions.   

Creation of monopole spin textures and synthetic fields in a Bose-Einstein condensate

We create two types of two-dimensional monopole spin textures in a spinor Bose-Einstein condensate using a stimulated optical Raman interaction. The first is a topological monopole spin texture, characterized by a radial local spin. The second has a cross-disgyration local spin that corresponds to a radial synthetic field in the vorticity of the condensate. Both of these structures are generated by engineering vortices of opposite handedness in opposite magnetic Zeeman spin states with an additional precisely-tuned relative phase between the spin states. We control and measure this relative phase using atom optics polarimetry [1] and verify the vortex handedness using atom interferometry. This optical wavefunction engineering technique will allow us to generate multiple point defects within the condensate and study their interaction. \\[4pt] [1] J. T. Schultz, A. Hansen, and N. P. Bigelow. ``A Raman Waveplate for Spinor Bose-Einstein condensates.'' Optics Letters {\bf 39}, 4271 (2014).   

Magnetic Fluctuations in a trapped binary Bose gas

We demonstrate that measurements of number fluctuations within finite cells provide a direct means to study scaling in a trapped two-component, or binary Bose gas. This system supports a second-order quantum phase transition between miscible (co-spatial) and immiscible states that is driven by a diverging susceptibility to magnetic fluctuations. As the transition is approached from the miscible side, the magnetic susceptibility is found to diverge, but with an exponent that depends strongly on the geometry and orientation of the observation cell. We show that the behavior expected in the homogeneous gas, can be recovered by using an observation cell that covers half of the trapped system. Interestingly, as the transition is approached from the immiscible (symmetry-broken) side, the magnetic susceptibility exhibits a scaling, but with a non-trivial exponent.   

Singular Atom Optics with Spinor BECs

We create and study singular spin textures in pseudo-spin-1/2 BECs. A series of two-photon Raman interactions allows us to not only engineer the spinor wavefunction but also perform the equivalent of atomic polarimetry on the BEC. Adapting techniques from optical polarimetry, we can image two-dimensional maps of the atomic Stokes parameters, thereby fully reconstructing the atomic wavefunction. In a spin-1/2 system, we can represent the local spin superposition with ellipses in a Cartesian basis. The patterns that emerge from the major axes of the ellipses provide fingerprints of the singularities that enable us to classify them as lemons, stars, saddles, or spirals similar to classification schemes for singularities in singular optics, condensed matter, and liquid crystals. These techniques may facilitate the study of geometric Gouy phases in matter waves as well as provide an avenue for utilizing topological structures as quantum gates.   

Low energy damping of collective modes in spinor Bose-Fermi mixtures

Motivated by the recent experimental push to study quasiparticle excitations in Bose-Fermi mixtures [1,2] we theoretically study the low energy bosonic excitations in an ultra-cold three-dimensional spinor Bose-Fermi mixture [3]. In particular, we consider a spin-1 Bose gas forming either a ferromagnetic or polar superfluid interacting with a spin-1/2 Fermi gas. Using field theoretic techniques we show the Bogoliubov quasiparticles become damped at low energy with a damping rate that is linear in momentum while the linear dispersion is preserved with a renormalized sound velocity. For the polar superfluid we find both density and spin modes become damped, whereas for the ferromagnetic superfluid only the density mode becomes damped. Such a damping mechanism is drastically different then known damping mechanisms in Bose gases (Baliaev and Landau) and is due to the presence of the Fermi surface and gapless particle-hole excitations. \\[4pt] [1] H. Hara, et. al. , Journal of the Physical Society of Japan 83, 014003 (2014).\\[0pt] [2] I. Ferrier-Barbut, et. al., Science 345, 1035 (2014).\\[0pt] [3] J. H. Pixley, X. Li, and S. Das Sarma, arXiv:1501.05015 (2015).   

Antiferromagnetic spinor condensates in a two-dimensional optical lattice

We experimentally demonstrate that spin dynamics and the phase diagram of spinor condensates can be conveniently tuned by a two-dimensional optical lattice. Spin population oscillations and a lattice-tuned separatrix in phase space are observed in every lattice where a substantial superfluid fraction exists. In a sufficiently deep lattice, we observe a phase transition from a longitudinal polar phase to a broken-axisymmetry phase in steady states of lattice-confined spinor condensates. The steady states are found to depend sigmoidally on the lattice depth and exponentially on the magnetic field. We also introduce a phenomenological model that semi-quantitatively describes our data without adjustable parameters.   

Sum rules for spin-$1/2$ quantum gases in well-defined-spin states

A many-body eigenstate of spin-$1/2$ atoms with the defined total spin is represented as a sum of products of the spin and spatial wavefunctions, dependent on spins or coordinates, respectively, of all atoms. Unless the total spin has the maximal allowed value, the spin and spatial functions belong to multidimensional, non-Abelian, irreducible representations of the symmetric group, beyond the conventional paradigm of symmetric-antisymmetric functions. The symmetric group methods allow to evaluate the matrix elements between these wavefunctions for spin-dependent external fields and two-body interactions. These matrix elements agree to the selection rules [1]. Explicit dependence on the total spin projection is obtained [2] using the Wigner-Eckart theorem. Analytical expressions are obtained [2] for sums of the matrix elements and sums of their squared modules over irreducible representations. The sum rules are applied to perturbative analysis of energy spectra.\\[4pt] [1] V.A. Yurovsky, Phys. Rev. Lett. {\bf 113}, 200406 (2014).\\[0pt] [2] V.A. Yurovsky, arXiv:1501.06182.   

Spinor dynamics in a partially Bose-condensed sodium gas

Spin-exchange collisions have been shown to drive coherent population oscillations of the F=1 ground state magnetic sublevels in both a sodium Bose-Einstein condensate and in a non-condensed Bose gas. We investigate the spin dynamics of a partially Bose-condensed gas where the normal and condensed fractions are nearly equal. Our experiments show population oscillations in both the thermal and condensed components, accompanied by an oscillation in the momentum distribution of the thermal gas. We present evidence of spin-oscillation-dependent cooling of the thermal component due to the transfer of atoms from the condensate and discuss the dynamics of spin-1 BEC/thermal mixtures.   

Coherent heteronuclear spin dynamics in an ultracold spin-1 mixture

We report the observation of interspecies spin-spin interaction driven coherent heteronuclear spin dynamics in an ultracold spinor mixture, which manifests itself as periodical and well correlated magnetization transfer between two atomic species. In particular, we investigate the magnetic field dependence and control of the spin dynamics, and find excellent agreement with a many-body theoretical model. Furthermore, we present a unique knob for fine control of spinor mixtures with species dependent vector light shift.