Bose-Einstein condensates on a ring with periodic scattering length: Spontaneous symmetry breaking and entanglement

Abstract

We study the properties of Bose-Einstein condensates in a one-dimensional ring with periodically modulated interaction strength. We demonstrate that within the semiclassical mean-field theory, a condensate can undergo a quantum phase transition between a solitonlike state and a spatially periodic condensate that matches the scattering length modulation. However, we show via exact diagonalization of the full many-body Hamiltonian that the solitonic ground states do not exist in the true quantum treatment. Instead, the system is driven into an entangled macroscopic-quantum-superposition-like state and the semiclassical soliton state may be regarded as a decohered macroscopic quantum superposition state. We investigate how the properties of the quantum ground state scales with the total number of atoms. Our work elucidates how semiclassical properties emerge from quantum behavior.