Entanglement assisted fast reordering of atoms in an optical lattice within a cavity at T = 0

Laser-illuminated atoms in an optical resonator exhibit a phase transition between the homogenous distribution and two possible ordered configurations in the optical lattice formed by the cavity and pump fields. At zero temperature, atom-field entanglement plays a crucial role in the spatial reordering of the atoms from a homogeneous towards the two ordered states, where all atoms occupy either only even or only odd lattice sites. Concurrent with the buildup of atom-field entanglement, the homogeneous atomic cloud evolves immediately into the superposition of the two stable patterns entangled with opposite cavity field amplitudes. This possibility is absent in a factorized (classical) treatment of atoms and field and should be generic for spontaneous symmetry breaking in quantum phase transitions in optical potentials.