Resonant effects in a SQUID qubit subjected to nonadiabatic changes

By quickly modifying the shape of the effective potential of a double SQUID flux qubit from a single-well to a double-well condition, we experimentally observe an anomalous behavior, namely, an alternation of resonance peaks, in the probability to find the qubit in a given flux state. The occurrence of Landau-Zener transitions as well as resonant tunneling between degenerate levels in the two wells may be invoked to partially justify the experimental results. A quantum simulation of the time evolution of the system indeed suggests that the observed anomalous behavior can be imputable to quantum coherence effects. The interplay among all these mechanisms has a practical implication for quantum computing purposes, giving a direct measurement of the limits on the sweeping rates possible for a correct manipulation of the qubit state by means of fast flux pulses, avoiding transitions to noncomputational states.

Figure 1

(a) Scheme of the double SQUID. (b) Effective potential of the double SQUID in the single-well case, with relative eigenwaves vertically shifted by the corresponding eigenenergies. (c) Double-well case with a slight asymmetry.

Figure 2

(a) Energy potential of the system and relative eigenstates in the single-well case (for ${\Phi }_c=-429$ m${\Phi }_0$). (b) Energy potential of the system and relative eigenstates in the double-well case (for ${\Phi }_c=-412$ m${\Phi }_0$), with a slight asymmetry ensuring the degeneracy (for ${\Phi }_x=0.543$ m${\Phi }_0$). (c) Variation of the energy levels positions for different fluxes ${\Phi }_c$ (for ${\Phi }_x=0.543\text{m}{\Phi }_0$). Note that for convenience all energies are expressed as frequencies in GHz, and are shifted by subtracting the ground-state energy.

Figure 3

Experimental results for the probability $P$ to measure a right flux state for different unbalancings ${\Phi }_x$ at three different rise times $t_R$. Resonance peaks are visible for faster transitions (arrows in second and third plots)

Figure 4

Experimental results for the probability $P$ to measure a right flux state for different unbalancings ${\Phi }_x$ at different rise times $t_R$, plotted as a 3D surface.

Figure 5

Probability $P$ to find the system in the right well against the unbalancing ${\Phi }_x$ and rise time $t_R$, supposing that at $t=0$ it is in its ground state.

Figure 6

Probability $P$ to find the system in the right well against the unbalancing ${\Phi }_x$ and rise time $t_R$, supposing that at $t=0$ it is in the linear superposition $|\Psi \left(0\right)\rangle =x|{\psi }_0\left(0\right)\rangle +{\mathbf{e}}^{i\theta }\sqrt{(1-x^2)}|{\psi }_1\left(0\right)\rangle$ of its ground and first excited states in correspondence to $x=0.95$ and $\theta =0$.