Is there any current technology that depends upon a deep understanding of quarks?

Is there any current technology that depends upon a deep understanding of quarks?

No, there isn't. There are technologies that depend in various ways upon nuclear physics and knowledge of nuclear forces. However, those technologies predate the quark model. If the quark model had never been discovered, it would have had no effect on nuclear power, nuclear weapons, MRI, radiation therapy, biological use of radioactive tracers, radioactive dating, or any other application I can think of. Every application on that list predates the quark model, at least in principle. (E.g., NMR is the only nuclear physics principle used in MRI.)

Of course, it's hard to prove a negative. I'm a nuclear physicist by training, but that's no guarantee that I'm not missing a counterexample.

I cannot think of any technology which exploits in any way the properties of quarks directly, however nuclear processes ultimately depend on the existence of quarks. So indirectly, nuclear power, radioactive dating, NMR all involve in a way the existence of quarks. The existence of stars and nuclear bombs are perhaps the most striking examples of the implications of the existence of quarks.

Another example of the is air showers, where a high energy cosmic ray strikes the nucleus of an atom in the upper atmosphere, creating a chain reaction which produces a shower of hadrons (bound quarks) and various other particles. One use of this is muon tomography, where the resulting muons are used to image the interiors of large objects. For example, it was used to discover a hidden chamber inside the Great Pyramid. Again, it's not a direct use of quarks, but as with anything involving the nuclei of atoms, it is only possible due to their existence.

The issue of course is quark confinement. Quarks cannot exist freely except at extremely high energies/temperatures such as those achieved for fractions of a second in the LHC. or in the very earliest times in the universe. Even in the core of a star the quarks are not free. Though there is the hypothetical quark star, which would be denser even than neutron stars, and could potentially be formed at the core of neutrons stars.

Well, many details of cutting edge particle detectors at SLAC, Fermilab, and the LHC depend on details of the quark interactions. (In the sense that, if we already knew the interiors of nucleii were different from the quark model, we would make detectors generally optimized for the dynamics we expect.) Of course, this answer is defensibly circular, given the "What is ... good for" context.