I am researching low temperature, near absolute zero, and in particular Bose Einstein Condensate. There is a lot of research information, but it is confusing, and not explained. Technically a BEC is formed from a Gas or liquid at somewhere below 1K. The only three elements that could still be in a liquid state at <1k are Helium, Hydrogen and Neon. Hydrogen and Neon would need to be at a pressure, below atmospheric. So, these are the only three elements that can become BEC's in their natural state. Most of the experiments using other elements, are not in their natural state, but are carried out, using a non natural vapour, of the element's atoms. It appears to me, that Helium is the only element which naturally becomes a BEC,at atmospheric pressure, but even Wiki., when it talks about Helium's strange properties, below its Lambda point, does not mention, it becoming a BEC. My questions are: 1. Does Helium just naturally display BEC properties at <1K, or does it become a BEC? 2, Are you aware of anyone lowering Hydrogen and/or Neon to a temperature where they enter a BEC state. IE. Can Hydrogen and Neon become BEC's. 3. Am I assuming correctly, that H,He and Ne are the only three elements that can enter a BEC state naturally. IE. Other elements at <1K are in a solid state, and can not, become a BEC. Thank you Clive Ballard
A quick Google suggests that the triple point of Hydrogen is 13.8K and the triple point of Neon is 24.6K, so neither can exist as liquids at temperatures low enough to form BECs.
You use the word "natural" several times in your question, but it isn't clear what this means. There is nothing especially natural about the liquid state. If you count the plasma in stars as being a gas, the most "natural" state is a gas - well, I suppose a plasma.
Addressing your specific questions:
a BEC just means the majority of the system is in the lowest quantum state. Any gas or liquid will do this if you lower the temperature enough, though Helium is the only element that is liquid at the required temperature. So Helium becomes a BEC at low temperature. I'm not sure what questions of naturalness mean in this context.
Hydrogen and Neon don't remain liquid at temperatures low enough to form a BEC. A BEC has been made from gaseous hydrogen (http://prl.aps.org/abstract/PRL/v81/i18/p3811_1). I couldn't find any references to condensation of Neon, but this may simply be because experimenters haven't got round to it yet.
Helium is the only known liquid BEC. I'd guess it's the only possible liquid BEC, but the universe is a strange place so I wouldn't bet my life on it.
The reason it isn't called a BEC is because the Helium is not dilute, so it isn't a pure gas. The interactions in the Helium make it a BEC liquid, not a BEC gas, and traditionally, when the atoms are close-packed in a liquid state, people don't call it a BEC, rather they call it a superfluid. The escription of a superfluid is with a constant average density ground state wavefunction, whose peturbations are long-wavelength variations in phase, which give a superflow. This is described in Feynman's He4 work from the 1950s.
A dilute BEC gas is described by the Gross-Pitaevsky equation, which is just the Schrodinger field equation in the field limit. It allows for density changes from point to point, and these density perturbations are not particularly stiff, since the gas is dilute, but are described by the Schrodinger field equation.
Unlike He, Hydrogen is a molecule, and will not form a BEC, but a crystal. Neon has too many electrons, the attractive Van-Der-Waals forces will lead to crystallization, not a fluid. Only Helium is superfluid at absolute zero.
Despite this, if you take dilute bosonic atoms, you can make a BEC which is metastable to crystallization. This procedure doesn't care about the stable thermodynamic state too much, because it is exploiting the diluteness and coherence to make a long-lived metastable state.
So far, Bose-Einstein condensation has been realized experimentally in dilute gases of Rubidium, Sodium, Lithium, Hydrogen and metastable Helium. The first three are spin-polarized boson alkali atoms [you need to have non-zero spin in this atoms to be able to cool them enough in magnetic traps, for this reason you can't lower the temperature enough of Neon gases to be able to do evaporative cooling. There is not proof of principle of why a Neon gas would not condensate if you lower the temperature enough, it is just that we haven't found the way to do it.]. The case of Helium is different because it is the only of this elements which is liquid at the temperatures of condensation. This will also imply superfluidity.
The temperature of $1$ K you talk about in your question is completely arbitrary and has nothing to do with the condensation of the above Helium. Helium is superfluid below the lambda temperature which is $T =2.17$ K.