698 research outputs found
Error of truncated Chebyshev series and other near minimax polynomial approximations
AbstractIt is well known that a near minimax polynomial approximation p is obtained by truncating the Chebyshev series of a function ƒ; after n + 1 terms. It is shown that if ƒ; ϵ C(n + 1)[−1, 1], then ∥ƒ; − p ∥ may be expressed in terms of ƒ;(n + 1) in the same manner as the error of minimax approximation. The result is extended to other types of near minimax approximation
Towards non-classical light storage via atomic-vapor Raman scattering
We present experimental work that investigates whether quantum information carried by light can be stored via reversible mapping of the quantum state of such light onto a collective atomic coherence. Such a quantum memory could be utilized to allow quantum communication over long, lossy channels. Current efforts concentrate on writing a photon-number-squeezed state of light onto a collective coherence between the ground-state hyperfine levels of 87Rb atoms in a warm vapor cell, and subsequent on-demand retrieval of this light. In this approach, intensity squeezing between the written and retrieved photon fields provides evidence for storage of a photon-number-squeezed state of light. The scheme is based on spontaneous Raman transitions that create the atomic coherence, and at the same time convert control fields into signal fields that propagate under conditions of electromagnetically induced transparency. We present experimental results demonstrating the storage and retrieval of light using this method, and discuss techniques for measuring intensity squeezing between these photon fields
Phase Coherence and Control of Stored Photonic Information
We report the demonstration of phase coherence and control for the recently
developed "light storage" technique. Specifically, we use a pulsed magnetic
field to vary the phase of atomic spin excitations which result from the
deceleration and storing of a light pulse in warm Rb vapor. We then convert the
spin excitations back into light and detect the resultant phase shift in an
optical interferometric measurement. The coherent storage of photon states in
matter is essential for the practical realization of many basic concepts in
quantum information processing.Comment: 5 pages, 3 figures. Submitted to Phys. Rev. Let
Three-dimensional theory for interaction between atomic ensembles and free-space light
Atomic ensembles have shown to be a promising candidate for implementations
of quantum information processing by many recently-discovered schemes. All
these schemes are based on the interaction between optical beams and atomic
ensembles. For description of these interactions, one assumed either a
cavity-QED model or a one-dimensional light propagation model, which is still
inadequate for a full prediction and understanding of most of the current
experimental efforts which are actually taken in the three-dimensional free
space. Here, we propose a perturbative theory to describe the three-dimensional
effects in interaction between atomic ensembles and free-space light with a
level configuration important for several applications. The calculations reveal
some significant effects which are not known before from the other approaches,
such as the inherent mode-mismatching noise and the optimal mode-matching
conditions. The three-dimensional theory confirms the collective enhancement of
the signal-to-noise ratio which is believed to be one of the main advantage of
the ensemble-based quantum information processing schemes, however, it also
shows that this enhancement need to be understood in a more subtle way with an
appropriate mode matching method.Comment: 16 pages, 9 figure
Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models
We report on a non-perturbative approach to the 1D and 2D Hubbard models that
is capable of recovering both strong and weak-coupling limits. We first show
that even when the on-site Coulomb repulsion, U, is much smaller than the
bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D.
Consequently, the Hubbard model at half-filling is always in the
strong-coupling non-perturbative regime. For both large and small U, we find
that the population of nearest-neighbour singlet states approaches a value of
order unity as as would be expected for antiferromagnetic order. We
also find that the double occupancy is a smooth monotonic function of U and
approaches the anticipated non-interacting limit and large U limits. Finally,
in our results for the heat capacity in 1D differ by no more than 1% from the
Bethe ansatz predictions. In addition, we find that in 2D, the heat capacity vs
T for different values of U exhibits a universal crossing point at two
characteristic temperatures as is seen experimentally in a wide range of
strongly-correlated systems such as , , and . The
success of this method in recovering well-established results that stem
fundamentally from the Coulomb interaction suggests that local dynamics are at
the heart of the physics of strongly correlated systems.Comment: 10 pages, 16 figures included in text, Final version for publication
with a reference added and minor corrections. Phys. Rev. B, in pres
Storing and releasing light in a gas of moving atoms
We propose a scheme of storing and releasing pulses or cw beams of light in a
moving atomic medium illuminated by two stationary and spatially separated
control lasers. The method is based on electromagnetically induced transparency
(EIT) but in contrast to previous schemes, storage and retrieval of the probe
pulse can be achieved at different locations and without switching off the
control laser.Comment: 4 pages, 3 figures, revised versio
Testing Lorentz and CPT symmetry with hydrogen masers
We present details from a recent test of Lorentz and CPT symmetry using
hydrogen masers. We have placed a new limit on Lorentz and CPT violation of the
proton in terms of a recent standard model extension by placing a bound on
sidereal variation of the F = 1 Zeeman frequency in hydrogen. Here, the
theoretical standard model extension is reviewed. The operating principles of
the maser and the double resonance technique used to measure the Zeeman
frequency are discussed. The characterization of systematic effects is
described, and the method of data analysis is presented. We compare our result
to other recent experiments, and discuss potential steps to improve our
measurement.Comment: 26 pages, 16 figure
From Storage and Retrieval of Pulses to Adiabatons
We investigate whether it is possible to store and retrieve the intense probe
pulse from a -type homogeneous medium of cold atoms. Through numerical
simulations we show that it is possible to store and retrieve the probe pulse
which are not necessarily weak. As the intensity of the probe pulse increases,
the retrieved pulse remains a replica of the original pulse, however there is
overall broadening and loss of the intensity. These effects can be understood
in terms of the dependence of absorption on the intensity of the probe. We
include the dynamics of the control field, which becomes especially important
as the intensity of the probe pulse increases. We use the theory of adiabatons
[Grobe {\it et al.} Phys. Rev. Lett. {\bf 73}, 3183 (1994)] to understand the
storage and retrieval of light pulses at moderate powers.Comment: 15 pages, 7 figures, typed in RevTe
Temporal build-up of electromagnetically induced transparency and absorption resonances in degenerate two-level transitions
The temporal evolution of electromagnetically induced transparency (EIT) and
absorption (EIA) coherence resonances in pump-probe spectroscopy of degenerate
two-level atomic transition is studied for light intensities below saturation.
Analytical expression for the transient absorption spectra are given for simple
model systems and a model for the calculation of the time dependent response of
realistic atomic transitions, where the Zeeman degeneracy is fully accounted
for, is presented. EIT and EIA resonances have a similar (opposite sign) time
dependent lineshape, however, the EIA evolution is slower and thus narrower
lines are observed for long interaction time. Qualitative agreement with the
theoretical predictions is obtained for the transient probe absorption on the
line in an atomic beam experiment.Comment: 10 pages, 9 figures. Submitted to Phys. Rev.
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