25,009 research outputs found
U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator
We show that a Dirac Hamiltonian with equal scalar and vector harmonic
oscillator potentials has not only a spin symmetry but an U(3) symmetry and
that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials
equal in magnitude but opposite in sign has not only a pseudospin symmetry but
a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.Comment: 8 pages, 0 figures, pusblished in Physical Review Letters 95, 252501
(2005
Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement
We show that the effect of measurement back-action results in the generation
of multiple many-body spatial modes of ultracold atoms trapped in an optical
lattice, when scattered light is detected. The multipartite mode entanglement
properties and their nontrivial spatial overlap can be varied by tuning the
optical geometry in a single setup. This can be used to engineer quantum states
and dynamics of matter fields. We provide examples of multimode generalizations
of parametric down-conversion, Dicke, and other states, investigate the
entanglement properties of such states, and show how they can be transformed
into a class of generalized squeezed states. Further, we propose how these
modes can be used to detect and measure entanglement in quantum gases.Comment: 6 Pages, 3 Figures, Supplemental Material include
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