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My first question is: Is atomic Bose-Einstein condensate a gas?

My second question is: What are the difference between BEC and quantum liquid droplets?

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  • 1) Yes, a Bose-Einstein condensate (BEC) is a gas. Hence, it is a metastable stable, as you know solids are the most stable state of matter. Three-body collisions happen at a rate $\propto n^2$, $n$ being the number density of atoms - these collisions make two atoms bond into a molecule, releasing the binding energy as kinetic energy of the third atom. The molecule is the start of the formation of the solid, while the third atom has enough energy to be ejected from whatever trap the BEC was sitting in, potentially colliding with other atoms in the process and heating them up.
    This is why BECs only exist in dilute gases, i.e. low $n$, otherwise they would "die" very quickly.
    I should also say that a BEC is only achievable is some kind of trap - when released, the non-zero (miniscule) temperature is still enough to disperse the cloud and kill it off.

  • 2) Quantum liquid droplets are denser (!= dilute) objects, hence why they are referred to as liquid or solid.
    In order to achieve this one usually starts off with a BEC (as it is the easiest macroscopic quantum wavefunction to experimentally manufacture) and then modifies something in order for it to increase in density without dying. Usually this comprises changing the scattering length a, which measures the strength and the sign (attractive or repulsive) of atomic interactions. As an example, $^{39}K$ has a negative background scattering length so it will have attractive interactions, meaning a cold cloud of $^{39}K$ will implode and eventually explode (when $n$ becomes large enough for the 3-body losses mentioned earlier to win) - this is called a Bose-nova.
    The point I am making here is that, if the intraspecies interactions were more repulsive, then the cloud could be squished a bit more (making it denser) without resulting in too much loss.
    It seems that one of the most successful ways to get quantum liquids though (according to here) is by making a mixture of atoms in the BEC, and then turning the interspecies scattering length so as to balance it with the intraspecies interaction. Same idea as above, but within different species.

Quantum liquid droplets then become interesting because they are self-bound by this interaction. I.e. they do not need an external trap like the BEC. This draws interesting parallels to other self-bound objects in nature, like atomic nuclei or astronomical objects like white dwarfs or neutron stars, all allowed by a particular stabilisation mechanism arising from a balance of attractive forces and repulsive interactions

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  • $\begingroup$ I think the system that was traditionally described as quantum droplet is actual drops of liquid helium (The universe in a helium droplet / Grigory E. Volovik.) but most recently they have been observed in an ultracold dipolar gas of dysprosium $\endgroup$ – Quasilattice Apr 22 '18 at 19:08

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