The article “Ultradilute quantum droplets” by Igor Ferrier-Barbut (Physics Today, April 2019, page 46) was really nice to see. It reported on the creation, at last, of real ultradilute liquid droplets and on the tremendous progress that has been made in that area. However, I was disappointed to see no mention or discussion that ultradilute liquid quantum droplets were predicted a long time ago.1,2 That early work was a major source of inspiration for Dmitry Petrov’s 2015 paper on the subject,3 at least according to what he told me years ago.
In his discussion of mean-field quantum gases, Ferrier-Barbut doesn’t note that the Efimov effect, which involves the creation of an infinite number of three-body bound states, can also allow Bose liquids to exist when the scattering length is negative (that is, when the two-particle interaction is attractive). Such a system is not always unstable. Tsung-Dao Lee, Kerson Huang, and Chen Ning Yang (LHY) proposed in 1957 a leading-order correction to the mean-field approximation due to two-body collisions, which was used by Petrov;3 that “game-changing correction,” as Ferrier-Barbut calls it, can alter the nature of the Bose–Einstein condensate.
However, as was discussed quite some time ago,1,2 the strength of three-body interactions can dominate over LHY corrections and can be infinite even if the two-body scattering length is finite.1 A liquid model based on the Efimov effect1,2 is more robust than the one Petrov envisioned and much more flexible than the van der Waals model. Unlike the quantum liquid droplets created in mixtures of Bose–Einstein condensates,4 which have practically the same size for particle numbers up to tens of thousands, the quantum liquid droplets I suggested are truly saturating systems, with basically constant interior density. A droplet can have any size, and it can be formed even from a single element. It is a real liquid, with constant density inside and a well-defined surface, and its density and surface tension can be controlled. Also, it is stable against quantum corrections to the mean field.2
Moreover, in a rather special system—an ensemble of spin-polarized tritium atoms—three-body recombination processes are most likely absent.2,5 Although I did not make the estimates, which should be straightforward, I am sure that by controlling the density and thus the rate of four-body recombination, one could create droplets with basically arbitrarily long lifetimes. A droplet of spin-polarized tritium atoms would be a totally unique object, perhaps as unique as macroscopic superfluid helium, but amenable to precise quantum many-body calculations, both static and time-dependent. Quantum turbulence could be studied in a large class of systems, for which a microscopic theory exists, and unlike in the case of superfluid helium, theory could be directly confronted with experiment.
Quantum liquid droplets could be either boselets or fermilets and would undergo at least two types of phase transitions, from superfluid to normal and from liquid to gas. Their physics should be fascinating. Mixing bosons and fermions can lead to even more interesting and complex objects.
