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APS March Meeting 2010

## Volume 55, Number 2

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Monday–Friday, March 15–19, 2010;
Portland, Oregon

### Session H6: Artificial Electromagnetism and other Gauge Fields in Cold Atomic Gases

8:00 AM–11:00 AM,
Tuesday, March 16, 2010

Room: Portland Ballroom 253

Sponsoring
Unit:
DAMOP

Chair: Lindsay LeBlanc, University of Toronto

Abstract ID: BAPS.2010.MAR.H6.4

### Abstract: H6.00004 : Single particle to many-body physics in rotating optical lattices*

9:48 AM–10:24 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.

*Supported by TUBITAK-KARIYER Grant no 104T165

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.MAR.H6.4