Resolving Abrikosov vortex entry in superconducting nanostring resonators via displacement-noise spectroscopy in cavity optomechanics.

Abstract

Abrikosov vortices in type-II superconductors influence current flow, dissipation and coherence, thereby limiting superconducting quantum technologies. In mesoscopic circuit elements, the entry and pinning of a single vortex can shift resonant frequencies, redistribute flux and degrade device performance. Here, we use a flux-mediated cavity-optomechanical platform, in which a suspended superconducting aluminum nanostring forms one arm of a SQUID terminating a microwave resonator, to investigate vortex-entry processes through nanomechanical elastic signatures. Operating at T ≈ 85 mK with 0.25 mT in-plane-field resolution, we resolve discrete jumps of the mechanical resonance frequency consistent with the stochastic entry of one or a few singly quantized Abrikosov vortices. Their field positions vary between thermal cycles, indicating disorder-mediated nucleation through a quenched pinning landscape. These events are superimposed on a smooth power-law stiffening background identified with the collective Campbell-Labusch elastic response. Recasting the jumps as equivalent force signatures yields attonewton-scale forces and, within a single-event pinning model, characteristic vortex-pinning energies of 0.09 - 0.44 eV. The smooth background gives a collective Labusch parameter of order 10¹⁴ N m^-4. Our results establish cavity-optomechanical sensing as an in situ probe of vortex matter and identify vortex entry as a quantitative design constraint for flux-mediated superconducting quantum circuits.