Positronium Bose-Einstein condensation in liquid ${}^4\mathrm{He}$ bubbles

A hollow spherical bubble containing thousands of spin-aligned triplet positronium (Ps) atoms in superfluid liquid ${}^4\mathrm{He}$ would be stable against breakup into smaller bubbles, and the Ps would form a Bose-Einstein condensate (BEC) with a number density of $\sim {10}^{20}{\mathrm{cm}}^{-3}$ and a BEC critical temperature $T_c\approx 300$ K. Estimates suggest that one could make such bubbles in the laboratory containing ${10}^5$ Ps atoms using presently known methods.

Figure 1

Calculated bubble radius $r$ and Ps number density $n$ at 2 K as a function of the total number of BEC Ps atoms $N$ for various pressures neglecting the vapor pressure of the Ps gas. Note that the plots are on log-log scales.

Figure 2

Geometry of a target for forming BEC positronium bubbles in superfluid He. Energetic positrons stop in a thin diamond film. The positrons thermalize and diffuse to the back surface of the film, and are emitted into the He as positronium which collects into bubbles.