Cyclotron spin-flip excitation in a ν=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. Van'kov, 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 ~1 s. 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 μs), switching it on and off.