211 research outputs found
Coherent Particle Transfer in an On-Demand Single-Electron Source
Coherent electron transfer from a localized state trapped in a quantum dot
into a ballistic conductor, taking place in on-demand electron sources, in
general may result in excitation of particle-hole pairs. We consider a simple
model for these effects, involving a resonance level with time-dependent
energy, and derive Floquet scattering matrix describing inelastic transitions
of particles in the Fermi sea. We find that, as the resonance level is driven
through the Fermi level, particle transfer may take place completely without
particle-hole excitations for certain driving protocols. In particular, such
noiseless transfer occurs when the level moves with constant rapidity, its
energy changing linearly with time. A detection scheme for studying the
coherence of particle transfer is proposed.Comment: 5 pages, 3 figures. Updated introduction, Fig. 1, and reference
Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement
Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled
successfully using a zero-range delta-function potential, while that of bosonic
3D atoms has been modeled successfully using Fermi-Huang's regularized s-wave
pseudo-potential. Here, we derive the eigenenergies of two spin-polarized 1D
fermions under external harmonic confinement interacting through a zero-range
potential, which only acts on odd-parity wave functions, analytically. We also
present a divergent-free zero-range potential treatment of two spin-polarized
3D fermions under harmonic confinement. Our pseudo-potential treatments are
verified through numerical calculations for short-range model potentials.Comment: 9 pages, 4 figures (subm. to PRA on 03/15/2004
Quantum theory of an atom laser originating from a Bose-Einstein condensate or a Fermi gas in the presence of gravity
We present a 3D quantum mechanical theory of radio-frequency outcoupled atom
lasers from trapped atomic gases in the presence of the gravitational force.
Predictions for the total outcoupling rate as a function of the radio-frequency
and for the beam wave function are given. We establish a sum rule for the
energy integrated outcoupling, which leads to a separate determination of the
coupling strength between the atoms and the radiation field.
For a non-interacting Bose-Einstein condensate analytic solutions are derived
which are subsequently extended to include the effects of atomic interactions.
The interactions enhance interference effects in the beam profile and modify
the outcoupling rate of the atom laser. We provide a complete quantum
mechanical solution which is in line with experimental findings and allows to
determine the validity of commonly used approximative methods.
We also extend the formalism to a fermionic atom laser and analyze the effect
of superfluidity on the outcoupling of atoms.Comment: 13 pages, 8 figures, slightly expanded versio
Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models and STIRAP
We investigate the dynamics of a Bose--Einstein condensate (BEC) in a
triple-well trap in a three-level approximation. The inter-atomic interactions
are taken into account in a mean-field approximation (Gross-Pitaevskii
equation), leading to a nonlinear three-level model. New eigenstates emerge due
to the nonlinearity, depending on the system parameters. Adiabaticity breaks
down if such a nonlinear eigenstate disappears when the parameters are varied.
The dynamical implications of this loss of adiabaticity are analyzed for two
important special cases: A three level Landau-Zener model and the STIRAP
scheme. We discuss the emergence of looped levels for an equal-slope
Landau-Zener model. The Zener tunneling probability does not tend to zero in
the adiabatic limit and shows pronounced oscillations as a function of the
velocity of the parameter variation. Furthermore we generalize the STIRAP
scheme for adiabatic coherent population transfer between atomic states to the
nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds
the detuning.Comment: RevTex4, 7 pages, 11 figures, content extended and title/abstract
change
Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings
We generalize the Brundobler-Elser hypothesis in the multistate Landau-Zener
problem to the case when instead of a state with the highest slope of the
diabatic energy level there is a band of states with an arbitrary number of
parallel levels having the same slope. We argue that the probabilities of
counterintuitive transitions among such states are exactly zero.Comment: 9 pages, 5 figure
Classification of zero-energy resonances by dissociation of Feshbach molecules
We study the dissociation of Feshbach molecules by a magnetic field sweep
across a zero-energy resonance. In the limit of an instantaneous magnetic field
change, the distribution of atomic kinetic energy can have a peak indicating
dominance of the molecular closed-channel spin configuration over the entrance
channel. The extent of this dominance influences physical properties such as
stability with respect to collisions, and so the readily measurable presence or
absence of the corresponding peak provides a practical method of classifying
zero-energy resonances. Currently achievable ramp speeds, e.g. those
demonstrated by Duerr et al. [Phys. Rev. A 70, 031601 (2005)], are fast enough
to provide magnetic field changes that may be interpreted as instantaneous. We
study the transition from sudden magnetic field changes to asymptotically wide,
linear ramps. In the latter limit, the predicted form of the atomic kinetic
energy distribution is independent of the specific implementation of the
two-body physics, provided that the near-resonant scattering properties are
properly accounted for.Comment: 10 pages, 5 eps figure
Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions
We study few-body problems in mixed dimensions with heavy atoms
trapped individually in parallel one-dimensional tubes or two-dimensional
disks, and a single light atom travels freely in three dimensions. By using the
Born-Oppenheimer approximation, we find three- and four-body bound states for a
broad region of heavy-light atom scattering length combinations. Specifically,
the existence of trimer and tetramer states persist to negative scattering
lengths regime, where no two-body bound state is present. These few-body bound
states are analogous to the Efimov states in three dimensions, but are stable
against three-body recombination due to geometric separation. In addition, we
find that the binding energy of the ground trimer and tetramer state reaches
its maximum value when the scattering lengths are comparable to the separation
between the low-dimensional traps. This resonant behavior is a unique feature
for the few-body bound states in mixed dimensions.Comment: Extended version with 14 pages and 14 figure
Degenerate Landau-Zener model: Exact analytical solution
The exact analytical solution of the degenerate Landau-Zener model, wherein
two bands of degenerate energies cross in time, is presented. The solution is
derived by using the Morris-Shore transformation, which reduces the fully
coupled system to a set of independent nondegenerate two-state systems and a
set of decoupled states. Due to the divergence of the phase of the off-diagonal
element of the propagator in the original Landau-Zener model, not all
transition probabilities exist for infinite time duration. In general, apart
from some special cases, only the transition probabilities between states
within the same degenerate set exist, but not between states of different sets.
An illustration is presented for the transition between the magnetic sublevels
of two atomic levels with total angular momenta J=2 and 1
Counterintuitive transitions between crossing energy levels
We calculate analytically the probabilities for intuitive and
counterintuitive transitions in a three-state system, in which two parallel
energies are crossed by a third, tilted energy. The state with the tilted
energy is coupled to the other two states in a chainwise linkage pattern with
constant couplings of finite duration. The probability for a counterintuitive
transition is found to increase with the square of the coupling and decrease
with the squares of the interaction duration, the energy splitting between the
parallel energies, and the tilt (chirp) rate. Physical examples of this model
can be found in coherent atomic excitation and optical shielding in cold atomic
collisions
Universal low-energy properties of three two-dimensional particles
Universal low-energy properties are studied for three identical bosons
confined in two dimensions. The short-range pair-wise interaction in the
low-energy limit is described by means of the boundary condition model. The
wave function is expanded in a set of eigenfunctions on the hypersphere and the
system of hyper-radial equations is used to obtain analytical and numerical
results. Within the framework of this method, exact analytical expressions are
derived for the eigenpotentials and the coupling terms of hyper-radial
equations. The derivation of the coupling terms is generally applicable to a
variety of three-body problems provided the interaction is described by the
boundary condition model. The asymptotic form of the total wave function at a
small and a large hyper-radius is studied and the universal logarithmic
dependence in the vicinity of the triple-collision point is
derived. Precise three-body binding energies and the scattering length
are calculated.Comment: 30 pages with 13 figure
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