Figure 1

(a) The double-SQUID system whose configurations and stability are investigated in the Letter. The switching between flux states, induced by the fluxes ${\Phi }_x$ and ${\Phi }_c$, can be recorded through the readout junction or through the readout SQUID. Examples of the control of the system potential through ${\Phi }_x$ and ${\Phi }_c$ are given in (b) and (c), respectively: the first modifies the symmetry while the second tunes the height of the barrier.Reuse & Permissions

Figure 2

(a) An experimental flux characteristic of the double-SQUID system for a fixed value of ${\Phi }_c$ where we also report for every region of the curve the potential configuration. (b) A diagram of the potential configuration in the (${\Phi }_x$, ${\Phi }_c$)-plane, obtained by plotting the positions at which the two minima disappear. For clarity, we superimpose the characteristics shown in (a) taken for various values of ${\Phi }_c$.Reuse & Permissions

Figure 3

Experimental ${\Phi }_x\mathrm{\text{−}}{\Phi }_c$ phase diagram obtained for two different asymmetry parameters determining the value of the coefficient to the third order power coefficient in Eq. (3). (a) Difference between the critical currents is 4%. (b) Enlargement of the tip region. Continuous line is the theoretical expression while the circles are the experimental points. (c) Butterfly catastrophe observed by enlarging the tip of the map when the coefficient to the third order in Eq. (3) is close to zero (asymmetry of 0.3%).Reuse & Permissions

Figure 4

(a) Characteristic surface described by possible phase solutions of a double-SQUID system. Shown surface is obtained by varying the two parameters that can be changed during measurements; this kind of surface represents a typical topological feature of systems exhibiting catastrophes. (b)–(d) Examples of parameter locations of catastrophes and sketch of the corresponding configurations of the potential [Eq. (3)]. (b) Parameter values identical to (a); (c) and (d) are projections of the surface for different parameter sets of the butterfly catastrophe. Solid and dashed curves are obtained by using, respectively, the full potential or a 6th order Taylor expansion.Reuse & Permissions