
Super-solid helium state confirmed in beautiful experiment - Tomte
https://arstechnica.com/science/2018/12/researchers-find-super-solid-by-looking-at-a-normal-solid/
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panic
I've always been curious -- how can two helium atoms enter the same quantum
state when their constituent particles can't? What is happening to the
spin-1/2 electrons, for example?

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cbkeller
This may be a bit mangled from the last time I took a relevant class, but my
recollection is that the "real" reason electrons can't share the same state is
that they're what's called _antisymmetric with respect to exchange_.

In general, most particles are fundamentally indistinguishable: if you swap
two of them you haven't really changed anything. This leads to most particles
being either _symmetric_ (bosons, integer spin) or _antisymmetric_ (fermions,
half-integer spin) with respect to exchange. If _symmetric_ then the wave
function doesn't change at all; if _antisymmetric_ then exchange reverses the
sign of the wavefunction. If we have two electrons in the same place, and
arbitrarily swap them (which we're allowed to do since they're identical),
then we've reversed the sign on one of the wavefunctions. But since they're in
the same place, the wave functions cancel. This would violate conservation of
energy, so isn't allowed; instead, we just never let them occupy the same
state in the same place, and call it the Pauli exclusion principle.

While a single electron has half-integer spin, a He-4 nucleus has integer
spin, so is symmetric to exchange, and it's wavefunction doesn't cancel if you
have two in the same place.

That was probably horribly oversimplified and unrigorous, but there's a bit of
relevant discussion (in bra-ket notation that I can't really read) here:
[https://en.wikipedia.org/wiki/Pauli_exclusion_principle#Conn...](https://en.wikipedia.org/wiki/Pauli_exclusion_principle#Connection_to_quantum_state_symmetry)

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nine_k
Key part:

 _At the lowest temperatures, the flow rate of helium-3 stopped decreasing. It
didn’t exhibit super-solid properties, but it also stopped behaving like a
normal solid. ... The researchers were not at a low-enough temperature to
expect a helium-3 super-solid. But the temperature was low enough that maybe,
just maybe, some pairing was occurring, which was allowing some super-solid
properties to start to become apparent._

So it's a tantalizing glimpse of the possibility of super-solids, but not yet
a hard proof.

~~~
cbkeller
It's a bit better than that from my reading: that quote's for He-3, which we
don't _expect_ to show any supersolidity (it's a fermion) unless the He-3
nuclei start forming pairs (the pair would have integer spin) -- which isn't
really expected until even lower temperatures.

The key part of this experiment as far as I could tell was that at the same
temperatures He-3 showed _decreasing_ flow rate with decreasing temperature,
He-4 showed _increasing_ flow rate with decreasing temperature. This is
exactly what we'd expect since He-4 nuclei are bosonic, while He-3 nuclei are
fermionic. That's pretty good IMO

