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 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 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.