This special issue of Journal of Optics B: Quantum and Semiclassical
Optics is composed mainly of extended versions of
talks and papers presented at the Eighth International Conference on
Squeezed States and Uncertainty Relations held in Puebla, Mexico
on 9–13 June 2003. The Conference was hosted by Instituto de
Astrofísica, Óptica y Electrónica, and the Universidad Nacional
Autónoma de México.
This series of meetings began at the University of Maryland,
College Park, USA, in March 1991. The second and third workshops
were organized by the Lebedev Physical Institute in Moscow,
Russia, in 1992 and by the University of Maryland Baltimore County,
USA, in 1993, respectively. Afterwards, it was decided that the
workshop series should be held every two years. Thus the fourth meeting
took place at the University of Shanxi in China and was supported
by the International Union of Pure and Applied Physics (IUPAP).
The next three meetings in 1997, 1999 and 2001 were held in Lake
Balatonfüred, Hungary, in Naples, Italy, and in Boston, USA,
respectively. All of them were sponsored by IUPAP. The ninth workshop
will take place in Besançon, France, in 2005.
The conference has now become one of the major international meetings
on quantum optics and the foundations of quantum mechanics, where most of
the active research groups throughout the world present their new
results. Accordingly this conference has been able to align itself
to the current trend in quantum optics and quantum mechanics.
The Puebla meeting covered most extensively the following areas:
quantum measurements, quantum computing and information theory,
trapped atoms and degenerate gases, and the generation and characterization
of quantum states of light. The meeting also covered squeeze-like
transformations in areas other than quantum optics, such as
atomic physics, nuclear physics, statistical physics and relativity,
as well as optical devices. There were many new participants at
this meeting, particularly from Latin American countries including,
of course, Mexico.
There were many talks on the subjects traditionally covered in this
conference series, including quantum fluctuations, different forms of
squeezing, unlike kinds of nonclassical states of light, and distinct
representations of the quantum superposition principle, such as even and odd
coherent states. The entanglement phenomenon, frequently in the form
of the EPR paradox, is responsible for the main advantages of quantum
engineering compared with classical methods. Even though
entanglement has been known since the early days of quantum mechanics, its
properties, such as the most appropriate entanglement measures, are still
under current investigation. The phenomena of dissipations and
decoherence of the initial pure states are very important because
the fast decoherence can destroy all the advantages of quantum processes
in teleportation, quantum computing and image processing. Due to this,
methods of controlling the decoherence, such as by the use of
different kinds of nonlinearities and deformations, are also under study.
From the very beginning of quantum mechanics, the uncertainty
relations were basic inequalities distinguishing the classical and
quantum worlds.
Among the theoretical methods for quantum optics and quantum mechanics,
this conference covered phase space and group representations, such as
the Wigner and probability distribution functions, which provide an
alternative approach to the Schr\"odinger or Heisenberg picture. Different
forms of probability representations of quantum states are important tools
to be applied in studying various quantum phenomena, such as quantum
interference, decoherence and quantum tomography. They have been
established also as a very useful tool in all branches of classical optics.
From the mathematical point of view, it is well known
that the coherent
and squeezed states are representations of the Lorentz
group. It was noted
throughout the conference that another form of the Lorentz group, namely,
the 2 x 2 representation of the SL(2,c) group, is becoming more
prominent while providing the mathematical basis for the Poincaré
sphere, entanglement, qubits and decoherence, as well as classical ray optics
traditionally based on 2 x 2 `ABCD' matrices.
The contributions of this special issue cover the most recent
trends in all areas of quantum optics and the foundations of quantum
mechanics.