42 research outputs found
Exact quantum jump approach to open systems in Bosonic and spin baths
A general method is developed which enables the exact treatment of the
non-Markovian quantum dynamics of open systems through a Monte Carlo simulation
technique. The method is based on a stochastic formulation of the von Neumann
equation of the composite system and employs a pair of product states following
a Markovian random jump process. The performance of the method is illustrated
by means of stochastic simulations of the dynamics of open systems interacting
with a Bosonic reservoir at zero temperature and with a spin bath in the strong
coupling regime.Comment: 4 pages, 2 figure
Beyond single-photon localization at the edge of a Photonic Band Gap
We study spontaneous emission in an atomic ladder system, with both
transitions coupled near-resonantly to the edge of a photonic band gap
continuum. The problem is solved through a recently developed technique and
leads to the formation of a ``two-photon+atom'' bound state with fractional
population trapping in both upper states. In the long-time limit, the atom can
be found excited in a superposition of the upper states and a ``direct''
two-photon process coexists with the stepwise one. The sensitivity of the
effect to the particular form of the density of states is also explored.Comment: to appear in Physical Review
Non-Markovian Decay of a Three Level Cascade Atom in a Structured Reservoir
We present a formalism that enables the study of the non-Markovian dynamics
of a three-level ladder system in a single structured reservoir. The
three-level system is strongly coupled to a bath of reservoir modes and two
quantum excitations of the reservoir are expected. We show that the dynamics
only depends on reservoir structure functions, which are products of the mode
density with the coupling constant squared. This result may enable pseudomode
theory to treat multiple excitations of a structured reservoir. The treatment
uses Laplace transforms and an elimination of variables to obtain a formal
solution. This can be evaluated numerically (with the help of a numerical
inverse Laplace transform) and an example is given. We also compare this result
with the case where the two transitions are coupled to two separate structured
reservoirs (where the example case is also analytically solvable)
Entanglement Sudden Death in Band Gaps
Using the pseudomode method, we evaluate exactly time-dependent entanglement
for two independent qubits, each coupled to a non-Markovian structured
environment. Our results suggest a possible way to control entanglement sudden
death by modifying the qubit-pseudomode detuning and the spectrum of the
reservoirs. Particularly, in environments structured by a model of a
density-of-states gap which has two poles, entanglement trapping and prevention
of entanglement sudden death occur in the weak-coupling regime
Quantum state engineering via unitary transformations
We construct a Hamiltonian for the generation of arbitrary pure states of the
quantized electromagnetic field. The proposition is based upon the fact that a
unitary transformation for the generation of number states has been already
found. The general unitary transformation here obtained, would allow the use of
nonlinear interactions for the production of pure states. We discuss the
applicability of this method by giving examples of generation of simple
superposition states. We also compare our Hamiltonian with the one resulting
from the interaction of trapped ions with two laser fields.Comment: 5 pages in RevTeX, no figures, accepted for publication in Phys. Rev.
de-Broglie Wave-Front Engineering
We propose a simple method for the deterministic generation of an arbitrary
continuous quantum state of the center-of-mass of an atom. The method's spatial
resolution gradually increases with the interaction time with no apparent
fundamental limitations. Such de-Broglie Wave-Front Engineering of the atomic
density can find applications in Atom Lithography, and we discuss possible
implementations of our scheme in atomic beam experiments.Comment: The figures' quality was improved, the text remains intact. 5 pages,
3 figures; submitted to PR
Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentials
We discuss a method to create two-dimensional traps as well as atomic shell,
or bubble, states for a Bose-Einstein condensate initially prepared in a
conventional magnetic trap. The scheme relies on the use of time-dependent,
radio frequency-induced adiabatic potentials. These are shown to form a
versatile and robust tool to generate novel trapping potentials. Our shell
states take the form of thin, highly stable matter-wave bubbles and can serve
as stepping-stones to prepare atoms in highly-excited trap eigenstates or to
study `collapse and revival phenomena'. Their creation requires gravitational
effects to be compensated by applying additional optical dipole potentials.
However, in our scheme gravitation can also be exploited to provide a route to
two-dimensional atom trapping. We demonstrate the loading process for such a
trap and examine experimental conditions under which a 2D condensate may be
prepared.Comment: 16 pages, 10 figure
Exact boundary conditions at finite distance for the time-dependent Schrodinger equation
Exact boundary conditions at finite distance for the solutions of the
time-dependent Schrodinger equation are derived. A numerical scheme based on
Crank-Nicholson method is proposed to illustrate its applicability in several
examples.Comment: Latex.tar.gz file, 20 pages, 9 figure
Grassmann Variables and the Jaynes-Cummings Model
This paper shows that phase space methods using a positive P type
distribution function involving both c-number variables (for the cavity mode)
and Grassmann variables (for the two level atom) can be used to treat the
Jaynes-Cummings model. Although it is a Grassmann function, the distribution
function is equivalent to six c-number functions of the two bosonic variables.
Experimental quantities are given as bosonic phase space integrals involving
the six functions. A Fokker-Planck equation involving both left and right
Grassmann differentiation can be obtained for the distribution function, and is
equivalent to six coupled equations for the six c-number functions.
The approach used involves choosing the canonical form of the (non-unique)
positive P distribution function, where the correspondence rules for bosonic
operators are non-standard and hence the Fokker-Planck equation is also
unusual. Initial conditions, such as for initially uncorrelated states, are
used to determine the initial distribution function. Transformations to new
bosonic variables rotating at the cavity frequency enables the six coupled
equations for the new c-number functions (also equivalent to the canonical
Grassmann distribution function) to be solved analytically, based on an ansatz
from a 1980 paper by Stenholm. It is then shown that the distribution function
is the same as that determined from the well-known solution based on coupled
equations for state vector amplitudes of atomic and n-photon product states.
The treatment of the simple two fermion mode Jaynes-Cummings model is a
useful test case for the future development of phase space Grassmann
distribution functional methods for multi-mode fermionic applications in
quantum-atom optics.Comment: 57 pages, 0 figures. Version
Quantum trajectory approach to stochastically-induced quantum interference effects in coherently-driven two-level atoms
Stochastic perturbation of two-level atoms strongly driven by a coherent
light field is analyzed by the quantum trajectory method. A new method is
developed for calculating the resonance fluorescence spectra from numerical
simulations. It is shown that in the case of dominant incoherent perturbation,
the stochastic noise can unexpectedly create phase correlation between the
neighboring atomic dressed states. This phase correlation is responsible for
quantum interference between the related transitions resulting in anomalous
modifications of the resonance fluorescence spectra.Comment: paper accepted for publicatio