Session P4: Multi-Component BECs and Mixtures

Analytical solutions to the spin-1 Bose-Einstein condensates

We present classes of exact stationary solutions for the one-dimensional coupled nonlinear Gross-Pitaevskii equations which describe the $F=1$ spinor Bose-Einstein condensates, both with and without the Zeeman splitting. The spin magnetization configurations and the spin currents are investigated. The soliton or the soliton train complexes are naturally produced.   

Geometry of Spinor Condensates with Large Spins

Laser cooled atoms with spin can become magnetically ordered in a variety of ways, like electrons in a frustrated lattice, but the phases are more geometrical in this setting. For spin one, two and three atoms, states have been predicted with a nematic symmetry (the symmetry of a toothpick), a hexagon, and an octahedron, as well as other possibilities. As the spin becomes larger, the phase diagrams become more and more complicated. I will present a geometrical way of predicting regularities in the phases as the spin increases. For a certain form of interaction, we find a phase diagram for arbitrarily large spin. (In particular, a nematic phase does not occur beyond spin 2.) We have used a mapping to a classical problem of interacting particles arranging themselves on a sphere.   

Pomeranchuk cooling of SU(N) ultracold fermions in optical lattice

We investigate thermodynamic properties of a half-filled SU($2N$) Fermi-Hubbard model in two-dimensional square lattice using the determinantal Quantum Monte Carlo simulation. We address the question how the large number of hyperfine-spin components makes thermodynamic properties of SU($N$) ultracold fermions different from the conventional Hubbard model with $N$=2. Various thermodynamic quantities such as entropy, charge fluctuations, and spin correlations have been calculated. We devote special attention to the interaction-induced adiabatic cooling: an analogue of the Pomeranchuk effect in Helium-3.   

Determinant Quantum Monte Carlo simulations on quantum magnetism of theSU(2N) ultra-cold fermions

We investigate the quantum magnetism of the repulsive $SU(2N)$-Hubbard model on a two-dimensional square lattice at half-filling. At $2N=4$, our numerical results suggest that there exists a long-range Neel ordering at large $U$. In this regime, both of the antiferromagnetic structure factor per site and the farthest two-point spin-spin correlation functions are saturated to finite values in the thermodynamic limit. The single-particle excitations are finite and the spin gaps vanish. All of above evidences support the presence of the Neel ordering in the SU(4)-Hubbard model. For $2N > 4$, such features are not explicitly observed.   

Multi-component integrable models in cold atoms

The quantum gases are intensively studied for the inspiring advances in ultra-cold atomic physics. Various kinds of lattice and gas systems are created in different dimensions. The multi-component cold atomic systems have rich phase diagrams. Our works focus on the one-dimensional integrable quantum systems. We find a series of integrable models of $Sp(2s+1)$ fermions and $SO(2s+1)$ bosons and solve them via Bethe ansatz techniques, where $s$ the hyperfine spin of the atoms. We find the paired bosons exist in both repulsive and attractive $SO(3)$ integrable bosonic gases with hyperfine spin-1. For the $Sp(2s+1)$ repulsive fermions, there are no bound states in the ground state, while 2-string bound solutions appear in the spin sector. We also calculate the spin-wave velocities and low temperature specific heat of the repulsive fermions. These systems have spin-charge separation property of Luttinger liquid. Different from the $SU(2s+1)$ repulsive models, the spin-wave velocities of the $Sp(2s+1)$ models are no longer the same. The holes of 1-strings (real rapidities) of different branches in the spin sector have a same spin-wave velocity $v_1$ and the ones of 2-strings share a same spin-wave velocity $v_2$. The two velocities are different.   

Haldane Phase of Ultra Cold Atom Gas Loaded on Pseudo-One-Dimensional Optical Lattice

Ultracold Fermi gas loaded on optical lattice (FGOL) has attracted considerable attention since its temperature, interaction, and filling factor are flexibly controllable and various quantum phases are accessible. In this study, we examine properties of pseudo-one-dimensional (P1D) FGOL obtained by including effects of the transverse excitations. At first, we prove that the P1D system at half-filling can be theoretically mapped on spin-1 Heisenberg chain. Secondly, we reveal by using DMRG scheme that Haldane phase emerges in the P1D FGOL. Finally, we clarify effects of trap potential and spin imbalance on not only the central Haldane phase but also various different magnetic structures around the Haldane phase.   

