28 research outputs found
Optical realization of nonlinear quantum dynamics
In a cavity filled with a Kerr medium it is possible to generate the
superposition of coherent states, i.e. Schroodinger cat states may be realized
in this system. We show that such a medium may be mimicked by the propagation
of a conveniently shaped Gaussian beam in a GRIN device. This is attained by
introducing a second order correction to the paraxial propagation of the beam.
An additional result is that a Gaussian beam propagating in GRIN media, may
split into two Gaussian beams
Quasiprobability distribution functions from fractional Fourier transforms
We show, in a formal way, how a class of complex quasiprobability
distribution functions may be introduced by using the fractional Fourier
transform. This leads to the Fresnel transform of a characteristic function
instead of the usual Fourier transform. We end the manuscript by showing a way
in which the distribution we are introducing may be reconstructed by using
atom-field interactions.Comment: 11 pages, 2 figure
The von Neumann Entropy for Mixed States
The Araki-Lieb inequality is commonly used to calculate the entropy of
subsystems when they are initially in pure states as this forces the entropy of
the two subsystems to be equal after the complete system evolves. Then, it is
easy to calculate the entropy of a large subsystem by finding the entropy of
the small one. To the best of our knowledge, there does not exist a way of
calculating the entropy when one of the subsystems is initially in a mixed
state. We show here that it is possible to use the Araki-Lieb inequality in
this case and find the von Neumann entropy for the large (infinite) system. We
show this in the two-level atom-field interaction.Comment: 10 pages, 4 figure