61 research outputs found
Collective states in highly symmetric atomic configurations, and single-photon traps
Abbreviated Abstract: We study correlated states in a circular and
linear-chain configuration of identical two-level atoms containing the energy
of a single quasi-resonant photon in the form of a collective excitation, where
the collective behaviour is mediated by exchange of transverse photons between
the atoms. For a circular configuration of atoms the effective Hamiltonian on
the radiationless subspace of the system can be diagonalized analytically. In
this case, the radiationless energy eigenstates carry a quantum
number which is analogous to the angular momentum quantum
number , carried by particles propagating in a central potential,
such as a hydrogen-like system. Just as the hydrogen s-states are the only
electronic wave functions which can occupy the central region of the Coulomb
potential, the quasi-particle corresponding to a collective excitation of the
circular atomic sample can occupy the central atom only for vanishing
quantum number . For large numbers of atoms in a maximally
subradiant state, a critical interatomic distance of emerges both
in the linear-chain and the circular configuration of atoms. The spontaneous
decay rate of the linear configuration exhibits a jump-like "critical"
behaviour for next-neighbour distances close to a half-wavelength. Furthermore,
both the linear-chain and the circular configuration exhibit exponential photon
trapping once the next-neighbour distance becomes less than a half-wavelength,
with the suppression of spontaneous decay being particularly pronounced in the
circular system. In this way, circular configurations containing sufficiently
many atoms may be natural candidates for {\it single-photon traps}.Comment: Invited contribution to "Xth International Conference on Quantum
Optics ICQO 2004" in Minsk, Belarus. To be published in Optics and
Spectroscop
Three fluid hydrodynamics of spin-1 Bose-Einstein condensates
We study excitations of the spin-1 Bose gas at finite temperatures and in the
presence of a not so strong magnetic field, or equivalently, when the gas
sample is partially polarized. Motivated by the success of two-fluid
hydrodynamics of scalar superfluids we develop a three-fluid hydrodynamic
description to treat the low frequency and long wavelength excitations of the
spin-1 Bose gas. We derive the coupled linear hydrodynamic equations of the
three sounds and evaluate them numerically in a self-consistent mean field
approximation valid for the dilute gas at the intermediate and critical
temperature regions. In this latter region we identify the critical mode
Femtosecond pulses and dynamics of molecular photoexcitation: RbCs example
We investigate the dynamics of molecular photoexcitation by unchirped
femtosecond laser pulses using RbCs as a model system. This study is motivated
by a goal of optimizing a two-color scheme of transferring
vibrationally-excited ultracold molecules to their absolute ground state. In
this scheme the molecules are initially produced by photoassociation or
magnetoassociation in bound vibrational levels close to the first dissociation
threshold. We analyze here the first step of the two-color path as a function
of pulse intensity from the low-field to the high-field regime. We use two
different approaches, a global one, the 'Wavepacket' method, and a restricted
one, the 'Level by Level' method where the number of vibrational levels is
limited to a small subset. The comparison between the results of the two
approaches allows one to gain qualitative insights into the complex dynamics of
the high-field regime. In particular, we emphasize the non-trivial and
important role of far-from-resonance levels which are adiabatically excited
through 'vertical' transitions with a large Franck-Condon factor. We also point
out spectacular excitation blockade due to the presence of a quasi-degenerate
level in the lower electronic state. We conclude that selective transfer with
femtosecond pulses is possible in the low-field regime only. Finally, we extend
our single-pulse analysis and examine population transfer induced by coherent
trains of low-intensity femtosecond pulses.Comment: 25 pages, 12 figure
Control of dipolar relaxation in external fields
We study dipolar relaxation in both ultra-cold thermal and Bose-condensed
chromium atom gases. We show three different ways to control dipolar
relaxation, making use of either a static magnetic field, an oscillatory
magnetic field, or an optical lattice to reduce the dimensionality of the gas
from 3D to 2D. Although dipolar relaxation generally increases as a function of
a static magnetic field intensity, we find a range of non-zero magnetic field
intensities where dipolar relaxation is strongly reduced. We use this resonant
reduction to accurately determine the S=6 scattering length of chromium atoms:
. We compare this new measurement to another new
determination of , which we perform by analysing the precise spectroscopy
of a Feshbach resonance in d-wave collisions, yielding . These two measurements provide by far the most precise determination of
to date. We then show that, although dipolar interactions are long-range
interactions, dipolar relaxation only involves the incoming partial wave
for large enough magnetic field intensities, which has interesting consequences
on the stability of dipolar Fermi gases. We then study ultra-cold chromium
gases in a 1D optical lattice resulting in a collection of independent 2D
gases. We show that dipolar relaxation is modified when the atoms collide in
reduced dimensionality at low magnetic field intensities, and that the