Half-quantum vortex state and its excitations in a spin-orbit coupled spinor Bose-Einstein condensate

We investigate theoretically the condensate state and collective excitations of a spin-orbit coupled spinor Bose gas in two-dimensional harmonic traps. In the weakly interacting regime, when the inter-species interaction is larger than the intra-species interaction ($g_{\uparrow \downarrow} > g$), we find that the condensate state has a half-quantum-angular-momentum vortex configuration (half-vortex state) with spatial rotational symmetry and skyrmion-type spin texture. We investigate the stability of half-vortex state in the regime when $g$ is greater than a threshold $g_c$, and in the regime when $g_{\uparrow \downarrow} < g$, by solving the Bogoliubov equations for collective density oscillations. In addition, we also investigate the dynamical properties of the half-vortex state. We present the phase diagram as a function of interatomic interaction and spin-orbit coupling.   

Searching for Non-abelian Phases in Bose-Einstein Condensate of Dy

Recently Bose-Einstein condensate of a spin 8 element, Dysprosium, has been realized. We compute the mean-field ground state and Bogoliubov excitation of Dy condensate for different scattering lengths and in presence of a magnetic field, and find various non-abelian phases in the parameter space. We suggest an experimental scheme for detecting the remaining discrete point group symmetry of these phases simply by looking at population of each spin components and the degeneracy of Goldstone modes. A BEC whose remaining symmetry is a non-abelian group can support exotic non-abelian vortices.   

Quasiparticles in a Bose-Fermi mixture in optical lattice

We investigate a mixture of interacting bosons and fermions using a generalized dynamical mean-field theory combined with the numerical renormalization group. We focus on many-body effects in the presence of the superfluidity. It is elucidated that fermionic particles are strongly renormalized by low-energy bosonic excitations via the boson-fermion interaction, giving rise to an anomalous peak structure in the density of states for fermions. We also address how the renormalization effects appear in the phases with long-range order such as a supersolid phase.   

Ultracold bosons in the presence of a second species in the Tonks-Girardeau regime: dynamics and quantum features

We develop a framework to study the interaction between two ultracold bosonic species in different regimes. One species is in the low correlation limit forming a Bose-Einstein condensate (BEC), while the other is in the strongly correlated Tonks-Girardeau regime. We use a Bose-Hubbard-like model where, due to the momentum distribution of the Tonks gas, many single particle states are considered and study the dynamics of the system by numerical simulation of the equations obtained. The atoms in the Tonks gas act as impurities submerged in the BEC, and the excitations created by their interactions with the BEC gas can be understood in terms of polarons. We focus on the fundamental quantum properties of the system and investigate the effects the condensed environment has on the Tonks-Girardeau gas as a function of the interspecies scattering strength.   

The Many-Body Correlation of Bose-Fermi Mixture in the Ring Trap

Since the realization of Bose-Einstein Condensation in alkali atoms in 1995, studies on cold atomic gases have greatly advanced. The cold atoms are precisely controlled by electromagnetism and optics, and flexible to design quantum systems. In 2001, A. G\"{o}rlitz's group has realized the Bose-Einstein condensates in the quasi-one-dimensional system [1]. One have now obtained the ideal system to study the one-dimensional many-body physics experimentally. The purpose of our study is to clarify the effect of quantum many-body correlation beyond the mean-field approximation. To accomplish this purpose, we first prepare the bosons and fermions in the ring trap [2]. We prepare the initial state in the trap with the small distortion and obtained that both kinds of particles tend to be localized. After taking off this distortion, we solved the time-dependent Schr\"{o}dinger equation. We derived the energy spectrum, density profile, and studied pair-correlation effect. Our results predict that the many-body correlation emerges, which has never been observed experimentally up to now. \\[4pt] [1] A. G\"{o}rlitz et al., Phys. Rev. Lett. 87, 130402 (2001)\\[0pt] [2] O. Morizot et al., Phys. Rev. A. 74, 023617 (2006)   

