Figure 1

Superinductor unit cells, potential energy, and phase diagram. (a) The unit cells of the tested device include small and large Josephson junctions with Josephson energies $E_{\mathrm{JS}}$ and $E_{\mathrm{JL}}$, respectively. The backbone of the superinductor is shown as a bold line; the adjacent cells share large Josephson junctions. The cells are threaded by the same magnetic flux $\Phi$; the phase difference across the device is ${\phi }_2-{\phi }_1=\phi$. (b) The Josephson energy $E_J(\phi )$ of a six-cell ladder calculated within the quasiclassical approximation at $\Phi =0$ (dashed curve) and $\Phi ={\Phi }_0/2$ (solid and dash-dotted curves); $E_{\mathrm{JS}}=3.5\mathrm{K}$ for all three curves, $E_{\mathrm{JL}}=16.8\mathrm{K}$ for dashed and solid curves and $E_{\mathrm{JL}}=14\mathrm{K}$ for the dash-dotted curve. For the optimal value of the ratio $E_{\mathrm{JL}}/E_{\mathrm{JS}}$, denoted as $r_o$, the dependence $E_J(\phi )$ becomes flat near $\phi =0$ at $\Phi ={\Phi }_0/2$ (solid curve). For smaller values of $E_{\mathrm{JL}}/E_{\mathrm{JS}}$, a double well potential is realized near full frustration. (c) ”Phase diagram” of the ladders on the $r\mathrm{\text{−}}\Phi$ plane. The values of $r_o$ are 4.1 and 4.5 for the ladders with $N=6$ and 24, respectively. The values of $r-r_o$ for the studied devices are shown as horizontal lines.Reuse & Permissions

Figure 2

Schematic description of the on-chip circuit. (a) Topology of two unit cells of the ladder. Josephson contacts are formed at the intersections of the bottom (horizontal) and top (vertical) electrodes. (b) The circuit diagram of the superinductor and $LC$ resonators coupled via the kinetic inductance $L_C$ of a narrow superconducting wire. The micrograph shows a ladder with six unit cells. (c) The on-chip circuit layout of two resonators inductively coupled to the microwave (MW) feedline.Reuse & Permissions

Figure 3

Spectroscopic data for the ladders with $N=6$ (a) and $N=24$ (b). The resonance frequencies ${\omega }_{01}(\Phi )/2\pi$ of the $|0⟩\leftrightarrow |1⟩$ transition measured in the second-tone experiments are shown by red dots. The horizontal dashed lines correspond to the resonance frequency of the $LC$ resonators. The blue curves represent the fits based on numerical diagonalization of the circuit Hamiltonian for device 1 (a) and the quasiclassical modeling for device 2 (a); for the simulation parameters, see Table . The gray scale insets show the microwave amplitude $|S_{21}|$ versus the first-tone microwave frequency ${\omega }_1/2\pi$ and the normalized flux $\Phi /{\Phi }_0$ measured near the avoided level crossings.Reuse & Permissions

Figure 4

(a) Rabi oscillations of the population of the first excited level of the superinductor resonator in device 1. The phase shift of the $LC$ resonance was measured while the superinductor resonator was excited by the second-tone pulsed microwaves with ${\omega }_2={\omega }_{01}$. The data are shown for the phase $\phi =2\pi \Phi /{\Phi }_0=0.94\pi$. The solid line represents the fit with the Rabi decay time $1.4\mu \mathrm{s}$. (b) Dependence of the Rabi frequency on the amplitude of microwaves with ${\omega }_2={\omega }_{01}$. (c) The response of the $LC$ resonator (measured at ${\omega }_1={\omega }_{LC}$) to the excitation of the superinductor resonator by a $0.4\mu \mathrm{s}$ second-tone pulse.Reuse & Permissions