RESUMO
We investigate pattern revivals in specially designed optical structures that combine different transverse modes. In general, the resulting pattern is not preserved under free propagation and gets transformed due to nonsynchronized Gouy phases. However, it is possible to build structures in which the Gouy phases synchronize at specific fractional values, thus recovering the initial pattern at the corresponding longitudinal positions. This effect is illustrated with a radially structured light spot in which the beam energy can be addressed to different positions without the need of intermediate optical components, which can be useful for optical communications and optical tweezing with structured beams.
RESUMO
Pairs of photons simultaneously entangled in their path and polarization degrees of freedom are used to measure the topological phase acquired by bipartite entangled states. Conditional phase local unitary operations having the polarization degree of freedom as the control variable are applied. Qudits of arbitrary dimensions are encoded on the photons transverse positions while polarization entanglement is used as an auxiliary resource for quantum interference measurements. With this scheme the fractional phases predicted for dimensions d = 2, 3 and 4 could be measured with visibilities for the interference curves beyond the limit allowed for classical sources, which is expected for a source of quantum correlated photons. The strategy of perform a quantum interferometry experiment with photons entangled in an auxiliary degree of freedom and apply unitary local operations conditioned to this auxiliary variable shows an increase to the signal to noise ratio, simplifies alignment and can be used in different applications. This offers an interesting perspective for the efficient implementation of phase gates in quantum computing with hyperentangled photon sources in polarization and path degrees of freedom. Furthermore, one can conjecture whether the measured phase can serve as a dimensionality identifier of the Hilbert space dimension for an unknown state preparation.
RESUMO
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their topological aspects are analyzed. The geometric phase is explicitly calculated in terms of the concurrence. As a main result, we predict a fractional phase for cyclic evolutions in the multiply connected space of maximally entangled states. This result is potentially useful for noise robust implementations of quantum gates.