##
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 *H*1 and *H*4
(which are squeezed vacuum states), and

**(b)** the ground state of *H*2 and *H*3
(which are squeezed coherent states).

The units for f and *n* are (*EC*/*EJ*)^0.25
and (*EJ*/*EC*)^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 *H*2
and *H*3. 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)/2*h*pw,
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.