The second quantum revolution aims at harnessing more subtle quantum characteristics, such as the non-cloning theorem, single atom and photon manipulation, Bose-Einstein condensation
, atom and ion trapping, and quantum entanglement.
In a weakly interacting Bose system, the macroscopic wave function [PSI] appears as the order parameter of the Bose-Einstein condensation
, obeying the Gross-Pitaevskii (GP) equation [18-21]:
Understanding Bose-Einstein condensation
is very important in the study of magnetism and superconductivity.
After setting out the foundations, they cover Bose-Einstein condensation
, quantum kinetic theory, quantum matter waves, ultra-cold molecules and scattering, ultra-cold Fermions, and atoms in optical lattices.
The discovery of Bose-Einstein condensation
. The discovery of a new state of matter in extreme temperature conditions--the Bose-Einstein condensate --in 1995 by American and German experimental physicists was another penetration of the inquisitive human mind into the secrets of the microscopic world of matter surrounding us.
Harko, "Cosmological dynamics of dark matter Bose-Einstein condensation
," Physical Review D, vol.
In distinction with the ideal Bose gas (IBG), which suffers the so-called Bose-Einstein condensation
(BEC) in three dimensions, the IFG shows a smooth thermodynamic behavior as function of the particle density and temperature; this, however, does not preclude interesting behavior as has been pointed out in [28, 40], where it is suggested that the IFG can suffer a condensation-like process at a characteristic temperature [T.sup.0].
For example, it is usually chosen as either a harmonic confining potential v(x,t) = -[[absolute value of x].sup.2]/2, or an optical lattice potential v(x,t) = [A.sub.1] cos([L.sub.1]x) + [A.sub.2] cos([L.sub.2]y) + [A.sub.3] cos([L.sub.3]z) with constants [A.sub.n], [L.sub.n], and n = 1,2,3, for studying the Bose-Einstein condensation
with internal degrees of freedom in alkali atom gases.
was first predicted by Einstein and Indian physicist Bose in 1924-1925.
By cooling fermions, in addition to bosons, researchers can explore a variety of phenomena such as Bose-Einstein condensation
, Cooper pairing of fermions, ultracold atomic interactions and superfluidity in dilute atomic gases.