QCJC: Knoernschild 2009

Trapped ion systems require lots of individual laser beams to address the ions, which is a fairly costly system. For instance, consider addressing a chain of 200 qubits, with just 20 milliwatts of power for each ion. When factoring in losses throughout the path (let’s say a factor of 2), we would already require a 8 watt laser. For even larger systems, it seems like it would be both challenging and expensive to obtain even more powerful lasers. In addition, that amount of power of light can be damaging for optical surfaces, such as mirrors and lenses, causing them to burn and reduce efficiency. It might be possible to have multiple smaller lasers and recombining their individual beams to address the ions, but then you enter a new realm of challenges regarding the alignment and stability of the different beam fans with respect to each other as well as to the ions.

However, is it really necessary to split a beam to that extent, such that every ion is individually addressed at all times? In fact, most algorithms do not require simultaneous gates on all available qubits. Currently, to achieve this, most trapped ion groups will use a diffractive optical element, or a DOE, to create the split. You can think of the DOE as some special diffraction grating, where the pattern printed on the surface is specially curved to create telecentric beams in the output. There might be limitations to how many beams a single DOE is able to output as well, but I’m not super clear on those numbers. Instead of a DOE, if we addressed ions only when they were needed in an algorithm, we could possibly get away with much fewer splittings of the initial laser beam, as well as more intrinsically stable systems.

One possible solution for this is explored by Kim’s group at Duke, using microelectromechanical systems (MEMS) to control the steering of a beam with very very small, very very fast mirrors. For example, consider initially splitting the input beam into 2 individual beams, so that you could operate 2-qubit gates. Now, when you want to entangle ions 2 and 9 together, you want it such that the two initial beams can be steered to point at those locations. You would twist and turn those MEMS mirrors so that only those two targets are hit, and then enable your gate.

The system described by Knoernschild seeks to achieve this kind of adaptability across any location on a 5 by 5 grid, where each grid location is 10 um apart from each other. The initial lasers they use have waists of waists of 5 um at the ion plane, and they seek to achieve a settling time of the mirrors within 4 microseconds. Why does the beam need to settle so quickly? The speed at which the beam is able to move would then set the minimum time between running gates. You would have to wait that amount of time between individual quantum gates for the system to be settled, so that you don’t just accidentally sweep a laser across all of your ions and messing up all of your coherence.

In order to create such devices, the authors give very careful thought to the micromechanical properties of the mirrors, constructing them to be just large enough to not ‘clip’ any of the beams and introducing intensity aberrations, while being small enough to have a minimal amount of mechanical resonance. They control the system to be critically damped for the kinds of motion, and note that there are only a few spots that the mirrors need to hit, thus reducing the complexity of the system.

Fig 1 – notice the double ray bounce in 1(b)

One interesting solution that this paper proposes is to use something that looks like a double-pass configuration with the MEMS mirrors. That is, the light doesn’t just bounce off of each MEMS mirror once, but instead, twice. See Fig 1b, c for the way that they implement this. Their reason for this additional fold is to get a factor of two magnification for each change in MEMS mirror angle. By having a double bounce, a small angle shift of the MEMS corresponds to a greater movement of the actual beam targeting on the ion. However, this process does lead to larger aberrations, especially when the beam is imaged through the relay telescope. The authors also note that, since mirrors are not 100% reflectively coated, this leads to some amount of uniform loss in intensity as well. This is their stated reason for not going to even more elaborate folding schemes (although imo it would also be incredibly difficult to engineer even more folds into such a small space).


Furthermore, to accomplish individual steering of the beams, the authors create two pairs of MEMS mirrors – one pair to address each input beam. This allows for completely decoupled motion, but the vertical separation between the pairs of mirrors does introduce new kinds of aberrations. To analyze this, the authors do a Zemax analysis where they study how the peak intensity varies for different vertical separations. The authors reference generic “Seidel Aberrations” as the cause of this, although that seems to refer to five very common aberration modes: spherical, coma, astigmatism, curvature of field, or distortion, and I’m not entirely clear what kind of aberrations are actually dominant here (or where they even arise from). The result of this analysis in section 4 is that with an offset of 2mm between the MEMS mirrors, there is a peak intensity variation of 12%, while an offset of 0.25mm results in a variation of 3.5%. One possible solution to these aberrations, as the authors shown in Fig 3 with an array of lovely spot diagrams, is to put in custom compensation lenses directly before the MEMS mirrors. This seems to have greatly resolved this issue, which might be quite promising for future work. The authors do not actually implement this lens, as it does seem to be a Zemax automatically optimized lens, and probably would have cost a ridiculous amount to actually machine, but the point still stands.


They then implement this device, and study the intensity plots of the resultant beam. The camera images of the beam seem quite curious – Fig 5a and b show very odd aberration patterns that look somewhat like speckle, although my eyes are not nearly trained enough to tell. There also seems to be some kind of streaking occurring with the “D” shaped electrode, which is not really explained. The authors also do a test of the speed of settling for the mirrors, pointing the laser beam at a fast PSD and observing the transient responses. I would be quite interested to also take a more detailed look at how stable these MEMS mirrors are, and if they are possibly introducing any fast noise even during the “stable” period.

All in all, a very interesting technique for the future of ion trapping!

Reference: Knoernschild, C. et al. Multiplexed broadband beam steering system utilizing high speed MEMS mirrors. Optics Express 17 7233-7244 (2009)

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