Figure 1

(a) Schematic layout of the qubit and the harmonic oscillator equivalent of the transmission line. (b) Picture of the qubit. The qubit is $500\mu \mathrm{m}$ long and each junction is $250\times 250{\mathrm{nm}}^2$ in size. On the upper loop the pickup transmission line is shown. (c) Mask art of the three shadow type Josephson junctions [blow up of dashed box in (b)].Reuse & Permissions

Figure 2

Instantaneous eigenvalues of $H$, Eq. (2), as a function of control flux ${\Phi }_C$, for main flux $\Phi \approx 0$. The exponentially rising tunnel splitting $\Delta$, and the ${\Phi }_C$-independent oscillator frequency ${\omega }_T$, are indicated. At $A$, the “resting state,” the double-well barrier is very high and the two lowest eigenstates are nearly degenerate; here the resting state is not quite symmetric, with $ϵ\approx 15\mathrm{MHz}$. For this nonideal case successful quantum operation requires that the system pass through the “portal” as described in the text. At point $B$, beyond the portal, quantum tunneling dominates the dynamics and the system is effectively symmetric. Beyond $B$ the qubit comes into resonance with the transmission line oscillator, with a splitting of $2g\approx 220\mathrm{MHz}$. At point $C$, the lowest lying states have purely harmonic oscillator character.Reuse & Permissions

Figure 3

(Color) Color density plot of first three first energy eigenstates of $H$ at points $A,$ $B$, and $C$ of Fig. 2. $\delta$ is the horizontal axis, and $\phi$ the vertical axis [see Eq. (2)]. For $A$ the first two eigenstates, localized in the left and right wells, are not quite degenerate because $ϵ\ne 0$ (see Fig. 2). In going from $A$ to $B$, on account of strong quantum tunneling, the first two eigenstates change rapidly in character, becoming symmetric and antisymmetric combinations of the well states. For both $A$ and $B$, the third state has one quantum of excitation of the harmonic oscillator. The states at $C$ have purely harmonic-oscillator character. In going from $A$ to $C$, the steady decrease of the well-well separation is evident.Reuse & Permissions