895 research outputs found
Collective generation of quantum states of light by entangled atoms
We present a theoretical framework to describe the collective emission of
light by entangled atomic states. Our theory applies to the low excitation
regime, where most of the atoms are initially in the ground state, and relies
on a bosonic description of the atomic excitations. In this way, the problem of
light emission by an ensemble of atoms can be solved exactly, including
dipole-dipole interactions and multiple light scattering. Explicit expressions
for the emitted photonic states are obtained in several situations, such as
those of atoms in regular lattices and atomic vapors. We determine the
directionality of the photonic beam, the purity of the photonic state, and the
renormalization of the emission rates. We also show how to observe collective
phenomena with ultracold atoms in optical lattices, and how to use these ideas
to generate photonic states that are useful in the context of quantum
information.Comment: 15 pages, 10 figure
Quantum simulation of the hexagonal Kitaev model with trapped ions
We present a detailed study of quantum simulations of coupled spin systems in
surface-electrode ion-trap arrays, and illustrate our findings with a proposed
implementation of the hexagonal Kitaev model [A. Kitaev, Annals of Physics
321,2 (2006)]. The effective (pseudo)spin interactions making up such quantum
simulators are found to be proportional to the dipole-dipole interaction
between the trapped ions, and are mediated by motion which can be driven by
state-dependent forces. The precise forms of the trapping potentials and the
interactions are derived in the presence of a surface electrode and a cover
electrode. These results are the starting point to derive an optimized
surface-electrode geometry for trapping ions in the desired honeycomb lattice
of Kitaev's model, where we design the dipole-dipole interactions in a way that
allows for coupling all three bond types of the model simultaneously, without
the need for time discretization. Finally we propose a simple wire structure
that can be incorporated in a microfabricated chip to generate localized
state-dependent forces which drive the couplings prescribed by this particular
model; such a wire structure should be adaptable to many other situations.Comment: 24 pages, 7 figures. v2: simplified the derivation of (28) without
changing conclusions; minor edits. v3: minor edit
Far-from-equilibrium noise heating and laser cooling dynamics in radio-frequency Paul traps
We study the stochastic dynamics of a particle in a periodically driven
potential. For atomic ions trapped in radio-frequency Paul traps, noise heating
and laser cooling typically act slowly in comparison with the unperturbed
motion. These stochastic processes can be accounted for in terms of a
probability distribution defined over the action variables, which would
otherwise be conserved within the regular regions of the Hamiltonian phase
space. We present a semiclassical theory of low-saturation laser cooling
applicable from the limit of low-amplitude motion to large-amplitude motion,
accounting fully for the time-dependent and anharmonic trap. We employ our
approach to a detailed study of the stochastic dynamics of a single ion,
drawing general conclusions regarding the nonequilibrium dynamics of
laser-cooled trapped ions. We predict a regime of anharmonic motion in which
laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as
it is to heat it), and can also turn into effective heating. This implies that
a high-energy ion could be easily lost from the trap despite being laser
cooled; however, we find that this loss can be counteracted using a laser
detuning much larger than Doppler detuning.Comment: 23 pages, 7 figure
Electrostatics of Gapped and Finite Surface Electrodes
We present approximate methods for calculating the three-dimensional electric
potentials of finite surface electrodes including gaps between electrodes, and
estimate the effects of finite electrode thickness and an underlying dielectric
substrate. As an example we optimize a radio-frequency surface-electrode ring
ion trap, and find that each of these factors reduces the trapping secular
frequencies by less than 5% in realistic situations. This small magnitude
validates the usual assumption of neglecting the influences of gaps between
electrodes and finite electrode extent.Comment: 9 pages, 9 figures (minor changes
Experiments towards quantum information with trapped Calcium ions
Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap
is the prerequisite for quantum information experiments with trapped ions. With
resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we
have cooled one and two 40Ca+ ions to the ground state of vibration with up to
99.9% probability. With a novel cooling scheme utilizing electromagnetically
induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous
ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the
motional ground state we have demonstrated coherent quantum state manipulation
on the S1/2 - D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations
within 1.4 ms have been observed in the motional ground state and in the n=1
Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along
the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more
than 5 micron for up to 4 ions. We are able to cool two ions to the ground
state in the trap and individually address the ions with laser pulses through a
special optical addressing channel.Comment: Proceedings of the ICAP 2000, Firenz
Fluorescence during Doppler cooling of a single trapped atom
We investigate the temporal dynamics of Doppler cooling of an initially hot
single trapped atom in the weak binding regime using a semiclassical approach.
We develop an analytical model for the simplest case of a single vibrational
mode for a harmonic trap, and show how this model allows us to estimate the
initial energy of the trapped particle by observing the fluorescence rate
during the cooling process. The experimental implementation of this temperature
measurement provides a way to measure atom heating rates by observing the
temperature rise in the absence of cooling. This method is technically
relatively simple compared to conventional sideband detection methods, and the
two methods are in reasonable agreement. We also discuss the effects of RF
micromotion, relevant for a trapped atomic ion, and the effect of coupling
between the vibrational modes on the cooling dynamics.Comment: 12 pages, 11 figures, Submitted to Phys. Rev.
Rabi oscillations in a quantum dot-cavity system coupled to a non-zero temperature phonon bath
We study a quantum dot strongly coupled to a single high-finesse optical
microcavity mode. We use a rotating wave approximation method, commonly used in
ion-laser interactions, tegether with the Lamb-Dicke approximation to obtain an
analytic solution of this problem. The decay of Rabi oscillations because of
the electron-phonon coupling are studied at arbitrary temperature and
analytical expressions for the collapse and revival times are presented.
Analyses without the rotating wave approximation are presented by means of
investigating the energy spectrum.Comment: 7 pages, 5 figures; Revised versio
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