Gravitomagnetic Field of a Rotating Superconductor and of a Rotating   Superfluid
  The quantization of the extended canonical momentum in quantum materials including the effects of gravitational drag is applied successively to the case of a multiply connected rotating superconductor and superfluid. Experiments carried out on rotating superconductors, based on the quantization of the magnetic flux in rotating superconductors, lead to a disagreement with the theoretical predictions derived from the quantization of a canonical momentum without any gravitomagnetic term. To what extent can these discrepancies be attributed to the additional gravitomagnetic term of the extended canonical momentum? This is an open and important question. For the case of multiply connected rotating neutral superfluids, gravitational drag effects derived from rotating superconductor data appear to be hidden in the noise of present experiments according to a first rough analysis. 
M. Tajmar, C.J. de Matos