8,827 research outputs found
Analytical results for a Bessel function times Legendre polynomials class integrals
When treating problems of vector diffraction in electromagnetic theory, the
evaluation of the integral involving Bessel and associated Legendre functions
is necessary. Here we present the analytical result for this integral that will
make unnecessary numerical quadrature techniques or localized approximations.
The solution is presented using the properties of the Bessel and associated
Legendre functions.Comment: 4 page
Optimized generation of spatial qudits by using a pure phase spatial light modulator
We present a method for preparing arbitrary pure states of spatial qudits,
namely, D-dimensional (D > 2) quantum systems carrying information in the
transverse momentum and position of single photons. For this purpose, a set of
D slits with complex transmission are displayed on a spatial light modulator
(SLM). In a recent work we have shown a method that requires a single
phase-only SLM to control independently the complex coefficients which define
the quantum state of dimension D. The amplitude information was codified by
introducing phase gratings inside each slit and the phase value of the complex
transmission was added to the phase gratings. After a spatial filtering process
we obtained in the image plane the desired qudit state. Although this method
has proven to be a good alternative to compact the previously reported
architectures, it presents some features that could be improved. In this paper
we present an alternative scheme to codify the required phase values that
minimizes the effects of temporal phase fluctuations associated to the SLM
where the codification is carried on. In this scheme the amplitudes are set by
appropriate phase gratings addressed at the SLM while the relative phases are
obtained by a lateral displacement of these phase gratings. We show that this
method improves the quality of the prepared state and provides very high
fidelities of preparation for any state. An additional advantage of this scheme
is that a complete 2\pi modulation is obtained by shifting the grating by one
period, and hence the encoding is not limited by the phase modulation range
achieved by the SLM. Numerical simulations, that take into account the phase
fluctuations, show high fidelities for thousands of qubit states covering the
whole Bloch sphere surface. Similar analysis are performed for qudits with D =
3 and D = 7.Comment: 12 pages, 7 figure
A 3-form Gauge Potential in 5D in connection with a Possible Dark Sector of 4D-Electrodynamics
We here propose a 5-dimensional {\bf Abelian gauge} model based on the mixing
between a potential and an Abelian 3-form field by means of a
topological mass term. An extended covariant derivative is introduced to
minimally couple a Dirac field to the potential, while this same
covariant derivative non-minimally couples the 3-form field to the charged
fermion. A number of properties are discussed in 5D; in particular, the
appearance of a topological fermionic current. A 4-dimensional reduced version
of the model is investigated and, { \bf in addition to the electric- and
magnetic-sort of fields,} there emerges an extra set of electric- and
magnetic-like fields which contribute a negative pressure and may be identified
as a possible fraction of dark energy. The role of the topological fermionic
current is also contemplated upon dimensional reduction from 5D to 4D. Other
issues we present in 4 space-time dimensions are the emergence {\bf of a
pseudo-scalar massive particle,} an extra massive neutral gauge boson,{\bf
which we interpret as a kind of paraphoton}, and the calculation of spin- and
velocity-dependent interparticle potentials associated to the exchange of the
intermediate bosonic fields of the model.Comment: -- 30 pages -- L. P. R. Ospedal appears as a new co-author;
modifications by inclusion of the gravitational sector and the attainment of
a spin- and velocity-dependent potential as an application have been worked
out in this Revised Versio
Order and Disorder in AKLT Antiferromagnets in Three Dimensions
The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a
family of quantum antiferromagnets on arbitrary lattices, where the local spin
S is an integer multiple M of half the lattice coordination number. The equal
time quantum correlations in their ground states may be computed as finite
temperature correlations of a classical O(3) model on the same lattice, where
the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping
implies that all AKLT states are quantum disordered. We consider AKLT states in
d=3 where the nature of the AKLT states is now a question of detail depending
upon the choice of lattice and spin; for sufficiently large S some form of Neel
order is almost inevitable. On the unfrustrated cubic lattice, we find that all
AKLT states are ordered while for the unfrustrated diamond lattice the minimal
S=2 state is disordered while all other states are ordered. On the frustrated
pyrochlore lattice, we find (conservatively) that several states starting with
the minimal S=3 state are disordered. The disordered AKLT models we report here
are a significant addition to the catalog of magnetic Hamiltonians in d=3 with
ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure
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