The idea of a hidden sector of mirror partners of elementary particles has attracted considerable interest as a possible candidate for dark matter. Recently it was pointed out by Berezhiani and Bento that the present experimental data cannot exclude the possibility of a rapid oscillation of the neutron n to a mirror neutron n′ with oscillation time much smaller than the neutron lifetime. A dedicated search for vacuum transitions
n→n′ has to be performed at weak magnetic field, where both states are degenerate. We report the result of our experiment, which compares rates of ultracold neutrons after storage at a weak magnetic field well below 20 nT and at a magnetic field strong enough to suppress the seeked transitions. We obtain a new limit for the oscillation time of n–n′ transitions,
τosc(90 % C.L.)>414 s. The corresponding limit for the mixing energy of the normal and mirror neutron states is
δm(90 % C.L.)<1.5×10−18 eV.