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Is there a (known) theoretical limit on density/mm^3?

The Bekenstein bound? A maximum number of bits can be placed on the surface of sphere. Beyond that it turns into a black hole.

Mind you, one or two other practical limits might come into play before a memory chip hits that one. :-)

[1] https://en.wikipedia.org/wiki/Bekenstein_bound

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Edit:

The maximum information capacity of a radio antenna is limited by the surface area enclosing the antenna. One could theorise that that in addition to a maximum density of information storage there will also be a limit on the error free rate at which information can be sent to/from a storage system system, probably related to the surface area enclosing the system.

Well under normal conditions (no degenerate matter)- the material with the lowest molar volume should give a good idea. At least on earth, this happens to be diamond: so ~1.7 * 10^20 atoms / mm^3.

With one bit per atom: 20 million TB.

I think we would be in trouble way before that. Quantum effects would mean you would change a decent percentage of adjacent bits while setting one. We’re probably struggling with such effects already.

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