Entangling atoms in a molecule

[BillKet]

Hello! I came across several papers that use entangled states of 2 ions in a trap to perform measurements with a much higher accuracy than classical (non-entanglement) methods. Here is an example of such a paper where they achieve the best measurement to date of an isotope shift. I was wondering if something similar can be done (or has been done) in diatomic molecules. In that case we already have 2 ions close to each other, so I was wondering if there is a way to entangle the 2 constituents atoms such that you gain some further advantage over normal spectroscopy techniques. Thank you!

 

[Twigg]

I've been out of the loop for a while, but I remember there were groups at NIST and Hannover that did spectroscopic measurements like that. Looks like there's a publication from Basel too in recent times. The technique you describe is called quantum logic spectroscopy. When I was in precision measurement, we would half-heartedly talk about pros and cons of using quantum logic. The biggest disadvantage is that you reduce your sample size to N=1. More molecules is more better for statistical reasons, especially in precision measurement. Quantum logic spectroscopy only pays off if your one entangled atom/molecule is more sensitive on its own than averaging down on a whole gas. There are cases where it pays off, like NIST's aluminum ion clock which is a more precise timekeeper than JILA's strontium lattice clock with its 1000 strontium atoms.

Also, please keep in mind that with molecules just preparing a single unentangled quantum state is cause for several bottles of champagne.

 

[Twigg]

Ah, sorry, realized you meant entangling the constituent atoms in a molecule, not entangling a molecule with an atom (that's what quantum logic spectroscopy is). The issue is that constituent atoms are already incredibly well entangled! Consider this, in quantum computing experiments where atomic ions are entangled, two ions are coupled by Coulomb forces acting over a distance on the order of a few microns. Compare that to a molecule where two "ions" are coupled over a few angstroms. The atomic states are so well mixed you'd be hard pressed to project them out. That's what molecular states are, after all.

With "halo dimers" it might be another story, but I haven't the faintest idea how you would project the molecular state onto an atomic state without first dissociating the dimer.

 

[BillKet]

Ah, sorry, realized you meant entangling the constituent atoms in a molecule, not entangling a molecule with an atom (that's what quantum logic spectroscopy is). The issue is that constituent atoms are already incredibly well entangled! Consider this, in quantum computing experiments where atomic ions are entangled, two ions are coupled by Coulomb forces acting over a distance on the order of a few microns. Compare that to a molecule where two "ions" are coupled over a few angstroms. The atomic states are so well mixed you'd be hard pressed to project them out. That's what molecular states are, after all.

With "halo dimers" it might be another story, but I haven't the faintest idea how you would project the molecular state onto an atomic state without first dissociating the dimer.

Thank you for your reply! Yes, I was thinking about atoms in a molecule (maybe at high vibrational energy levels, where they are quite far apart relative to the ground state level), but I see your point. However the paper you sent me are really useful. I looked a bit over them and over some other similar experiments. It seems like this method is mainly useful when you can't measure that specific molecule directly for some reason (e.g. maybe it is hard to prepare it in a desired state) and it also offers an advantage as you can repeat the measurement on the same molecule without removing it from the trap. I was wondering if this can actually offer an advantage over molecules that are already measured with high accuracy using classical methods. For example they set bound on the electron electric dipole moment using classical Ramsey spectroscopy on ThO. Would this quantum spectroscopy methods in principle allow more accurate measurements of the energy levels and hence better bounds (or even a discovery!)? Or are we still to far from that and for now these methods are more of a proof of principle?

 

[Twigg]

mainly useful when you can't measure that specific molecule directly for some reason (e.g. maybe it is hard to prepare it in a desired state)

This is also true but I didn't think to mention it! Especially for the aluminum ion clock. One day, there could even be a thorium-229 clock operating on this principle using the low-lying, super forbidden nuclear transition. Nuke clock!

For example they set bound on the electron electric dipole moment using classical Ramsey spectroscopy on ThO. Would this quantum spectroscopy methods in principle allow more accurate measurements of the energy levels and hence better bounds (or even a discovery!)?

Funnily enough, when I was talking about my conversation with other folks in precision measurement I was actually talking about my conversations with the HfF+ eEDM team. What I said there is exactly why no one has proposed a quantum logic eEDM search to the best of my knowledge. To justify using quantum logic, you'd need a molecule with such a high sensitivity to eEDM that it'd outperform a gas of 1000 HfF+ (I forget the final flux of useful molecules for ThO, but these experiments have comparable overall sensitivity). Recall that averaging over shot noise gives you an improvement of $\sqrt{N}$, so to use quantum logic to compete with HfF+ you'd need a molecule that was $\sqrt{1000} = 32$ times more sensitive to eEDM.

Edit: sorry, I should've toned down the lingo, eEDM = electon electric dipole moment

 

[DrDu]

quantum computations have been performed using NMR to entangle the nuclear spins in molecules like caffeine.