Quantum Entangled Dark Solitons*

We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices [1,2]. Using time-evolving block decimation to simulate the single-band Bose- Hubbard Hamiltonian, we consider the quantum dynamics of density- and phase-engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. Quantum fluctuations cause the dark soliton to fill in and can induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals. [1] Phys. Rev. Lett. {\bf 103}, 140403 (2009). [2] Phys. Rev. A {\bf 80}, 053612 (2009).