110 research outputs found
Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
We investigate the dynamics of neutral atoms in a 2D optical lattice which
traps two distinct internal states of the atoms in different columns. Two Raman
lasers are used to coherently transfer atoms from one internal state to the
other, thereby causing hopping between the different columns. By adjusting the
laser parameters appropriately we can induce a non vanishing phase of particles
moving along a closed path on the lattice. This phase is proportional to the
enclosed area and we thus simulate a magnetic flux through the lattice. This
setup is described by a Hamiltonian identical to the one for electrons on a
lattice subject to a magnetic field and thus allows us to study this equivalent
situation under very well defined controllable conditions. We consider the
limiting case of huge magnetic fields -- which is not experimentally accessible
for electrons in metals -- where a fractal band structure, the Hofstadter
butterfly, characterizes the system.Comment: 6 pages, RevTe
Quantum statistics of atoms in microstructures
This paper proposes groove-like potential structures for the observation of
quantum information processing by trapped particles. As an illustration the
effect of quantum statistics at a 50-50 beam splitter is investigated. For
non-interacting particles we regain the results known from photon experiments,
but we have found that particle interactions destroy the perfect bosonic
correlations. Fermions avoid each other due to the exclusion principle and
hence they are far less sensitive to particle interactions. For bosons, the
behavior can be explained with simple analytic considerations which predict a
certain amount of universality. This is verified by detailed numerical
calculations.Comment: 18 pages incl. 13 figure
Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
Dirac points lie at the heart of many fascinating phenomena in condensed
matter physics, from massless electrons in graphene to the emergence of
conducting edge states in topological insulators [1, 2]. At a Dirac point, two
energy bands intersect linearly and the particles behave as relativistic Dirac
fermions. In solids, the rigid structure of the material sets the mass and
velocity of the particles, as well as their interactions. A different, highly
flexible approach is to create model systems using fermionic atoms trapped in
the periodic potential of interfering laser beams, a method which so far has
only been applied to explore simple lattice structures [3, 4]. Here we report
on the creation of Dirac points with adjustable properties in a tunable
honeycomb optical lattice. Using momentum-resolved interband transitions, we
observe a minimum band gap inside the Brillouin zone at the position of the
Dirac points. We exploit the unique tunability of our lattice potential to
adjust the effective mass of the Dirac fermions by breaking inversion symmetry.
Moreover, changing the lattice anisotropy allows us to move the position of the
Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a
critical limit, the two Dirac points merge and annihilate each other - a
situation which has recently attracted considerable theoretical interest [5-9],
but seems extremely challenging to observe in solids [10]. We map out this
topological transition in lattice parameter space and find excellent agreement
with ab initio calculations. Our results not only pave the way to model
materials where the topology of the band structure plays a crucial role, but
also provide an avenue to explore many-body phases resulting from the interplay
of complex lattice geometries with interactions [11, 12]
Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field
The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs
heterostructures is studied in the case where the two-dimensional electron gas
(2DEG) is subject to a strong magnetic field and a smooth random potential with
correlation length Lambda and amplitude Delta. The electron wave functions are
described in a quasiclassical picture using results of percolation theory for
two-dimensional systems. In accordance with the experimental situation, Lambda
is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts
the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to
electrons occupying extended trajectories of fractal structure. Both
piezoelectric and deformation potential interactions of surface acoustic
phonons with electrons are considered and the corresponding interaction
vertices are derived. These vertices are found to differ from those valid for
three-dimensional bulk phonon systems with respect to the phonon wave vector
dependence. We derive the appropriate dielectric function varepsilon(omega,q)
to describe the effect of screening on the electron-phonon coupling. In the low
temperature, high frequency regime T << Delta (omega_q*Lambda
/v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron
drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q)
are independent of temperature. The classical percolation indices give
alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW
occurs is found to be given by the scaling law |Delta \bar{\nu}| approx
(omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon
coupling and the screening due to the 2DEG on the filling factor leads to a
double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad
Thermometry with spin-dependent lattices
We propose a method for measuring the temperature of strongly correlated
phases of ultracold atom gases confined in spin-dependent optical lattices. In
this technique, a small number of "impurity" atoms--trapped in a state that
does not experience the lattice potential--are in thermal contact with atoms
bound to the lattice. The impurity serves as a thermometer for the system
because its temperature can be straightforwardly measured using time-of-flight
expansion velocity. This technique may be useful for resolving many open
questions regarding thermalization in these isolated systems. We discuss the
theory behind this method and demonstrate proof-of-principle experiments,
including the first realization of a 3D spin-dependent lattice in the strongly
correlated regime.Comment: 22 pages, 8 figures v2: Several references added; Section on heating
rates updated to include dipole fluctuation terms; Section added on the
limitations of the proposed method. To appear in New Journal of Physic
Polarization state of the optical near-field
The polarization state of the optical electromagnetic field lying several
nanometers above complex dielectric structures reveals the intricate
light-matter interaction that occurs in this near-field zone. This information
can only be extracted from an analysis of the polarization state of the
detected light in the near-field. These polarization states can be calculated
by different numerical methods well-suited to near--field optics. In this
paper, we apply two different techniques (Localized Green Function Method and
Differential Theory of Gratings) to separate each polarisation component
associated with both electric and magnetic optical near-fields produced by
nanometer sized objects. The analysis is carried out in two stages: in the
first stage, we use a simple dipolar model to achieve insight into the physical
origin of the near-field polarization state. In the second stage, we calculate
accurate numerical field maps, simulating experimental near-field light
detection, to supplement the data produced by analytical models. We conclude
this study by demonstrating the role played by the near-field polarization in
the formation of the local density of states.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.
