26,980 research outputs found
Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing
We study the strong coupling between photons and atoms that can be achieved
in an optical nanofiber geometry when the interaction is dispersive. While the
Purcell enhancement factor for spontaneous emission into the guided mode does
not reach the strong-coupling regime for individual atoms, one can obtain high
cooperativity for ensembles of a few thousand atoms due to the tight
confinement of the guided modes and constructive interference over the entire
chain of trapped atoms. We calculate the dyadic Green's function, which
determines the scattering of light by atoms in the presence of the fiber, and
thus the phase shift and polarization rotation induced on the guided light by
the trapped atoms. The Green's function is related to a full
Heisenberg-Langevin treatment of the dispersive response of the quantized field
to tensor polarizable atoms. We apply our formalism to quantum nondemolition
(QND) measurement of the atoms via polarimetry. We study shot-noise-limited
detection of atom number for atoms in a completely mixed spin state and the
squeezing of projection noise for atoms in clock states. Compared with
squeezing of atomic ensembles in free space, we capitalize on unique features
that arise in the nanofiber geometry including anisotropy of both the intensity
and polarization of the guided modes. We use a first principles stochastic
master equation to model the squeezing as function of time in the presence of
decoherence due to optical pumping. We find a peak metrological squeezing of ~5
dB is achievable with current technology for ~2500 atoms trapped 180 nm from
the surface of a nanofiber with radius a=225 nm.Comment: To be appeared on PR
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions
We develop a robust uncertainty principle for finite signals in C^N which
states that for almost all subsets T,W of {0,...,N-1} such that |T|+|W| ~ (log
N)^(-1/2) N, there is no sigal f supported on T whose discrete Fourier
transform is supported on W. In fact, we can make the above uncertainty
principle quantitative in the sense that if f is supported on T, then only a
small percentage of the energy (less than half, say) of its Fourier transform
is concentrated on W.
As an application of this robust uncertainty principle (QRUP), we consider
the problem of decomposing a signal into a sparse superposition of spikes and
complex sinusoids. We show that if a generic signal f has a decomposition using
spike and frequency locations in T and W respectively, and obeying |T| + |W| <=
C (\log N)^{-1/2} N, then this is the unique sparsest possible decomposition
(all other decompositions have more non-zero terms). In addition, if |T| + |W|
<= C (\log N)^{-1} N, then this sparsest decomposition can be found by solving
a convex optimization problem.Comment: 25 pages, 9 figure
Band offsets and stability of BeTe/ZnSe (100) heterojunctions
We present ab-initio studies of band offsets, formation energy, and stability
of (100) heterojunctions between (Zn,Be)(Se,Te) zincblende compounds, and in
particular of the lattice-matched BeTe/ZnSe interface. Equal band offsets are
found at Be/Se and Zn/Te abrupt interfaces, as well as at mixed interfaces, in
agreement with the established understanding of band offsets at isovalent
heterojunctions. Thermodynamical arguments suggest that islands of non-nominal
composition may form at the interface, causing offset variations over about 0.8
eV depending on growth conditions. Our findings reconcile recent experiments on
BeTe/ZnSe with the accepted theoretical description.Comment: RevTeX 5 pages, 3 embedded figure
Sparsity and `Something Else': An Approach to Encrypted Image Folding
A property of sparse representations in relation to their capacity for
information storage is discussed. It is shown that this feature can be used for
an application that we term Encrypted Image Folding. The proposed procedure is
realizable through any suitable transformation. In particular, in this paper we
illustrate the approach by recourse to the Discrete Cosine Transform and a
combination of redundant Cosine and Dirac dictionaries. The main advantage of
the proposed technique is that both storage and encryption can be achieved
simultaneously using simple processing steps.Comment: Revised manuscript- Software for implementing the Encrypted Image
Folding proposed in this paper is available on
http://www.nonlinear-approx.info
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