Session U5: Spin-orbit Coupled and Low Dimensional Gases

Magnetically Generated Spin-Orbit Coupling for Ultracold Atoms

We present a new technique for producing two- and three-dimensional Rashba-type spin-orbit couplings for ultracold atoms without involving light. The method relies on a sequence of pulsed inhomogeneous magnetic fields imprinting suitable phase gradients on the atoms. For sufficiently short pulse durations, the time-averaged Hamiltonian well approximates the Rashba Hamiltonian. Higher order corrections to the energy spectrum are calculated exactly for spin-1/2 and perturbatively for higher spins. The pulse sequence does not modify the form of rotationally symmetric atom-atom interactions. Finally, we present a straightforward implementation of this pulse sequence on an atom chip.   

Dark Solitons with Majorana Fermions in Spin-Orbit-Coupled Fermi Gases

Solitons, which maintain their solitary wavepacket shape while traveling, are crucially important in many physical branches. Recently, dark solitons have been experimentally observed in spin- balanced ultra-cold degenerate Fermi gases. Here we show that a single dark soliton can also exist in a spin-orbit-coupled Fermi gas with a high spin imbalance, where spin-orbit coupling favors uniform superfluids over non-uniform Fulde-Ferrell-Larkin-Ovchinnikov states, leading to dark soliton excitations in highly imbalanced gases. Above a critical spin imbalance, two topological Majorana fermions (MFs) without interactions can coexist inside a dark soliton, paving a way for manipulating MFs through controlling solitons. At the topological transition point, the atom density contrast across the soliton suddenly vanishes, suggesting a signature for identifying topological solitons.   

Majorana fermions in quasi-1D and higher dimensional ultracold optical lattices

We show that Majorana fermions (MFs) exist in quasi-one dimensional (quasi-1D) and higher dimensional fermionic optical lattices with strictly 1D spin-orbit coupling which has already been realized in experiments. For a quasi-1D topological BCS superfluid, there are multiple MFs at each end which are topologically protected by a chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero energy flat band. An additional experimentally tunable in-plane Zeeman field drives the system to a topological Fulde-Ferrell (FF) superfluid phase. We find that even though the multiple MFs are robust against the in-plane Zeeman field if the order parameters at the different chains are enforced to be identical, they are destroyed in the self-consistently obtained FF phase where the order parameters are inhomogeneous on the boundaries. Our results are useful to guide the experimentalists on searching for MFs in the context of ultracold fermionic atoms.   

Realization and Detection of Three Dimensional Chiral Topological Insulators in Optical Lattices

Chiral topological insulators are protected by the chiral symmetry, which does not occur naturally in condensed matter systems. Here, we propose an experimental scheme to realize and detect chiral topological insulators in three dimensions (3D) with cold atoms in optical lattices. Three nearly degenerate internal states are used and all terms in the Hamiltonian are realized by two-photon Raman transitions. Unlike time-reversal-invariant $Z_{2}$ topological insulators, these chiral topological insulators are characterized by a $Z$ index. A notable feature of the model Hamiltonian is the presence of an exactly zero-energy flat band with nontrivial topology. The macroscopic degeneracy may provide an excellent testing ground for fractional topological physics in 3D, as it occurred in 2D fractional quantum Hall states. We show that Lifshitz transitions and the symmetry-protected Dirac cones can be probed through time-of-flight measurements and momentum-resolved interband transitions. The flat band can be detected via atomic density measurements in the trap.   

Breakdown of the scale invariance in a near-Tonks-Girardeau gas: some exact results and beyond

In this Letter, we consider the elementary monopole excitations of the harmonically trapped Bose gas in the vicinity of Tonks-Girardeau limit. Using Girardeau's Fermi-Bose duality and subsequently, an effective fermion-fermion odd-wave interaction, we obtain the dominant correction to the scaleinvariance- protected value of the excitation frequency. We produce a series of diffusion Monte Carlo results that confirm our analytic perturbative value for three particles. And less expectedly, our result stands in an excellent agreement with the result of a hydrodynamic simulation of the collective excitations in the limit of a large number of atoms (with the Lieb-Liniger equation of state as an input). The sub-leading term in the near-Tonks-Girardeau expansion of the sum rule upper bound to the monopole frequency, by Menotti and Stringari [Phys. Rev. A 66, 043610 (2002)], also gives the same number. Surprisingly it was found that the usually successful hydrodynamic perturbation theory predicts a shift that is 9/4 higher than its ab initio numerical counterpart. We conjecture that the sharp boundary of the cloud in local density approximation-characterized by an infinite density gradient-renders the perturbation theory for the collective excitation frequencies inapplicable.   

Traces of Integrability in Relaxation of One-Dimensional Two-Mass Mixtures

We study relaxation in a one-dimensional two-mass mixture of hard-core particles. Special attention is paid to the region of light-to-heavy mass ratios around $m/M = \sqrt{5}-2 = 0.236\ldots$. At this mass ratio, each heavy-light-heavy subsystem constitutes a little known non-equal-mass generalization of Newton's Cradle, and an anomalous slow-down of relaxation is expected as a result. We further list and classify all other instances of integrability in the one-dimensional three-body hard-core systems, where integrability is especially prominent at the quantum level and leads to the famous ``scattering without diffraction'' phenomenon. The principal experimental application of our results is with two-specie mixtures in optical lattices, in which the effective masses---that can be controlled at will---are assumed to replace the real ones.   

Relaxation and thermalization dynamics in the one-dimensional Bose-Hubbard-model

Motivated by experiments recently carried out with ultracold atomic gases [1], we study the relaxation and thermalization dynamics of several observables in the one-dimensional Bose-Hubbard-model with integer filling after a global interaction quantum quench. Using exact diagonalization, we analyze the distribution of the diagonal matrix elements and the energy distribution of initial states in the framework of the eigenstate thermalization hypothesis, discussing its applicability in different regimes of U/J. We observe that time-averages of typical observables are well described by standard statistical ensembles. \\[4pt] [1] Ronzheimer et al., Phys. Rev. Lett., 110, 205301 (2013)   

Universal Scaling Properties of N-Body States in Low Dimensions

In this work, the scaling properties of $N$ attractive bosons are examined using the functional integral formalism. The energy levels for the low lying and high lying excitations are found. Using the same scaling anszats, it is possible to obtain quite robust results on the maximum number of states and the lifetime of said states.