27 research outputs found
Measuring Pancharatnam's relative phase for SO(3) evolutions using spin polarimetry
In polarimetry, a superposition of internal quantal states is exposed to a
single Hamiltonian and information about the evolution of the quantal states is
inferred from projection measurements on the final superposition. In this
framework, we here extend the polarimetric test of Pancharatnam's relative
phase for spin proposed by Wagh and Rakhecha [Phys. Lett. A {\bf 197},
112 (1995)] to spin undergoing noncyclic SO(3) evolution. We
demonstrate that the output intensity for higher spin values is a polynomial
function of the corresponding spin intensity. We further propose a
general method to extract the noncyclic SO(3) phase and visibility by rigid
translation of two spin flippers. Polarimetry on higher spin states
may in practice be done with spin polarized atomic beams.Comment: New title, minor corrections, journal reference adde
Exact solutions of n-level systems and gauge theories
We find a relationship between unitary transformations of the dynamics of
quantum systems with time-dependent Hamiltonians and gauge theories. In
particular, we show that the nonrelativistic dynamics of spin-
particles in a magnetic field can be formulated in a natural way as
an SU(2) gauge theory, with the magnetic field playing the role of the
gauge potential A^i. The present approach can also be applied to systems of n
levels with time-dependent potentials, U(n) being the gauge group. This
geometric interpretation provides a powerful method to find exact solutions of
the Schr\"odinger equation. The root of the present approach rests in the
Hermiticity property of the Hamiltonian operators involved. In addition, the
relationship with true gauge symmetries of n-level quantum systems is
discussed.Comment: LaTeX file, 5 pages, published versio
Berry phase from a quantum Zeno effect
We exhibit a specific implementation of the creation of geometrical phase
through the state-space evolution generated by the dynamic quantum Zeno effect.
That is, a system is guided through a closed loop in Hilbert space by means a
sequence of closely spaced projections leading to a phase difference with
respect to the original state. Our goal is the proposal of a specific
experimental setup in which this phase could be created and observed. To this
end we study the case of neutron spin, examine the practical aspects of
realizing the "projections," and estimate the difference between the idealized
projections and the experimental implementation.Comment: 13 pages, 2 figure
Higher dimensional dust collapse with a cosmological constant
The general solution of the Einstein equation for higher dimensional (HD)
spherically symmetric collapse of inhomogeneous dust in presence of a
cosmological term, i.e., exact interior solutions of the Einstein field
equations is presented for the HD Tolman-Bondi metrics imbedded in a de Sitter
background. The solution is then matched to exterior HD Scwarschild-de Sitter.
A brief discussion on the causal structure singularities and horizons is
provided. It turns out that the collapse proceed in the same way as in the
Minkowski background, i.e., the strong curvature naked singularities form and
that the higher dimensions seem to favor black holes rather than naked
singularities.Comment: 7 Pages, no figure