Anyons-particles carrying fractional statistics that interpolate between bosons and fermions-have been conjectured to exist in low-dimensional systems. In the context of the fractional quantum Hall effect, quasi-particles made of electrons take the role of anyons whose statistical exchange phase is fixed by the filling factor. Here we propose an experimental setup to create anyons in one-dimensional lattices with fully tuneable exchange statistics. In our setup, anyons are created by bosons with occupation-dependent hopping amplitudes, which can be realized by assisted Raman tunnelling. The statistical angle can thus be controlled in situ by modifying the relative phase of external driving fields. This opens the fascinating possibility of smoothly transmuting bosons via anyons into fermions and of inducing a phase transition by the mere control of the particle statistics as a free parameter. In particular, we demonstrate how to induce a quantum phase transition from a superfluid into an exotic mott-like state where the particle distribution exhibits plateaus at fractional densities.

Spin waves in a one-dimensional spinor Bose gas Fuchs, J.N.; Gangardt, D.; Keilmann, T.; Shlyapnikov, G. Published in:Physical Review Letters Link to publication Citation for published version (APA):Fuchs, J. N., Gangardt, D., Keilmann, T., & Shlyapnikov, G. V. (2005). Spin waves in a one-dimensional spinor Bose gas. Physical Review Letters, 95, 150402. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We study a one-dimensional (iso)spin 1=2 Bose gas with repulsive -function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or ''spin-charge'') separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.

We propose a Pfaffian-like Ansatz for the ground state of bosons subject to 3-body infinite repulsive interactions in a 1D lattice. Our Ansatz consists of the symmetrization over all possible ways of distributing the particles in two identical Tonks-Girardeau gases. We support the quality of our Ansatz with numerical calculations and propose an experimental scheme based on mixtures of bosonic atoms and molecules in 1D optical lattices in which this Pfaffian-like state could be realized.Our findings may open the way for the creation of non-abelian anyons in 1D systems.Beyond bosons and fermions, and even in contrast to the fascinating abelian anyons (AA) [1], non-abelian anyons (NAA) [2] exhibit an exotic statistical behavior: If two different exchanges are performed consecutively among identical NAA, the final state of the system will depend on the order in which the two exchanges were made. NAA appeared first in the context of the fractional quantum Hall effect (FQHE) [2], as elementary excitations of exotic states like the Pfaffian state [3,4], the exact ground state of quantum Hall Hamiltonians with 3-body contact interactions. Recently, the possibility of a fault tolerant quantum computation based on NAA [5] has boosted the investigation of new models containing NAA [6], as well as the search for techniques for their detection and manipulation [7]. Meanwhile, the versatile and highly controllable atomic gases in optical lattices [8] have opened a door to the near future implementation of those models as well as for the artificial creation of non-Abelian gauge potentials [9].All actual models containing NAA are 2D models. The motivation of the present work is the foreseen possibility of creating NAA in one-dimension (1D). This long-term goal requires in the first place to define the concept of NAA, which is essentially 2D, in 1D. For abelian anyons (AA) this generalization has been already made by Haldane [10]. Within his generalized definition the spinon excitations of 1D Heisenberg antiferromagnets are classified as 1 2 -AA [10]. This classification becomes very natural through the connection between the 1D antiferromagnetic ground state (for a long-range interaction model, the Haldane-Shastry model [11]) and the Laughlin state [12] for bosons at ν = 1/2. In a similar way we anticipate that a connection can be established between quantum Hall models containing NAA and certain long-range 1D spin models exhibiting NAA within a generalized definition [13].Here, far from analyzing the above questions in general, our aim is to pave the way for the creation of exotic Pfaffian-like states in 1D systems, which we believe may serve as the basis to create NAA. We present a realistic 1D system whose ground state is very close to a Pfaffian-like state. The actual system we consider is that of bosonic atoms in a 1D lattice with infinite re-pulsive 3-body on-site interactions, which we call 3-hardcore bosons. Inspired by the form of the fractional quantum Hall Pfaffian state for bosons [4,14], we propose an Ansatz for the...

We propose a scheme to dynamically create a supersolid state in an optical lattice, using an attractive mixture of mass-imbalanced bosons. Starting from a "molecular" quantum crystal, supersolidity is induced dynamically as an out-of-equilibrium state. When neighboring molecular wave functions overlap, both bosonic species simultaneously exhibit quasicondensation and long-range solid order, which is stabilized by their mass imbalance. Supersolidity appears in a perfect one-dimensional crystal, without the requirement of doping. Our model can be realized in present experiments with bosonic mixtures that feature simple on-site interactions, clearing the path to the observation of supersolidity.