Uncertainty Area (n, f) for Several States Describing Superconducting Josephson Junctions
Schematic diagram of the uncertainty area in the phase difference and charge number (f, n) phase space of
(a) the ground states of H1 and H4 (which are squeezed vacuum states), and
(b) the ground state of H2 and H3 (which are squeezed coherent states).
The units for f and n are (EC/EJ)^0.25
respectively. It can be seen from the diagram (a) that the uncertainty
of the charge number n is squeezed by a factor of 1/16l,
where l = (EJ/EC)^0.5.
In (b) the uncertainty area has been displaced away from the origin by
an amount d, because linear driving terms are present in both H2
and H3. Again, the uncertaintry of the charge
number n is squeezed by a factor s = 1/16l,
with l = (EJ/EC)^0.5.
The displacement d from the origin is - 2^0.5a(1+2d)/2hpw,
where a is the coefficient of the linear driving
term and d reflects the relative strength of
the nonlinear correction terms.
Image Source: X. Hu, Quantum Fluctuations In Condensed Matter Systems, UM Ph.D. thesis 1997, Page 113.
X. Hu and F. Nori, UM Preprint, 1995.