  Explicitly Correlated Gaussian basis is used to calculate the energies and
wave functions of one dimensional few-electron systems in confinement
potentials created by external potentials or coupling to light in cavity. The
appearance and properties of Wigner crystal-like structures are discussed. It
is shown that one dimensional Wigner crystals can be formed by coupling
electrons to light due to the dipole self-interaction term in the light-matter
Hamiltonian, provided an additional extremely weak confining potential is
present.
