When antiparticles contact matter particles, they annihilate, releasing the mass as energy.
For positrons and electrons, this is a nice simple process of "two photons with a combined energy of just over 1MeV" (in the collision frame of reference they are equal in energy, 511 keV, and going in opposite directions); for protons and antiprotons, each quark does its thing separately so you get a whole mess of other things that are themselves unstable and I don't know the characteristic signatures of, only that they have one and you can look for it.
- "how do they actually know/analyze that they are making antimatter atoms ?"
That's answered in the OP paper: they detect the radiation from matter-antimatter annihilation that happens when the anti-atoms escape, and hit the experiment walls.
- "Central to the observations reported here is the antihydrogen annihilation detector[13] (Fig. 1a), situated coaxially with the mixing region, between the outer radius of the trap and the magnet bore. The detector is designed to provide unambiguous evidence for antihydrogen production by detecting the temporally and spatially coincident annihilations of the antiproton and positron when a neutral antihydrogen atom escapes the electromagnetic trap and strikes the trap electrodes. An antiproton typically annihilates into a few charged or neutral pions[14]. The charged pions are detected by two layers of double-sided, position-sensitive silicon microstrips. The path of a charged particle passing through both microstrip layers can be reconstructed, and two or more intersecting tracks allow determination of the position, or vertex, of the antiproton annihilation. The uncertainty in vertex determination is approximately 4 mm (1σ) and is dominated by the unmeasured curvature of the charged pions' trajectories in the magnetic field. The temporal coincidence window is approximately 5 µs. The solid angle coverage of the interaction region is about 80% of 4π."
- "A positron annihilating with an electron yields two or three photons. The positron detector, comprising 16 rows, each row containing 12 scintillating, pure CsI crystals[15], is designed to detect the two-photon events, consisting of two 511-keV photons that are always emitted back-to-back. The energy resolution of the detector is 18% full-width at half-maximum (FWHM) at 511 keV, and the photo-peak detection efficiency for single photons is about 20%."
As for the analysis, anti-particles are pretty much the same as their mirror particles save for some mirrored attribute(s), so charged antimatter particles carry the same charge as matter particles, but of opposite sign. An antiproton is negatively charged and an antielectron (positron) is positively charged.
Looking at particle tracks they'll see matching masses but curves in charged fields going in opposite directions.
Uncharged particles have some other mirrored attribute, so again "it's just like regular Alice only it's a mirror Alice wrt { X? }"
Create several thousand anti hydrogen atoms. Put them in a magnet trap. Open top and bottom of the trap. Detect collisions with wall. If more down. It's affected by gravity.
The answer you gave is like the meme of how to draw an owl in two steps (1. draw a perfect circle, 2. draw the rest of the owl).
A more helpful answer might be something like:
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Each particle has a corresponding field over all of space.
The substance-like particles obey certain rules, called Fermi statistics, which leads to a model called the Dirac sea; this makes all of space analogous to semiconductors, with electrons and holes, except that because this is just an analogy the holes are actually antiparticles.
The analogy is useful, in that it takes a certain minimum energy level to create a particle-antiparticle pair, just as it does an electron-hole pair.
For fundamental particles like electrons-positrons, this is fine and works as expected; the only extra step is knowing what has to absorb the energy to create the pair… but it turns out that all normal matter will do.
For composite particles like protons and neutrons, this is much harder, as the thing you make this way are quark-antiquark pairs, and to make either an antiproton or antineutron you need a specific combination of three specific "colours" (not real colours) of quark, and we have only extremely limited control in this regard.
When you have both positrons and antiprotons, "cool" them from the absurdly high energy states necessary to create them and let them combine just like electrons and normal protons recombining after getting ionised.