79 research outputs found
Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation
In this article we introduce a differential equation for the first order
correlation function of a Bose-Einstein condensate at T=0. The
Bogoliubov approximation is used. Our approach points out directly the
dependence on the physical parameters. Furthermore it suggests a numerical
method to calculate without solving an eigenvector problem. The
equation is generalized to the case of non zero temperature.Comment: 9 pages, ps format. This article was published in EPJD vol. 14(1)
(2001), pp.105-11
Output-sensitive algorithm for generating the flats of a matroid
We present an output-sensitive algorithm for generating the whole set of
flats of a finite matroid. Given a procedure, P, that decides in S_P time steps
if a set is independent, the time complexity of the algorithm is O(N^2 M S_P),
where N and M are the input and output size, respectively. In the case of
vectorial matroids, a specific algorithm is reported whose time complexity is
equal to O(N^2 M d^2), d being the rank of the matroid. In some cases this
algorithm can provide an efficient method for computing zonotopes in
-representation, given their representation in terms of Minkowski sum of
known segments
Exponential complexity and ontological theories of quantum mechanics
Ontological theories of quantum mechanics describe a single system by means
of well-defined classical variables and attribute the quantum uncertainties to
our ignorance about the underlying reality represented by these variables. We
consider the general class of ontological theories describing a quantum system
by a set of variables with Markovian (either deterministic or stochastic)
evolution. We provide the first proof that the number of continuous variables
can not be smaller than 2N-2, N being the Hilbert space dimension. Thus, any
ontological Markovian theory of quantum mechanics requires a number of
variables which grows exponentially with the physical size. This result is
relevant also in the framework of quantum Monte Carlo methods
Non-Locality of Experimental Qutrit Pairs
The insight due to John Bell that the joint behavior of individually measured
entangled quantum systems cannot be explained by shared information remains a
mystery to this day. We describe an experiment, and its analysis, displaying
non-locality of entangled qutrit pairs. The non-locality of such systems, as
compared to qubit pairs, is of particular interest since it potentially opens
the door for tests of bipartite non-local behavior independent of probabilistic
Bell inequalities, but of deterministic nature
Quantum decoherence reduction by increasing the thermal bath temperature
The well-known increase of the decoherence rate with the temperature, for a
quantum system coupled to a linear thermal bath, holds no longer for a
different bath dynamics. This is shown by means of a simple classical
non-linear bath, as well as a quantum spin-boson model. The anomalous effect is
due to the temperature dependence of the bath spectral profile. The decoherence
reduction via the temperature increase can be relevant for the design of
quantum computers
Generating Schr\"{o}dinger-cat states in momentum and internal-state space from Bose-Einstein condensates with repulsive interactions
Resonant Raman coupling between internal levels induced by continuous
illumination of non-collinear laser beams can create double-well momentum-space
potentials for multi-level ``periodically-dressed'' atoms. We develop an
approximate many-body formalism for a weakly interacting, trapped
periodically-dressed Bose gas which illustrates how a tunable exchange
interaction yields correlated many-body ground states. In contrast to the case
of a position-space double well, the ground state of stable
periodically-dressed Bose gases with repulsive interactions tends toward a
Schr\"{o}dinger cat state in the regime where interactions dominate the
momentum-space tunnelling induced by the external trapping potential. The
dependence of the momentum-space tunnelling and exchange interaction on
experimental parameters is derived. We discuss how real-time control of
experimental parameters can be used to create Schr\"{o}dinger cat states either
between momentum or internal states, and how these states could be dynamically
controlled towards highly sensitive interferometry and frequency metrology.Comment: 7 pages, 3 figures. Submitted to PR
- …