 
Summary: Atomic tunnel arrays
B.P. Anderson and M.A. Kasevich
Physics Department, Yale University, New Haven, CT 065208120, USA
1. Introduction
The demonstration of BoseEinstein condensation in atomic gases [1] raises the possi
bility of exploring relationships between coherence properties of atom vapor condensates
[2, 3, 4, 5], superfluid He [6, 7], and superconductivity [8]. These quantum systems share
common theoretical framework and exhibit similar observable characteristics. In this lec
ture, we discuss observed behavior [9] of an optically trapped BoseEinstein condensate
(BEC) analogous to the Josephson effect of superconducting systems.
2. Josephson effects in superconductors
Josephson effects are a range of phenomena exhibited by two superconductors sepa
rated by a thin insulating barrier. Cooper pair electron tunneling through the barrier
couples the dynamics of the two macroscopically occupied quantum states. Under appro
priate conditions [10, 11], the wavefunction of each superconductor can be approximated
as
q = n1/2
q eiq(t)
,(1)
where q represents either superconductor 1 or 2, n is the Cooper pair number density
