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On a quantum mechanical model for a maser I†

Published online by Cambridge University Press:  24 October 2008

Martin Hasler
Martin Hasler
Affiliation:
Bedford College, London
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Abstract

The model is closely connected with a model by Lamb and Scully (10). Atoms described as two-level systems, initially in an incoherent superposition of the two levels, interact successively during a time T with an electromagnetic field of which only one mode is taken into consideration. In the limit as infinitely many atoms have interacted, it is shown that the field either approaches a thermal distribution or is excited to arbitrarily high Photon numbers according to whether or not the lower level of the atoms is initially more probable than the upper level. It is also shown that in any case the correlations between pure Photon number states converge to 0. If the atoms are initially in the upper level it is proved that the Photon number grows roughly as the square root of the number of atoms that have interacted. Throughout the discussion number-theoretical properties of T play a disturbing role. The last mentioned result in fact depends on a sharp (but arbitrary) value for T and is therefore disqualified for physical interpretation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 2 , March 1976 , pp. 351 - 371
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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