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I'm wondering what is the procedure to just remain with a single atom of an element after several of them were put into an atrificial vacuum.

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There are many possible answers to this question - I will offer one approach that we use in our lab to trap individual Rubidium atoms.

The key idea is that of the 'optical tweezer', which is a tightly focused laser that is off-resonant from an atomic transition. Since the laser is off-resonance, it does not scatter very many photons from atoms, but instead it forms a potential well in which atoms can be trapped. If the focused laser is not too tightly focused, then it can trap a large number of atoms. If it is very tightly focused (ie., a waist of around a micron), then the tweezer is in the 'collisional blockade' regime. In this case, shining a near-resonant laser (often used for laser cooling) will cause two trapped atoms to collide and be lost from the trap.

In this case, pairs of atoms are ejected from the trap. But if a single atom is left in the trap, it will happily remain there by itself. Tweezers in this configuration can therefore trap at most a single atom, which can be detected by fluorescence imaging. People have used this technique to create large arrays of individual neutral atoms, which then can be used for a variety of experiments in quantum physics.

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Another example from atomic physics:

You start with a large atomic cloud loaded into an optical lattice. Some lattice sites have just one atom, some other lattice sites may have more than one atom. Because of interaction between atoms, an interband transition for singly-occupied site and multiply-occupied site becomes spectroscopically distinguishable. Using this, you can excite one atom from multiply-occupied site into an excited band (more weakly trapped) and remove them, while singly-occupied sites are left unaffected. After this "algorithmic cooling", all the lattice sites are singly-occupied. (Note: term "cooling" is used because the randomly multiply-occupied sites store entropy in the system under study.)

Now if you want to select just one site, you can probably use a high-resolution microscope to select a specific singly-occupied site. Even if the resolution of your microscope is not enough to resolve a single lattice site (Airy radius > lattice constant), you can still achieve a sub-diffraction resolved addressing. The trick is to combine spatially-varying detuning (AC stark shift from a laser) with a sharp transition (microwave transition).

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There are several methods for performing this task. If my understanding is correct, this is how all elements above 101 have been found. This is an excerpt from Berkley describing how they found Mendelevium.

In 1955, mendelevium (101) was formed by bombardment of einsteinium-253 with a beam of helium-4 ions (alpha particles). The successful identification of mendelevium was performed using separation by a recoil method proposed by Berkeley Lab’s Albert Ghiorso (1915–2010). This method took advantage of the feeble recoil imparted in the fusion reaction of helium with the highly radioactive einsteinium target. Recoil kicked the mendelevium atoms out of the thin target onto a gold foil catcher. Chemical processing then proved that, indeed, a new element had been produced. Seventeen atoms in all were detected. This new separation technique was a powerful tool that would be used for subsequent new element experiments. Mendelevium was the first element identified on an “atom-at-a-time” basis and the heaviest element to be first identified by chemical separation. (source)

There are several older and new pieces of equipment designed to do exactly what you ask.. some are surprisingly simple and others enormously complex...

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