Quantum Breakup of Higher Order Bright Solitons

Semiclassical mean field theory in the form of the nonlinear Schrodinger equation (NLS) has had incredible success in modeling the dynamics of repulsive Bose-Einstein condensates (BECs): experimentally observed predictions range from dark solitons to skyrmions. A key prediction for attractive BECs is the bright soliton. An order-two soliton can be produced in a BEC simply by increasing the interaction strength by a factor of four, via a Feshbach resonance. The NLS is exactly solvable in this case and predicts a beautiful time-periodic dynamical pattern. Using matrix-product state methods, we show that such far-from-equilibrium higher order bright solitons exhibit quantum depletion and in fact break up rapidly in the more complete underlying quantum theory. Such break-up presents a smoking gun signal for emergent phenomena in quantum systems that do not have a semiclassical limit, and are therefore truly quantum in nature at macroscopic scales. They also indicate a breakdown of semiclassical integrability at a more fundamental quantum level.