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Seminário do grupo de Óptica e Informação Quântica

Data: Sexta-Feira 03/08/2018, Sala A5-01, 11 am.

Palestrante: Markus GRASSL (Max Planck Institute for the Science of Light)

Título: Multi-Photon States with Extremal Polarization

Abstract: The polarization of light can be characterized by four Stokes
parameters, corresponding to the intensity of the light and the three
components of the polarization direction.  In the realm of quantum
mechanics, one obtains Stokes operators that can be expressed in terms
of creation/annihilation operators of two modes.  Fixing the total
number of photons, one is left with three Stokes operators
corresponding to the algebra su(2).

An SU(2) coherent state with N photons is a state where all N photons
have the same polarization direction.  Such a state can be considered
as the most classical one.  In contrast, already for N=2 photons there
are pure states for which the expectation value of the three Stokes
operators vanishes, that is, they are unpolarized to first order. The
second moment of the operators, however, will be direction dependent.

This leads to the question of finding pure states of N photons for
which the higher moments of the Stokes operators are isotropic up to a
certain order t.  In some sense, those states can be considered to be
the opposite of coherent states, termed the Kings of Quantumness.

We will discuss in particular the multi-pole representation that
allows us to find many examples of such states, and how these states
can be illustrated in terms of the Majorana representation by N points
on the unit sphere.

The maximal order t up to which the Stokes operators are isotropic
appears to be the same as the maximal order of so-called spherical
t-designs, objects that have been widely studied in mathematics.
However, a putative connection between the two different objects has
yet to be identified.


The talk is based on joint theoretical work with Gunnar Björk,
Pablo de la Hoz, Andrei B. Klimov, Gerd Leuchs, Luis L. Sánchez-Soto,
and Ulrich Seyfarth.