The phase diagram of ultra quantum liquids

We discuss the dependence of the phase diagram of a hypothetical isotope of helium with nuclear mass less than 4 atomic mass units. We argue that with decreasing nucleus mass, the temperature of the superfluid phase transition (about 2.2 K in real He-4) increases, while that of the liquid-gas critical point (about 5.2 K in real He-4) decreases. We discuss various scenarios that may occur when the two temperatures approach each other and the order parameters of the superfluid and the liquid-gas phase transitions interact with each other. The simplest scenario, in which both order parameters become critical at particular values of the nuclear mass, temperature, and pressure, can be ruled out through on an analysis of the Landau theory. We argue that in the most likely scenario, as the nuclear mass decreases, first, a tricritical point appears on the line separating the superfluid and the normal fluid phase, then the critical point disappears under the first-order part of superfluid phase transition line, and in the end the tricritical point disappears. The last change in the phase diagram occurs when the two-body scattering length crosses zero, which corresponds to the nuclear mass of about 1.55 u. We develop a quantitative theory that allows one to determine the phase diagram in the vicinity of this point. Finally, we discuss several ways to physically realize such liquids.

Automated summary

The study discusses the dependence of the phase diagram of a hypothetical isotope of helium with nuclear mass less than 4 atomic mass units. As the nuclear mass decreases, the temperatures of the superfluid phase transition and the liquid-gas critical point show different trends. Various scenarios are proposed, ruling out the simplest scenario through analysis of the Landau theory and suggesting a more likely sequence of changes in the phase diagram with decreasing nuclear mass.