  Cyclotron spin-flip excitation in a nu=2 quantum Hall system, being separated
from the ground state by a slightly smaller gap than the cyclotron energy and
from upper magnetoplasma excitation by the Coulomb gap [S. Dickmann and I.V.
Kukushkin, Phys. Rev. B 71, 241310(R) (2005) ; L.V. Kulik, I.V. Kukushkin, S.
Dickmann, V.E. Kirpichev, A.B. Vankov, A.L. Parakhonsky, J.H. Smet, K. von
Klitzing, and W. Wegscheider, Phys. Rev. B 72, 073304 (2005)] cannot relax in a
purely electronic way except only with the emission of a shortwave acoustic
phonon (k~3*10^7/cm). As a result, relaxation in a modern wide-thickness
quantum well occurs very slowly. We calculate the characteristic relaxation
time to be ~1s. Extremely slow relaxation should allow the production of a
considerable density of zero-momenta cyclotron spin-flip excitations in a very
small phase volume, thus forming a highly coherent ensemble - the Bose-Einstein
condensate. The condensate state can be controlled by short optical pulses (<1
mcs), switching it on and off.
