# Gas or liquid? a Bose-Einstein condensate

It is often said that a Bose-Einstein condensate of cold atoms is a gas. But because of Andrews' discovery of the critical temperature, we know that a gas and a liquid is not fundamentally different. So, why is it called a gas but not a liquid?

Neither gas, nor liquid, nor something in between. In a classical phase scheme, there are 4 states of matter:

• Solid
• Liquid
• Gas
• Plasma

Bose-Einstein condensate is a non-classical state of matter (sometimes referred to as a fifth state of matter) where the macroscopic body (cold atom condensate) exhibits microscopic features - aggregate wavefunction applicable to whole atom set.

So it's not fair to try to push this condensate back into classical phase scheme, when it has very unique and different features. It's like if you would want to call plasma a "hot gas" or liquid a "flowing solid". Sure, these states are related, because we can transit from one state to another, but there's a reason why we have a clear-cut distinction in phase classification. So I would opt for leaving BEC in a honorable fifth matter phase.

It is possible to distinguish between a gas and a liquid only below the critical point, where the coexistence between two phases of different densities is present. Indeed, above the critical point, there is no firm way to distinguish between gas and liquid, and people generally speak about a unique fluid phase.

The usual liquid-gas coexistence signals a first-order transition with a jump in density and entropy (the latent heat). The density can be used as the order parameter of the transition. The Bose-Einstein condensation is considered a continuous phase transition because the order parameter (the density of the condensate) varies continuously, and there is no coexistence (see this other question and answers on PSE).

This fact is the basis of the usual way of referring to the condensate as a gas.

The other answers provide a nice explanation from a phase transition perspective. Here is a more cold atom centric perspective.

BEC's are commonly realized in (i.e. starting from) dilute gases of bosonic neutral alkali atoms, e.g. Rb-87, Na-23, Li-7, etc. Typically, you start with solid alkali metal, place it in a vacuum chamber, and generate a gas by e.g. heating the metal to a temperature where there is significant vapor pressure (i.e. gas) present. Some subset of the atoms in the gaseous state are then laser cooled and trapped. At low enough temperature, the atomic gas undergoes a phase transition and a BEC forms. However, depending on the temperature, interactions, etc., not all of the atoms will be in the condensate. Some will still be in a gaseous thermal state

We often generically refer to cold atom systems as "gases", because the atoms are in a gas phase most of the time. So saying a cold atom BEC is a gas is a slight abuse of terminology.

The simple "solid, liquid, gas" and "solid, liquid, gas, plasma" categorizations are far too simplistic for to describe the different states of matter that exist.

Quantum phases like superfluids and Bose-Einstein condensates have very different mechanical and macroscopic properties compared to everyday materials. I don't think it makes sense to try to shoehorn them into the solid-liquid-gas-plasma tetrachotomy.

These categories don't even capture liquid crystals (of which there are different types) that have solid-like order in some directions but liquid-like behavior in others. The distinction between amorphous solids and liquids is not always clear and there is often an arbitrary cutoff in viscosity between what is considered solid and what is considered liquid.

Just like considering Pluto as a planet requires you to consider other bodies as planets (especially Eris), adding plasma as the "fourth state of matter" (who decided this anyway?), really opens the door fifth, sixth, seventh states of matter. If you just stuck to solids, liquids, and gases, maybe you could argue for categories based on viscosity alone. Even based simply on viscosity, superfluids and neutron degenerate matter probably need to be considered distinct states.

I might even argue that molecular solids (ice, sugar), covalent network solids (quartz, most minerals), ionic solids (salt), and van der Waals solids (graphite, hexagonal boron nitride) are distinct states (at least as distinct as plasma). Different solid polymorphs have different types of order as well (hexagonal close packed versus face centered cubic). And this is ignoring electronic (metals, semiconductors, nonmetals, superconductors) and magnetic states (ferromagnetism, paramagnetism, diamagnetism, antiferromagnetism).