Ultracold atomic Bose and Fermi spinor gases in optical lattices

Eckert, K.; Zawitkowski, L.; Leskinen, M. J.; Sanpera, Anna; Lewenstein, Maciej

doi:10.1088/1367-2630/9/5/133

Cited by 27 publications

(29 citation statements)

References 95 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such superexchange interactions are believed to play an important role in the context of high-T c superconductivity (9). Furthermore, they can form the basis for the generation of robust quantum gates similar to recent work in electronic double quantum dot systems (10, 11), and can be used for the efficient generation of multi-particle entangled states (12, 13), as well as for the production of many-body quantum phases with topological order (14,15,16).We report on the direct observation of superexchange interactions with ultracold atoms in optical lattices (17,18). Previous experiments have shown that spin-spin interactions between neighboring atoms can be implemented in discrete time steps (19,20) by bringing the atoms together on a single site and carrying out controlled collisions (21,20,22) or onsite exchange interactions (23).…”

mentioning

confidence: 83%

Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices

Trotzky

Cheinet

Fölling

et al. 2008

Science

683

895

View full text Add to dashboard Cite

These authors contributed equally to this work.Quantum mechanical superexchange interactions form the basis of quantum magnetism in strongly correlated electronic media. We report on the direct measurement of superexchange interactions with ultracold atoms in optical lattices. After preparing a spin-mixture of ultracold atoms in an antiferromagnetically ordered state, we measure a coherent superexchange-mediated spin dynamics with coupling energies from 5 Hz up to 1 kHz. By dynamically modifying the potential bias between neighboring lattice sites, the magnitude and sign of the superexchange interaction can be controlled, thus allowing the system to be switched between antiferromagnetic or ferromagnetic spin interactions. We compare our findings to predictions of a two-site Bose-Hubbard Quantum spin systems on a lattice have served for decades as paradigms for condensed matter and statistical physics, elucidating fundamental properties of phase transitions and acting as models for the emergence of quantum magnetism in strongly correlated electronic media.In all these cases, the underlying systems rely on a spin-spin interaction between particles on neighboring lattice sites, such as in the Ising or Heisenberg model (1,2,3). As initially proposed for electrons by Dirac (4, 5) and Heisenberg (2, 6), effective spin-spin interactions can arise due to the interplay between the spin-independent Coulomb repulsion and exchange symmetry and do not require any direct coupling between the spins of the particles. The nature of such spin-exchange interactions is typically short-ranged, as it is governed by the wave function overlap of the underlying electronic orbitals. In several topical insulators, such as ionic solids like e.g. CuO and MnO, however, antiferromagnetic order arises even though the wave function overlap between the magnetic ions is practically zero. In this case a "superexchange" interaction mediated by higher order virtual hopping processes can be effective over large distance (7,8) which leads to an (anti)-ferromagnetic coupling between bosons (fermions) on neighboring lattice sites (3). Such superexchange interactions are believed to play an important role in the context of high-T c superconductivity (9). Furthermore, they can form the basis for the generation of robust quantum gates similar to recent work in electronic double quantum dot systems (10, 11), and can be used for the efficient generation of multi-particle entangled states (12, 13), as well as for the production of many-body quantum phases with topological order (14,15,16).We report on the direct observation of superexchange interactions with ultracold atoms in optical lattices (17,18). Previous experiments have shown that spin-spin interactions between neighboring atoms can be implemented in discrete time steps (19,20) by bringing the atoms together on a single site and carrying out controlled collisions (21,20,22) or onsite exchange interactions (23). The superexchange interactions demonstrated here, however, directly implement nearest-neigh...

show abstract

mentioning

confidence: 83%

Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices

Trotzky

Cheinet

Fölling

et al. 2008

Science

683

895

View full text Add to dashboard Cite

show abstract

“…In this work, different families of multicolor bright spatial optical solitons were found by numerical integration of the corresponding stationary equations only. Cases 3 and 4 also emerge in the context of fermionic condensates of ultracold atoms [27][28][29][30], although there are some difficulties in both the justification of mean-field condensate wave function for fermions as well as possible pairing instabilities of superconducting types. Nevertheless, with sufficient care, our cases 3 and 4 can model four-component spin-3/2 cold atomic systems under special circumstances.…”

Section: Casementioning

confidence: 99%

Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations

et al. 2018

View full text Add to dashboard Cite

The inverse scattering transform (IST) is developed for a class of matrix nonlinear Schrödinger-type systems whose reductions include two equations that model certain hyperfine spin F = 1 spinor Bose-Einstein condensates, and two novel equations that were recently shown to be integrable, and that have applications in nonlinear optics and four-component fermionic condensates. In addition, the general behavior of the soliton solutions for all four reductions is analyzed in detail, and some novel solutions are presented.

show abstract

“…[11][12][13]). In this case, in principle, the number of (relevant) components can be controlled (from 2 to 2F + 1) using optical methods, and Feshbach resonances may be used to tune the desired collisional channels.…”

Section: Introductionmentioning

confidence: 99%

Generation of optical and matter-wave solitons in binary systems with a periodically modulated coupling

2010

View full text Add to dashboard Cite

We present a systematic study of the generation of the array of optical or matter-wave kinks (dark solitons) in the ground state (GS) of binary systems. We consider quasi-one-dimensional systems described by a pair of nonlinear Schrödinger (NLSE's) or Gross-Pitaevskii equations (GPE's), which are coupled by the linear mixing, with local strength , and by nonlinear interactions. We assume the self-repulsive nonlinearity in both components, and include the effects of a harmonic trapping potential, while the nonlinear interaction between the components may be both repulsive and attractive. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics and also in Bose-Einstein condensates. Depending on the sign and strengths of the linear and nonlinear couplings between the components, the ground states in such binary systems may be symmetric, antisymmetric, or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making an odd or even function of the coordinate (x). The sign flips of (x) strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of . Using a systematic numerical analysis and an analytic approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. The final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd (even) modulation function giving rise to the odd (even) number of the kinks. The modulation of (x) also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.

show abstract

Ultracold atomic Bose and Fermi spinor gases in optical lattices

Cited by 27 publications

References 95 publications

Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices

Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices

Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations

Generation of optical and matter-wave solitons in binary systems with a periodically modulated coupling

Contact Info

Product

Resources

About