Number-resolved imaging of $^{88}$Sr atoms in a long working distance optical tweezer

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The authors present initial studies of imaging and temperature for strontium atoms confined within an optical tweezer formed with a relatively low NA lens. The key claims to novelty are:

1) The long working-distance of the system is a key attribute for future studies involving Rydberg states
2) Number resolved imaging can be achieved
3) Parity projection can be avoided in the larger-volume trap.
4) The use of a SPAD array detector for atomic detection, providing performance advantages over typical CCD’s.

In my opinion, these claims all require further quantitative justification. In order:
1) This would be a nice feature to have, if NA were not also severely sacrificed. Currently, there are major demonstrated advantages to a high-NA setup (reduced optical power requirements, lower effects of atomic motion, possibility of sideband cooling, higher collection efficiency), but no demonstration that setups with ~5mm separation between atoms and glass surfaces are incompatible with Rydberg physics.

2) No quantitative demonstration of number resolved imaging is presented. This claim cannot be made without providing the fidelity with which different number states can be distinguished, and the measured rate of atom loss associated with imaging at this fidelity. Further, it is claimed that this imaging technique can be used to to deterministically prepare loaded tweezers. In estimating the fidelity of this approach, no mention is made of the imaging fidelity, which would limit one’s ability to load single atoms.

3) No quantitative measurement of parity projection avoidance is presented. The authors claim that parity projection is avoided by using a larger trap, but no quantitative information is presented to substantiate this claim. Further, the authors argue that the lack of parity projection in their system contrasts with previous strontium tweezer experiments. However, as indicated in the appendices of references 15, 16, substantially longer parity projection steps are used to isolate single atoms, presumably because parity projection actually takes a while in those systems as well.

4) The authors claim that the use of a SPAD array provides advantages over CCD or CMOS cameras, and specifically that unlike CCD or CMOS cameras, SPAD arrays are limited by photon shot noise instead of dark counts or readout noise. However, the cooled EMCCD cameras used in tweezer and quantum gas microscope experiments are typically dominated by shot noise (with a contribution from the excess noise factor associated with gain, though this can also be avoided), and have much lower dark count rates than those of the SPAD array, much higher quantum efficiency, and negligible readout noise. There may be a cost advantage to the SPAD array, but if this is the reason to use them then it should be stated.

Other issues:
• figure 3a: I think the X axis here is supposed to be microseconds, not milliseconds. After 50ms, gravity would have caused the atoms to drop by over 1 cm.
• figure 3b: Perhaps there is an issue with the axes here as well. The line implies a velocity of around 50m/s, which is not what one would expect for the quoted temperatures.
• Are the temperatures quoted in the axial or radial directions, or are the two assumed to be equal?

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