That's gotta be a really sharp knife

Is energy conserved in this scenario?

and really light

This is a purely theoretical exercise, from what I could understand:

[They] considered what would happen if a single photon passed through an optical shutter—essentially a very fast mirror that can be switched on and off to block part of a pulse of light. If the shutter was fast enough, it could intercept the photon mid-pulse, snipping off part of this extended wave.

They then did a bunch of calculations to simulate what would happen, but I'm wondering if such a shutter wouldn't have to travel at the speed of light to catch the photon, and if this doesn't make the experiment meaningless...

If you flipped a mirror back and forth fast enough to “split a photon” you’d end up generating a bunch of photons due to the heat energy generated by the system anyway. I’m sure that’s not what they’re talking about but just imagine something oscillating that quickly.

Sound like they are implying that photons can be collided and it creates a whole new set of particles.

No, thats the photon. The knife would have to be more solid