Doesn't the implication work in both directions? That is, to complete the relationship: You cannot have the field without the presence of mass/energy?
Quite possibly, but that's not really relevant for purposes of this particular topic.
I'm wondering how the field is produced
Well, the deepest of the "how" is probably quantum gravity, which we don't have worked out. "Presence of mass/energy created gravitational field" is sufficient for our purposes.
and why it would be better to create the field in a complicated way (with a magnetic field) rather than by simply adding/removing mass. Could a magnetic field produce a bigger mass/energy density, or somehow create an oscillation or a gradient which would be more useful for creating gravity waves?
Several things:
With normal matter, you have the issue of having to hold it in place, and you can't actually change the amount present very easily ("Hold on, Fred, shut it down! I have to add another grain of sand!"). Also, matter has this annoying tendency to be opaque, as does whatever holds the matter in place, which may make shining a laser through the area difficult.
Meanwhile, with a magnetic field, you get to run a current through some superconducting loops, and some distance away you have a thoroughly transparent region that is still packed with energy/mass in the form of magnetic field. And, by only small changes in the current, you get to play with changes in "mass". Yes, you could even pulse the current to produce changes in mass, and thus waves, but I am not sure that's the actual goal.
But I didn't think that magnetic fields affected photons (
http://van.physics.illinois.edu/qa/listing.php?id=2009), so I'm not even understanding how detection would work.
You *want* the magnetic fields to not affect the laser directly - you want the area to be as transparent as possible. But it is actually wave-nature you're looking at, not photons, because we are going to use the same basic concept we use for LIGO or other gravity detectors - interferometry.
Consider - have the current off, shine the laser through, it travels some distance. Turn the current on. That packs a region with energy/mass, and so creates a (small) gravitational field. With that present, you shine the laser, and its path *bends* just slightly, which means it travels a slightly different distance. Compare the path difference with interferometry, and you can detect *very* small differences in path length.
Actually, what you probably do is take a laser beam, and split it. You have two beams travel some distance separately, and recombine them. You tune the apparatus so they're travelling the *exact* same distance (or, some multiple of whole wavelengths, so when they recombine, the waves are in-step, and constructively interfere). Now, on one of the paths, you turn on that magnetic field. The path on that one side bends ever so slightly. When they recombine, the waves will be *slightly* out of synch, and you can see the drop in intensity from destructive interference. Measure that, you have measured the path difference, and thus the strength of the gravitational field.