Cooling by corralling: a route to antiferromagnetism in optical lattices

Cold atoms in optical lattices have emerged as a promising tool for emulating condensed matter Hamiltonians. Current experiments have observed ``Mott insulating'' behavior in the Fermi-Hubbard model at an average entropy $S/N \approx 1 k_B$/atom. Our quantum Monte Carlo simulations [1], in agreement with other methods, show that $S/N \approx 0.65 k_B$/atom is low enough to produce antiferromagnetism (AF) at the center of a harmonic trap. However, further progress in the field requires even lower entropies that are beyond the reach of traditional cooling techniques. I have proposed a way to attain very low temperatures and entropies ($S/N < 0.03 k_B$/atom) by trapping fermions in a corral formed from another species of atoms [2]. This Fermi system can then be evolved into an antiferromagnet by morphing the lattice into a set of double wells, quasi-adiabatically. Quantum dynamics simulations have, so far, given promising results.\\[4pt] [1] Thereza Paiva, Yen Lee Loh, Mohit Randeria, Richard T. Scalettar, and Nandini Trivedi, ``Fermions in 3D optical lattices: Cooling protocol to obtain antiferromagnetism,'' PRL 107, 086401 (2011).\\[0pt] [2] Yen Lee Loh, ``Proposal for achieving very low entropies in optical lattice systems,'' arxiv:1108.0628.   

Magnetic order in the doped Hubbard model and the crossover from two- to three-dimensions: a Hartree-Fock study

We report unrestricted Hartree-Fock (UHF) results for the ground state of the single-band Hubbard model in three-dimensions (3D), with repulsive onsite interactions and nearest-neighbor hopping. Magnetic and charge properties are determined by full numerical solutions of the self-consistent UHF equation in large supercells, and quantified as a function of hole doping $h$. We focus on weak to intermediate interaction strengths, where UHF has been shown to capture the main characteristics of the magnetic correlations in two-dimensions (2D).~\footnote{J. Phys.: Condens. Matter, in press (arXiv:1107.0976v2).} We find linear spin-density wave (SDW) states with AFM order and a long wavelength modulation whose wavelength is inversely proportional to $h$. We also study the dimensional crossover from 2D to 3D as the inter-plane distance is increased.   

Continuous measurement quantum state tomography of atomic spins

Quantum state tomography is a fundamental tool in quantum information science and technology. It requires estimates of the expectation values of an ``informationally complete'' set of observables. This is, in general, a very time-consuming process that requires a large number of measurements to gather sufficient statistics. There are, however, systems in which the data acquisition can be done more efficiently. An ensemble of quantum systems can be prepared and driven by external fields while being continuously and collectively probed, producing enough information in the time evolving measurement record to estimate the initial state. Such protocol has the advantage of being fast and robust. In this talk, we present a study of a continuous-measurement quantum-state tomography protocol and its application to controlling large spin ensembles. We perform reconstruction of quantum states prepared in the 16 dimensional ground-electronic hyperfine manifolds of an ensemble of 133Cs atoms, controlled by microwaves and radio-frequency magnetic fields and probed via polarization spectroscopy. We present theoretical and experimental results of its implementation and discuss two estimation methods: constrained maximum likelihood and compressed sensing.   

Measuring spin correlations in optical lattices

The study of ultracold atoms in optical lattices has produced several groundbreaking results. A major, but presently unrealized goal, is to study quantum magnetism using atoms in optical lattices. We suggest three different experimental methods for probing both short- and long-range spin correlations of atoms in optical lattices. The first method involves an adiabatic doubling of the periodicity of the underlying lattice to probe neighboring singlet (triplet) correlations for fermions (bosons) by the occupation of the resulting vibrational ground state. The second method utilizes a time-dependent superlattice potential to generate spin-dependent transport by any number of prescribed lattice sites, and probes correlations by the resulting number of doubly occupied sites. The third method relies on the difference in tunneling times for the vibrational ground state and the first excited state. Correct timing then allows for the spin correlations to be fingerprinted. For experimentally relevant parameters, we demonstrate how all three methods yield large signatures of antiferromagnetic correlations of strongly repulsive fermionic atoms in a single shot of the experiment.