  Zel'dovich proposed that electromagnetic (EM) waves with angular momentum
reflected from a rotating metallic, lossy cylinder will be amplified. However,
we are still lacking a direct experimental EM-wave verification of this
fifty-year old prediction due to the challenging conditions in which the
phenomenon manifests itself: the mechanical rotation frequency of the cylinder
must be comparable with the EM oscillation frequency. Here we propose an
experimental approach that solves this issue and is predicted to lead to a
measurable Zel'dovich amplification with existing superconducting circuit
technology. We design a superconducting circuit with low frequency EM modes
that couple through free-space to a magnetically levitated and spinning
micro-sphere placed at the center of the circuit. We theoretically estimate the
circuit EM mode gain and show that rotation of the micro-sphere can lead to
experimentally observable amplification, thus paving the way for the first
EM-field experimental demonstration of Zel'dovich amplification.
