We report measurement of the ensemble averaged transverse spin relaxation time (T2*) in bulk and few molecules of the organic semiconductor tris(8-hydroxyquinolinolato aluminum) or Alq3. This system exhibits two characteristic T2* times, the longer of which is temperature-independent and the shorter is temperature-dependent, indicating that the latter is most likely limited by spin-phonon interaction. Based on the measured data, we infer that the single particle T2 time is long enough to meet Knills criterion for fault tolerant quantum computing, even at room temperature. Alq3 is also an optically active organic and we propose a simple optical scheme for spin qubit read out. Moreover, we found that the temperature-dependent T2* time is considerably shorter in bulk Alq3 powder than in few molecules confined in 1-2 nm sized cavities, which is suggestive of a new type of ``phonon bottleneck effect. This is very intriguing for organic molecules where carriers are always localized over individual molecules but the phonons are delocalized.
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