  The singlet state of a system of two two-level atoms changes smoothly,
remaining dark, as the Hamiltonian TC is slowly deformed, despite the
inapplicability of the adiabatic theorem to this case. In this case, there is a
small probability of emission of free photons, which does not depend on the
smoothness of the deformation of the Hamiltonian. The effect of spontaneous
emission is enhanced by the addition of one more pair of atoms in the singlet
state due to the exchange of virtual photons in the cavity. A similar effect
was also established for the case when atoms can move between two cavities, but
here, on the contrary, with an increase in the number of atoms, the emission
decreases. This purely quantum effect must be taken into account in practical
manipulations with atomic singlets; however, its weakness testifies, rather, to
the stability of dark states and the prospects for their use in information
exchange (quantum cryptographic protocols) and as an energy accumulator for
nono-devices.
