One-dimensional Bose gas dynamics: breather fragmentation and quantum correlations

Both exact conservation laws and dynamical invariants exist in the topical case of the one-dimensional ultra-cold atomic Bose gas, providing a validation of methods for precision quantum dynamics. The first four quantum conservation laws are exactly conserved in the approximate truncated Wigner approach to many-body quantum dynamics, which is a 1/N expansion for N atoms. Center-of-mass position variance is exactly calculable, and is nearly exact in the truncated Wigner approximation, apart from small terms that vanish as N^-3/2 as N→∞.

As an example, we calculate the dynamics of a higher-order soliton in the mesoscopic case of N=10³-10⁴ particles, giving predictions for quantum soliton breather fragmentation. Our results show evidence for gradual fragmentation with formation of multiple single particle condensate states and nonlocal quantum correlations. These results disagree with variational calculations that violate exact dynamical results, due to the use of too few natural modes in variational theories. Methods for going beyond the 1/N expansion will be treated as well.

Such dynamical predictions are testable in BEC experiments using attractive Bose gases with either ⁷Li or ⁸⁵Rb condensates.