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 $U(1)$ 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 $U(1)$ 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 $U(1)$ 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