30 research outputs found
Bose-Einstein Condensation and strong-correlation behavior of phonons in ion traps
We show that the dynamics of phonons in a set of trapped ions interacting
with lasers is described by a Bose-Hubbard model whose parameters can be
externally adjusted. We investigate the possibility of observing several
quantum many-body phenomena, including (quasi) Bose-Einstein condensation as
well as a superfluid-Mott insulator quantum phase transition.Comment: 5 pages, 3 figure
Quantum phases of interacting phonons in ion traps
The vibrations of a chain of trapped ions can be considered, under suitable
experimental conditions, as an ensemble of interacting phonons, whose quantum
dynamics is governed by a Bose--Hubbard Hamiltonian. In this work we study the
quantum phases which appear in this system, and show that thermodynamical
properties, such as critical parameters and critical exponents, can be measured
in experiments with a limited number of ions. Besides that, interacting phonons
in trapped ions offer us the possibility to access regimes which are difficult
to study with ultracold bosons in optical lattices, like models with attractive
or site--dependent phonon-phonon interactions.Comment: 10 page
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
Mesoscopic Spin-Boson Models of Trapped Ions
Trapped ions arranged in Coulomb crystals provide us with the elements to
study the physics of a single spin coupled to a boson bath. In this work we
show that optical forces allow us to realize a variety of spin-boson models,
depending on the crystal geometry and the laser configuration. We study in
detail the Ohmic case, which can be implemented by illuminating a single ion
with a travelling wave. The mesoscopic character of the phonon bath in trapped
ions induces new effects like the appearance of quantum revivals in the spin
evolution.Comment: 4.4 pages, 5 figure
DMRG and periodic boundary conditions: a quantum information perspective
We introduce a picture to analyze the density matrix renormalization group
(DMRG) numerical method from a quantum information perspective. This leads us
to introduce some modifications for problems with periodic boundary conditions
in which the results are dramatically improved. The picture also explains some
features of the method in terms of entanglement and teleportation.Comment: 4 page
Simulating quantum-optical phenomena with cold atoms in optical lattices
We propose a scheme involving cold atoms trapped in optical lattices to
observe different phenomena traditionally linked to quantum-optical systems.
The basic idea consists of connecting the trapped atomic state to a non-trapped
state through a Raman scheme. The coupling between these two types of atoms
(trapped and free) turns out to be similar to that describing light-matter
interaction within the rotating-wave approximation, the role of matter and
photons being played by the trapped and free atoms, respectively. We explain in
particular how to observe phenomena arising from the collective spontaneous
emission of atomic and harmonic oscillator samples such as superradiance and
directional emission. We also show how the same setup can simulate Bose-Hubbard
Hamiltonians with extended hopping as well as Ising models with long-range
interactions. We believe that this system can be realized with state of the art
technology
Renormalization algorithm for the calculation of spectra of interacting quantum systems
We present an algorithm for the calculation of eigenstates with definite
linear momentum in quantum lattices. Our method is related to the Density
Matrix Renormalization Group, and makes use of the distribution of multipartite
entanglement to build variational wave--functions with translational symmetry.
Its virtues are shown in the study of bilinear--biquadratic S=1 chains.Comment: Corrected version. We have added an appendix with an extended
explanation of the implementation of our algorith
Towards electron-electron entanglement in Penning traps
Entanglement of isolated elementary particles other than photons has not yet
been achieved. We show how building blocks demonstrated with one trapped
electron might be used to make a model system and method for entangling two
electrons. Applications are then considered, including two-qubit gates and more
precise quantum metrology protocols.Comment: 5 pages, 1 figure, accepted in PR
Effective Spin Quantum Phases in Systems of Trapped Ions
A system of trapped ions under the action of off--resonant standing--waves
can be used to simulate a variety of quantum spin models. In this work, we
describe theoretically quantum phases that can be observed in the simplest
realization of this idea: quantum Ising and XY models. Our numerical
calculations with the Density Matrix Renormalization Group method show that
experiments with ion traps should allow one to access general properties of
quantum critical systems. On the other hand, ion trap quantum spin models show
a few novel features due to the peculiarities of induced effective spin--spin
interactions which lead to interesting effects like long--range quantum
correlations and the coexistence of different spin phases.Comment: 11 pages, 13 figure