arXiv:cond-mat/0703641 · Physical Review Letters

Excitation of a d -Density Wave in an Optical Lattice with Driven Tunneling

Andreas Hemmerich, C. Morais Smith

Published Sep 13, 2007• 17 citations

Abstract

Quantum phases with unusual symmetries may play a key role in the understanding of solid state systems at low temperatures. We propose a realistic scenario, well in reach of present experimental techniques, which should permit us to produce a stationary quantum state with d x2-y2 symmetry in a two-dimensional bosonic optical square lattice. This state, characterized by alternating rotational flux in each plaquette, arises from driven tunneling implemented by a stimulated Raman scattering process. We discuss bosons in a square lattice; however, more complex systems involving other lattice geometries appear possible.

DOI: 10.1103/physrevlett.99.113002

Related papers

Stimulated Symmetry

Whereas the underlying parameters of condensed matter systems may be fixed, thereby limiting the phase space in which to vary the material properties, the ability to tune and manipulate atoms or molecules trapped in an optical lattice opens up that phase space. With success demonstrated already in systems with isotropic symmetry, as in the case of the superfluid-to-Mott-insulator transition of bosons on a square lattice, interest is now in describing systems with an anisotropic symmetry in the order parameter. Hemmerich and Morais Smith describe a scenario for imprinting a dx2-y2 wave symmetry onto an array of polarizable bosons confined to a two-dimensional (2D) optical lattice. They show theoretically that exciting the atoms by stimulated Raman scattering can result in the formation of a checkerboard-like pattern of staggered flux states on adjacent plaquettes of the 2D lattice, resulting in a d-wave momentum distribution. The proposed scenario offers the prospect of engineering optical lattices for the modeling of complex interacting phenomena from the likes of high-temperature superconductivity to magnetic frustration. — ISO

ScienceSep 27, 20070 citations

Quantum Phases of Cold Polar Molecules in 2D Optical Lattices

Barbara Capogrosso-Sansone, C. Trefzger, Maciej Lewenstein +2 more

We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil's staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.

arXiv:0906.2009Physical Review LettersMar 25, 2010304 citations

Cold atoms on a two-dimensional square optical lattice with an alternating potential

Huaiming Guo, Yu-Chuan Wen, Shiping Feng

The cold atom on a two-dimensional square optical lattice is studied within the hard-core boson Hubbard model with an alternating potential. In terms of the quantum Monte Carlo method, it is shown explicitly that a supersolid phase emerges due to the presence of the alternating potential. For the weak alternating potential, the supersolid state appears for the whole range of hard-core boson densities except the half-filling case, where the system is a Mott insulator. However, for the strong alternating potential, besides the supersolid and Mott insulating states, a charge-density wave phase appears.

arXiv:0903.4234Physical Review AMar 20, 20097 citations

Quantized vortex states of strongly interacting bosons in a rotating optical lattice

Rajiv Bhat, Brandon M. Peden, B. T. Seaman +3 more

Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of $2\ensuremath{\pi}$ in the phase winding of the condensate wave function. A lattice of size $L\ifmmode\times\else\texttimes\fi{}L$ can have at most $L\ensuremath{-}1$ quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.

arXiv:cond-mat/0607781Physical Review ADec 6, 200627 citations

Frustrated tunneling of ultracold atoms in a state-dependent optical lattice

Xiang-Fa Zhou, Zhixin Chen, Zheng-Wei Zhou +2 more

We propose a general method to realize frustrated tunneling of ultracold atoms in a state-dependent optical lattice. Two typical lattice configurations are considered, the square lattice with competing interaction and the kagom\'e lattice with geometrical frustration. The ideal can be extended to implement frustrated tunneling of ultracold atoms in various geometries, which enable us to investigate the physics of frustration in both bosonic and spin systems. We study the mean-field phase diagrams of the considered models and the experimental situations are also discussed.

Physical Review AFeb 9, 20105 citations

Quantum phase transitions in low-dimensional optical lattices

Marco Fedele Di Liberto

In this thesis, we discuss quantum phase transitions in low-dimensional optical lattices, namely one- and two-dimensional lattices. The dimensional confinement is realized in experiments by suppressing the hopping in the extra dimensions through a deep potential barrier that prevents the atoms to tunnel across dimensions. The dimensionality considerably affects the physical behavior of the system. For instance, in one dimension, the celebrated Fermi-liquid theory does not describe the many-body behavior of a fermionic system. There are no single particle excitations, but instead collective behavior, and spin and charge degrees of freedom are decoupled . In the first part of this thesis, we consider one-dimensional fermionic gases under the effect of time-dependent driving forces. First, we describe a proposal to realize non-standard Hubbard models that display correlated-hopping terms by modulating interactions through a time-dependent magnetic field. The extra terms describe hopping processes that depend on the particle-density difference in neighboring sites. The effective model is obtained in arbitrary spatial dimensions, but only in one-dimension it is known to be exactly solvable for specific values of the parameters. Moreover, an SU(2) symmetry in the charge sector allows to construct non-trivial superconducting eigenstates (eta-states), discovered by Yang as excited states of the Hubbard model. Then, we study a one-dimensional bipartite optical lattice with fermionic atoms at half-filling. The lattice potential barriers have heights alternating in magnitude. As a consequence, the hopping amplitudes also alternate in magnitude and the elementary unit cell has two sites. This system is known to display Peierls dimerization at half-filling: the fermions form dimers in neighboring sites that inhibit transport and open a gap in the spectrum. After applying shaking on this system we discover that one can dynamically induce a phase transition to an unconventional metallic state with four Fermi-points. The second part of this thesis describes bosonic systems in two-dimensional optical lattices. First, we consider a square optical lattice with alternating deep-shallow wells arranged in a checkerboard pattern. This lattice is realized in the experimental laboratory of Prof. Hemmerich in Hamburg. In the experiment, the visibility is extracted from the time-of-flight imaging to quantify the phase coherence of the bosonic gas. We develop a mean-field theory and determine the phase diagram of this model. We interpret the experimental data by assuming that at large detuning, only the deeper wells are populated and form an imbalanced Mott insulator with empty shallow wells and integer density on the deeper wells. We support this hypothesis by large-scale Gutzwiller calculations. Then, we investigate a system of bosons in the Lieb lattice, which is the lattice geometry of the Cu-O plane in cuprates . We consider configurations of the optical potential where s and p orbitals sitting on neighboring wells become resonant and hybridize. The interest in this problem comes from the possibility to realize time-reversal broken phases, usually known as Varma phases for electronic systems, which have been proposed to explain the pseudo-gap regime of cuprate superconductors. We show the conditions under which the symmetry breaking in a four-band model can lead to states with loop currents. Moreover, the lowest branch of the excitation spectrum has a non-vanishing Chern number and therefore supports topological excitations.

Jun 22, 20150 citations