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Letters in Mathematical Physics

Coherent decay of positronium bose condensate

V.S. Vanyashin

Published Jun 1, 1994• 6 citations
Publisher
DOI
10.1007/bf00750148

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We consider, in general, the collective two-photon annihilation decay of positronium atoms arising from the second quantized formalism. It is shown that two-photon annihilation of positronium atoms in a Bose-Einstein condensate (BEC) is unstable. Due to the BEC coherence, an absolute instability in such system takes place, i.e., the number of photons created as a result of positronium decay grows in every point within a BEC. The latter leads to an exponential buildup of a macroscopic population into the certain modes. Cooperative effects start for densities much smaller than the Dicke limit of spontaneous super radiation. For laserlike action, i.e., for directional radiation, we consider the BEC with elongated shape when the spontaneously emitted entangled and oppositely directed photon pairs are amplified, leading to an exponential buildup of a macroscopic population into the end-fire modes. We also consider the roles of confinement and interaction among positronium atoms in the amplification process.
A scheme of an intense coherent gamma-ray source based on the spontaneous radiation of positronium atoms in a Bose-Einstein condensate (BEC) due to two-photon collective annihilation decay is investigated analytically arising from the second quantized formalism. It is shown that because of the intrinsic instability of annihilation decay of BEC, the spontaneously emitted entangled photon pairs are amplified, leading to an exponential buildup of a macroscopic population into end-fire modes at a certain shape of the elongated condensate. The considered scheme may also be applied to a BEC of atoms or quasiparticles as a laser mechanism with double coherence to create entangled photonic beams with a macroscopic number of photons.