corresponding dipolar relaxation rate parameter is reduced by a factor up to 7
compared to the 3D case. Finally, we study dipolar relaxation in presence of
radio-frequency (rf) oscillating magnetic fields, and we show that both the
output channel energy and the transition amplitude can be controlled by means
of rf frequency and Rabi frequency.Comment: 25 pages, 17 figure
Dual-probe decoherence microscopy: Probing pockets of coherence in a decohering environment
We study the use of a pair of qubits as a decoherence probe of a non-trivial
environment. This dual-probe configuration is modelled by three
two-level-systems which are coupled in a chain in which the middle system
represents an environmental two-level-system (TLS). This TLS resides within the
environment of the qubits and therefore its coupling to perturbing fluctuations
(i.e. its decoherence) is assumed much stronger than the decoherence acting on
the probe qubits. We study the evolution of such a tripartite system including
the appearance of a decoherence-free state (dark state) and non-Markovian
behaviour. We find that all parameters of this TLS can be obtained from
measurements of one of the probe qubits. Furthermore we show the advantages of
two qubits in probing environments and the new dynamics imposed by a TLS which
couples to two qubits at once.Comment: 29 pages, 10 figure
Preparation of decoherence-free, subradiant states in a cavity
The cause of decoherence in a quantum system can be traced back to the
interaction with the environment. As it has been pointed out first by Dicke, in
a system of N two-level atoms where each of the atoms is individually dipole
coupled to the environment, there are collective, subradiant states, that have
no dipole coupling to photon modes, and therefore they are expected to decay
slower. This property also implies that these type of states, which form an N-1
dimensional subspace of the atomic subsytem, also decohere slower. We propose a
scheme which will create such states. First the two-level atoms are placed in a
strongly detuned cavity and one of the atoms, called the control atom is
excited. The time evolution of the coupled atom-cavity system leads to an
appropriately entangled state of the atoms. By applying subsequent laser pulses
at a well defined time instant, it is possible to drive the atomic state into
the subradiant, i. e., decoherence free subspace. Up to a certain average
number of the photons, the result is independent of the state of the cavity.
The analysis of the conditions shows that this scheme is feasible with present
day techniques achieved in atom cavity interaction experiments.Comment: 5 page
Mean field ground state of a spin-1 condensate in a magnetic field
We revisit the topic of the mean field ground state of a spin-1 atomic
condensate inside a uniform magnetic field () under the constraints that
both the total number of atoms () and the magnetization () are
conserved. In the presence of an internal state (spin component) independent
trap, we also investigate the dependence of the so-called single spatial mode
approximation (SMA) on the magnitude of the magnetic field and . Our
result indicate that the quadratic Zeeman effect is an important factor in
balancing the mean field energy from elastic atom-atom collisions that are
known to conserve both and .Comment: 13 pages, 9 figures, to be published in New J. Phys.
(http://www.njp.org/
Application of B-splines to determining eigen-spectrum of Feshbach molecules
The B-spline basis set method is applied to determining the rovibrational
eigen-spectrum of diatomic molecules. A particular attention is paid to a
challenging numerical task of an accurate and efficient description of the
vibrational levels near the dissociation limit (halo-state and Feshbach
molecules). Advantages of using B-splines are highlighted by comparing the
performance of the method with that of the commonly-used discrete variable
representation (DVR) approach. Several model cases, including the Morse
potential and realistic potentials with 1/R^3 and 1/R^6 long-range dependence
of the internuclear separation are studied. We find that the B-spline method is
superior to the DVR approach and it is robust enough to properly describe the
Feshbach molecules. The developed numerical method is applied to studying the
universal relation of the energy of the last bound state to the scattering
length. We numerically illustrate the validity of the quantum-defect-theoretic
formulation of such a relation for a 1/R^6 potential.Comment: submitted to can j phys: Walter Johnson symposu
Complete eigenstates of identical qubits arranged in regular polygons
We calculate the energy eigenvalues and eigenstates corresponding to coherent
single and multiple excitations of an array of N identical qubits or two-level
atoms (TLA's) arranged on the vertices of a regular polygon. We assume only
that the coupling occurs via an exchange interaction which depends on the
separation between the qubits. We include the interactions between all pairs of
qubits, and our results are valid for arbitrary distances relative to the
radiation wavelength. To illustrate the usefulness of these states, we plot the
distance dependence of the decay rates of the n=2 (biexciton) eigenstates of an
array of 4 qubits, and tabulate the biexciton eigenvalues and eigenstates, and
absorption frequencies, line widths, and relative intensities for polygons
consisting of N=2,...,9 qubits in the long-wavelength limit.Comment: Added a figure showing how these results can be used to compute
deviations from "equal collective decoherence" approximation
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