  It is proved on the example of electron spin resonance (ESR) studies of
anthracites, that by strong electron-photon and electron-phonon interactions
the formation of the coherent system of the resonance phonons takes place.
  The acoustic quantum Rabi oscillations were observed for the first time in
ESR-spectroscopy. Its Rabi frequency value on the first damping stage was found
to be equal 920.6 kHz, being to be independent on the microwave power level in
the range 20 - 6 dB [0 dB corresponds to 100 mW]. By the subsequent increase of
the microwave power the stepwise transition to the phenomenon of nonlinear
quantum Rabi oscillations, characterised by splitting of the oscillation group
of lines into two subgroups with doubling of the total lines' number takes
place. Linewidth of an individual oscillation line becomes approximately the
twofold narrower, being to be equal the only to $0.004 \pm 0.001$ G.
  Along with the absorption process of EM-field energy the emission process was
observed. It was found, that the emission process is the realization of the
acoustic spin resonance, the source of acoustic wave power in which is the
system of resonance phonons, accumulated in the samples by the registration
with AFC.
  It has been found, that the lifetime of coherent state of a collective
subsystem of resonance phonons in anthracites is very long and even by room
temperature it is evaluated by the value exceeding 4.6 minutes.
  The model of new kinds of instantons was proposed. They are considered to be
similar in the mathematical structure to Su-Schrieffer-Heeger solitons with
"propagation" direction along time $t$-axis instead of space $z$-axis.
  The proof, that the superconductivity state in the anthracite samples studied
is produced at the room temperature in ESR conditions in the accordance with
the theory of the quantised acoustic field, has experimentally been obtained.

Quantum Physics