Screening of magnetic fields by charged Bose condensate

The space-space component of the photon polarization operator is calculated in zero frequency limit for a medium with Bose-Einstein condensate (BEC) of electrically charged particles. It is found that the polarization operator tends to a finite value at vanishing photon 3-momentum, as it happens in superconducting media. It means that magnetic fields are exponentially screened in such a medium analogously to the Debye screening of electric charges. At non-zero temperature the screened magnetic field oscillates and contains a contribution which drops only as a power of distance. This phenomenon is unknown for superconductors, even in BEC phase and can be potentially observable. -- Highlights: → Penetration of magnetic field into plasma with charged Bose condensate is studied. → In addition to the usual exponential screening we found weaker power law one. → Moreover, the screened magnetic field oscillates as a function of distance. → The phenomena of power law decay and oscillations are new for superconductors.