It's a common thing in popular treatments of physics to point out that atoms are "mostly empty space". With hydrogen, for example, if you said that the proton was the size of a pea, then the 1

*s*orbital (describing the spatial probability distribution for finding the point-like electron) would be around 250 m in radius. So, if atoms are such big, puffy objects, then why can't two atoms overlap in real space? It's not just the electrostatic repulsion, since each atom is overall neutral.

The answer is (once again) the Pauli exclusion principle (PEP) and the fact that electrons obey Fermi statistics. Sometimes the PEP is stated in a mathematically formal way that can obscure its profound consequences. For our purposes, the bottom line is: It is apparently a fundamental property of the universe that you can't stick two identical fermions (including having the same spin) in the same quantum state. At the risk of getting technical, this can mean a particular atomic orbital, or more generally it can be argued to mean the same little "cell" of volume \(h^{3}\) in

*r*-

*p*phase space. It

*just can't happen*.

If you try to force it, what happens instead? In practice, to get two carbon atoms, say, to overlap in real space, you would have to make the electrons in one of the atoms leave their ordinary orbitals and make transitions to states with higher kinetic energies. That energy has to come from somewhere - you have to do work and supply that energy to squeeze two atoms into the volume of one. Books have been written about this.

Leaving aside for a moment the question of why rigid solids are rigid, it's pretty neat to realize that the physics principle that keeps you from falling through your chair or the floor is really the same principle that holds up white dwarf stars.

## 5 comments:

Very nice. Thanks.

Thank you - your notes and teaching resources look great!

Hi Doug,

My comment is not really related to this thread, but I was wondering if you could touch a word on this news story that Intel is making wafers full of qubits?

https://www.techspot.com/news/75020-intel-now-capable-producing-full-silicon-wafers-quantum.html

It is one thing to make billions of individual qubits by CMOS-industry standard, but another thing to build a real quantum computer out of them.

Intel's Jim Clarke is a back-end interconnect person at Intel, so I'm not sure how much to trust his statements.

What do the real experts on QC say?

Thanks in advance!

Hi Anon - Well, I'm no expert, but I think your skepticism is reasonable. From what I can tell, Intel is pursuing two QC approaches. On the one hand, they're making superconducting qubits of very much the same kind as google/John Martinis, and they've gotten up to about 50 of those on a chip, again similar to google's numbers. The article you link, which reads like it was machine-translated into English, is actually describing Intel's other approach, where they are making Si quantum dots (MOSFET-like structures, but very small, to hold single electrons), with the idea of using the spin of the charges in the dots as qubits. Integrated superconducting lines in this version control local dc magnetic fields and do electron spin resonance on the dots for qubit operations. This architecture is described here: https://arxiv.org/abs/1711.03807 . Since the Si quantum dots are based on Intel's CMOS processes, the dots themselves should be scalable to large numbers, though the remaining practical difficulties of decoherence, uniformity, and coupling qubits to each other are probably very significant.

Thanks a lot for the link Doug - I hadn't seen this article.

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