Evidence for coherent quantum phase slips across a Josephson junction array

Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2\ensuremath{\pi}$ slips of the phase of the order parameter. However, in a finite-length wire, coherent quantum phase slips would manifest themselves simply as shifts of energy levels in the excitation spectrum of an electrical circuit incorporating this wire. The higher the phase slips' probability amplitude, the larger are the shifts. Phase slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slip amplitudes random functions of time, and therefore turn energy level shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a ``slippery'' wire. The slip-induced linewidths, despite being only of order $100\phantom{\rule{0.28em}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$, were resolved from the flux-dependent dephasing of the fluxonium qubit.