Cooperative coupling of ultracold atoms and surface plasmons
Cooperative coupling between optical emitters and light fields is one of the
outstanding goals in quantum technology. It is both fundamentally interesting
for the extraordinary radiation properties of the participating emitters and
has many potential applications in photonics. While this goal has been achieved
using high-finesse optical cavities, cavity-free approaches that are broadband
and easy to build have attracted much attention recently. Here we demonstrate
cooperative coupling of ultracold atoms with surface plasmons propagating on a
plane gold surface. While the atoms are moving towards the surface they are
excited by an external laser pulse. Excited surface plasmons are detected via
leakage radiation into the substrate of the gold layer. A maximum Purcell
factor of is reached at an optimum distance of
from the surface. The coupling leads to the observation of
a Fano-like resonance in the spectrum.Comment: 9 pages, 4 figure
Generic model of an atom laser
We present a generic model of an atom laser by including a pump and loss term
in the Gross-Pitaevskii equation. We show that there exists a threshold for the
pump above which the mean matter field assumes a non-vanishing value in
steady-state. We study the transient regime of this atom laser and find
oscillations around the stationary solution even in the presence of a loss
term. These oscillations are damped away when we introduce a position dependent
loss term. For this case we present a modified Thomas-Fermi solution that takes
into account the pump and loss. Our generic model of an atom laser is analogous
to the semi-classical theory of the laser.Comment: 15 pages, including 5 figures, submitted to Phys. Rev. A, revised
manuscript, file also available at
http://www.physik.uni-ulm.de/quan/users/kne
Double-well magnetic trap for Bose-Einstein condensates
We present a magnetic trapping scheme for neutral atoms based on a hybrid of
Ioffe-Pritchard and Time-averaged Orbiting Potential traps. The resulting
double-well magnetic potential has readily controllable barrier height and well
separation. This offers a new tool for studying the behavior of Bose
condensates in double-well potentials, including atom interferometry and
Josephson tunneling. We formulate a description for the potential of this
magnetic trap and discuss practical issues such as loading with atoms,
evaporative cooling and manipulating the potential.Comment: 7 pages, 6 figures, Revtex
Theory of Bose-Einstein condensation in trapped gases
The phenomenon of Bose-Einstein condensation of dilute gases in traps is
reviewed from a theoretical perspective. Mean-field theory provides a framework
to understand the main features of the condensation and the role of
interactions between particles. Various properties of these systems are
discussed, including the density profiles and the energy of the ground state
configurations, the collective oscillations and the dynamics of the expansion,
the condensate fraction and the thermodynamic functions. The thermodynamic
limit exhibits a scaling behavior in the relevant length and energy scales.
Despite the dilute nature of the gases, interactions profoundly modify the
static as well as the dynamic properties of the system; the predictions of
mean-field theory are in excellent agreement with available experimental
results. Effects of superfluidity including the existence of quantized vortices
and the reduction of the moment of inertia are discussed, as well as the
consequences of coherence such as the Josephson effect and interference
phenomena. The review also assesses the accuracy and limitations of the
mean-field approach.Comment: revtex, 69 pages, 38 eps figures, new version with more references,
new figures, various changes and corrections, for publ. in Rev. Mod. Phys.,
available also at http://www-phys.science.unitn.it/bec/BEC.htm
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