#
41st Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics

## Volume 55, Number 5

##
Tuesday–Saturday, May 25–29, 2010;
Houston, Texas

### Session Q3: Quantum Gauge Theories and Ultra-cold Atoms

8:00 AM–10:00 AM,
Friday, May 28, 2010

Room: Imperial West

Chair: Erich Mueller, Cornell University

Abstract ID: BAPS.2010.DAMOP.Q3.4

### Abstract: Q3.00004 : Many-body physics in optical lattices under a synthetic magnetic field

9:30 AM–10:00 AM

Preview Abstract
Abstract

####
Author:

Mehmet Oktel

(Bilkent University)

Recent progress in creating artificial gauge fields for cold atom systems
holds promise for experimental realization of many interesting models. In
the presence of a periodic potential, the external gauge fields may be used
to realize many lattice-gauge theories for the first time. We consider the
simplest of such models, where an artificial magnetic field is coupled to
the cold atoms and investigate various scenarios. Such an artificial
magnetic field may simply be created by rotating the optical lattice, or by
more elaborate means like light induced potentials.
The physics of particles moving in a periodic potential in the presence of a
magnetic field is rich, as it contains three parameters which control
commensurate/incommensurate transitions. The first such parameter, flux
quanta per plaquette of the lattice, controls the single particle physics.
The energy spectrum as a function of this parameter is a fractal shape known
as the Hofstadter butterfly. A second parameter is the number of particles
per lattice site, which controls if certain insulating states like the Mott
state are possible. The ratio of these two parameters give the filling
factor, defined as the number of particles per flux quanta, which controls
the quantum Hall physics.
We first discuss the single particle physics where we investigate the
relation between the Wannier functions and local ground states for each
site. We show that the presence of the magnetic field requires a new
definition of the Wannier functions, and these functions have large overlaps
with local ground states. The Peirels substitution describes the hopping
between sites faithfully for the lowest band. We also investigate how
Peirels substitution has to be applied to higher bands such as the p-band,
and discuss the resulting spectra.
We then consider interacting Bosons in a rotating optical lattice and
investigate the effect of the external magnetic field on the Mott Insulator-
Superfluid transition. The phase boundary for this transition can be
calculated exactly within mean-field theory and is shown to be controlled by
the minimum eigenvalue of the Hofstadter butterfly. We argue that if one
goes beyond mean field theory the Mott Insulator-Superfluid boundary is
complex, and there are fractional quantum Hall phases of Bosons near every
Mott lobe.
As a third model we investigate the density profile for non-interacting
fermions in a rotating optical lattice and find that the gaps of the
Hofstadter butterfly are reflected as sharp plateaus in the density profile.
Each one of these regions are topological insulators with quantized Hall
conductivity. We argue that the Hall conductivity can be measured without
any transport measurements, as the Streda formula relates Hall conductivity
to the response of density to magnetic field change.
Finally we investigate the physics of fermions with on-site attraction in a
rotating optical lattice. We calculate the critical attraction strength for
the transition from a topological insulator to a BCS superfluid. We also
calculate the vortex lattice structures after BCS pairing takes place and
investigate the transitions between different configurations of vortices.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.DAMOP.Q3.4