Quantum logic spectroscopy in a quadrupole trap

[kelly0303]

Hello! I see that most experiments applying quantum computing techniques for high precision spectroscopy use a quadrupole trap. I don't know much about the experimental implementation of these kind of traps, so any help (or suggested paper) would be appreciated, but I was wondering how well can one control the electric field at the given ion? In a quadrupole trap, you have both static and RF fields, and given that they are not too long, you would also probably have edge effects leaking inside the trap (no idea how big that effect would be). Also in these experiments they don't mention anything about the xy motion of the ions (i.e. perpendicular to the central axis). Wouldn't that motion also disturb the energy levels? Can someone help me understand a bit how well (and how) can these fields be controlled in these kind of traps? Thank you!

 

[Twigg]

A lot to discuss here. There's a lot of different kinds of unwanted fields, and for quantum logic spectroscopy (per the title of the thread), most of them don't factor into the fidelity of the quantum logic operation.

As far as static fields go, these are almost entirely a non-issue because quadrupole ion traps can easily be shimmed with DC voltages applied to the RF electrodes (to shim out a static electric field in the xy plane) or opposite sign voltages applied to the endcaps (to shim out a static electric field along the z-axis aka trap axis). For a quantum logic experiment, you usually have just two ions a micron or so apart, so gradients in the electric field (or even higher order spatially-variant terms) don't really matter. In particular, the larger the volume of the trap (i.e. the more distance you put between RF electrodes), the less higher spatial terms will matter. (As a recurring theme, you'll notice that larger trap volume gives better suppression of unwanted electric field effects.)

Where static fields start to be an issue is when the static electric field drifts in time. This often happens because of accumulated static charges on nearby surfaces. Vacuum windows are often quite annoying sources of these static charges, so as a rule of thumb put your high precision experiments far away from the windows (which, again, usually means you need to make your experimental volume larger). One possibility is having the ability to automate the process of shimming static electric fields in the trap, and running that routine once every hour or so between data taking runs. I couldn't tell you for sure, but I'd bet good money that there are groups that do this. When I last worked on a precision measurement, we'd shim fields manually once a day, so that should give you an idea for the level of control needed. That trap had dimensions on the order of 10cm.

As far as RF fields, this entirely depends on how good your trap-driving electronics are. Spend a lot of time developing highly repeatable, high-precision trap voltage sources, and you won't regret it. As far as edge-effects and such, you probably won't see them affect your data at all unless you are planning a trap that is tiny. To estimate these effects, you can calculate a multipole expansion for the RF fields, and then evaluate how large the higher order terms are at 1 micron displacement from the trap center, just as a rough estimate. For a more realistic estimate, you'll want to know the actual displacement of your molecule ion from the trap center. In all probability, your ion will still move as if it was in a harmonic potential. (Edit: I believe the way in which you would actually see unwanted RF field effects would be as excess micromotion heating. That's how you would know you have an RF field problem.)

Wouldn't that motion also disturb the energy levels? Can someone help me understand a bit how well (and how) can these fields be controlled in these kind of traps?

Not on average. The effects of the RF field tend to average to 0 by symmetry and because the RF frequency is usually way way faster than the measurement integration time. It's only when the RF frequency timescale is within a few Hz relevant timescale that you have to stop and think (you might see some weird aliasing effect, for example). And that's a pretty outlandish scenario given that you can always just move the RF frequency away.