(Continued from previous message)

certain moment, also be oriented in the same way.  A moment later,
however, the electric field will have precessed a bit (from the one o'clock
position, say, to the three o'clock position; another way of saying
this is that the phase of the electric field will have advanced a
bit) but the orientation of the field at each point on the vertical
slice will be the same. With the use of special gratings one can
produce an entirely different mode of light, one in which the
electric field phase coils around the beam axis, and the light is
said to possess an orbital angular momentum, or OAM. This condition
is visualized at the following website prepared by physicists at
Colgate University:
departments.colgate.edu/physics/research/optics/oamgp/gp.htm.  This
extra property of "coiled light" might be exploitable for future
quantum computing.  For instance, recently a group at the University
of Vienna used OAM in light to create a three-dimensional entangled
state, or "qutrit" (Vaziri et al., Physical Review Letters, 9 Dec
2002).  Third issue: geometrical phase.   When a light pulse is made
to follow a closed loop path in real space, the phase of the
returning beam might be slightly off from the phase of light
starting off at that point.  This disparity (which can result in an
interference effect) can be modified by changing the path length.
It can also be modified by changing the path geometry.  In addition,
the space does not need to be real space. When the "mode" (set of
standing waves in the beam) is changed, it can also produce a phase
when changing the geometry of the path in "mode space,"  and it is
this that the Colgate physicists have measured. (see a schematic of
the setup at this website:
departments.colgate.edu/physics/research/optics/oamgp/geomph.htm ).
The change in phase that a quantum system undergoes in going around
a closed path in a space of states or parameters is called a
"geometrical phase," and can be measured when the light emerges from
the path to form a spiral shaped interference pattern at an external
detector (Galvez et al., Physical Review Letters, 23 May 2003;
contact Kiko Galvez, egalvez{at}mail.colgate.edu, 315-228-7205).  (For
further background, see Physical Review Focus item at
focus.aps.org/story/v9/st29 and an article on geometric phase in
Physics Today, Dec 1990.)

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