The process you are referring to is known as quark confinement or hadronization. It is the phenomenon that occurs when quarks are pulled apart with sufficient energy. As the distance between the quarks increases, the energy stored in the strong nuclear force field between them also increases. At some point, there is enough energy for the creation of a quark-antiquark pair from the vacuum, resulting in the formation of new hadrons (particles composed of quarks) rather than separating individual quarks.
Quark confinement has been extensively studied and confirmed through experimental observations and theoretical understanding. However, directly observing the process of quark confinement in a controlled laboratory setting is challenging due to the high energy scales involved.
In particle accelerators, such as the Large Hadron Collider (LHC) at CERN, high-energy collisions between particles can produce conditions where quark confinement occurs. These collisions create a "quark-gluon plasma," a state of matter where quarks and gluons are temporarily deconfined. By studying the properties and behavior of the quark-gluon plasma, scientists can gain insights into the mechanisms of quark confinement.
While quark confinement has been indirectly observed and studied in experiments, it is important to note that directly splitting individual quarks and observing the creation of new ones is currently beyond the capabilities of current technology and understanding.