Tl;dr Theoretically, yes, energy can produce matter by colliding way too many photons together to produce matter-antimatter pairs. Practically, we still need particles to create the photons that create particles. So, there are a few hurdles to solve.
Rest Mass is converted to energy by nuclear fusion and nuclear fission processes taking into account the binding energy and mass defect. But what about the other way round?
Can any arbitrary form/kind and amount of energy be used in this process? The answer to this question is no. Any arbitrary form of energy cannot be converted to any arbitrary type of mass (otherwise nuclei converters would use garbage as input!). For any type of energy to be converted to mass, a nuclear reaction (or something similar) is required that absorbs energy and releases a particle that has rest mass.
If an object gains energy it gains mass, and if an object gains mass it equivalently gains energy. This is called rest-mass energy. This conversion deals with very small amounts of mass and comparitively large amounts of energy.
How does all this even make sense? We recommend watching the following video.
Now that we are somewhat familiar with the concept of mass-energy equivalence and its implications, we move forward to our original question.
How do we convert energy to rest mass?
Matter – Antimatter Pair Production
Pair production is the creation of an elementary particle and its antiparticle from a neutral boson. Examples include creating an electron and a positron, a muon and an antimuon, or a proton and an antiproton. Pair production often refers specifically to a photon creating an electron-positron pair near a nucleus. In order for pair production to occur, the incoming energy of the interaction must be above a threshold in order to create the pair – at least the total rest mass energy of the two particles – and only if the situation allows energy-momentum to be conserved.
Experiments that prove that energy is and can be converted to mass
Although not by itself, scientists have observed in particle accelerators that while detecting radiation passing through a medium, if originally there were a only single photon with high energy, at a later time they observe three. The only explanation that they can come up with is that a part of the original energy breaks off to produce a matter-antimatter pair for a fraction of a second before it annihilates itself. The annihilation causes the formation of two new photons. While it may seem weird, there need to be at least two of these photons to conserve the momentum of the system. This is the only plausible explanation of this weird observation of one photon breaking into three.
Another experiment that proves that energy can create mass is high kinetic energy collisions of particles such as protons. Although no particles are annihilated, there are often new particles created which are observed in the collider. This is because 1. the collisions are inelastic, and 2. the energy is conserved. The residual energy that was previously the K.E. of these protons gets used up to create new particles.
Now, a suggested way of proving that energy can be by itself converted into mass is by colliding a pair of photons (particles of light) producing an electron and its antiparticle – positron inside a subatomic particle collider. In a study published online in the journal Nature Photonics, four physicists from Imperial College London and the Max Planck Institute for Nuclear Physics in Heidelberg, Germany, proposed a relatively straightforward method for witnessing the conversion of two photons into two particles.The experiment the physicists describe requires the construction of a new type of subatomic particle collider. But they insist this would be much less complicated than, say, building the Large Hadron Collider at CERN.
All that is needed to be done, according to them, is to accelerate electrons with a high-energy laser to a speed just below the speed of light. These high energy electrons are then shot into a slab of gold (target) creating a high energy photon beam (billion times more intense than the light from the sun). These photons generated are then aimed into a hollow gold shell/tube and fired through the middle of that specialized tube.
The tube is excited by another laser in order to create a thermal radiation field that emits light, whose brightness is similar to that of starlight. When light from these two sources crosses, some pairs of photons collide and create electrons and its antimatter particles, positrons. After the conversion of photon pairs into these two particles, a magnetic field separates the particles as they emerge from the end of the tube.
How do they know it would work? They used math to simulate the photons that would emerge from the gold target and how they’d behave inside the tube (a chamber called a vacuum hohlraum). According to their calculations, their photon-photon collider would work with “a wide variation of experimental parameters.”
The implementation of this idea is not void but is quite plausible with the existing forms of technology. For the math behind it, see here.