4,127 research outputs found
General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems
We generalize the correlation functions of the Clauser-Horne-Shimony-Holt
(CHSH) inequality to arbitrarily high-dimensional systems. Based on this
generalization, we construct the general CHSH inequality for bipartite quantum
systems of arbitrarily high dimensionality, which takes the same simple form as
CHSH inequality for two-dimension. This inequality is optimal in the same sense
as the CHSH inequality for two dimensional systems, namely, the maximal amount
by which the inequality is violated consists with the maximal resistance to
noise. We also discuss the physical meaning and general definition of the
correlation functions. Furthermore, by giving another specific set of the
correlation functions with the same physical meaning, we realize the inequality
presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].Comment: 4 pages, accepted by Phys. Rev. Let
Quantum phase transition in a three-level atom-molecule system
We adopt a three-level bosonic model to investigate the quantum phase
transition in an ultracold atom-molecule conversion system which includes one
atomic mode and two molecular modes. Through thoroughly exploring the
properties of energy level structure, fidelity, and adiabatical geometric
phase, we confirm that the system exists a second-order phase transition from
an atommolecule mixture phase to a pure molecule phase. We give the explicit
expression of the critical point and obtain two scaling laws to characterize
this transition. In particular we find that both the critical exponents and the
behaviors of ground-state geometric phase change obviously in contrast to a
similar two-level model. Our analytical calculations show that the ground-state
geometric phase jumps from zero to ?pi/3 at the critical point. This
discontinuous behavior has been checked by numerical simulations and it can be
used to identify the phase transition in the system.Comment: 8 pages,8 figure
Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap
We investigate the tunnelling dynamics of Bose-Einstein-Condensates(BECs) in
a symmetric as well as in a tilted triple-well trap within the framework of
mean-field treatment. The eigenenergies as the functions of the zero-point
energy difference between the tilted wells show a striking entangled star
structure when the atomic interaction is large. We then achieve insight into
the oscillation solutions around the corresponding eigenstates and observe
several new types of Josephson oscillations. With increasing the atomic
interaction, the Josephson-type oscillation is blocked and the self-trapping
solution emerges. The condensates are self-trapped either in one well or in two
wells but no scaling-law is observed near transition points. In particular, we
find that the transition from the Josephson-type oscillation to the
self-trapping is accompanied with some irregular regime where tunnelling
dynamics is dominated by chaos. The above analysis is facilitated with the help
of the Poicar\'{e} section method that visualizes the motions of BECs in a
reduced phase plane.Comment: 10 pages, 11 figure
Spinor Decomposition of SU(2) Gauge Potential and The Spinor Structures of Chern-Simons and Chern Density
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli
spinors is studied. Using this decomposition, the spinor strutures of the
Chern-Simons form and the Chern density are obtained. Furthermore, by these
spinor structures, the knot quantum number of non-Abelian gauge theory is
discussed, and the second Chern number is characterized by the Hopf indices and
the Brouwer degrees of -mapping.Comment: 11 page
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