Quantum Lattice Representation of Dark Solitons
COLLEGE OF WILLIAM AND MARY WILLIAMSBURG VA DEPT OF PHYSICS
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The nonlinear Schrodinger NLS equation in a self-defocusing Kerr medium supports dark solitons. Moreover the mean field description of a dilute Bose-Einstein condensate BEC is described by the Gross-Pitaevskii equation, which for a highly anisotropic cigar-shaped magnetic trap reduces to a one-dimensional 1D cubic NLS- in an external potential. A quantum lattice algorithm is developed for the dark solitons. Simulations are presented for both black stationary solitons as well as moving dark solitons. Collisions of dark solitons are compared with the exact analytic solutions and coupled dark-bright vector solitons are examined. The quantum algorithm requires 2 qubits per scalar field at each spatial node. The unitary collision operator quantum mechanically entangles the on-site qubits, and this transitory entanglement is spread throughout the lattice by the streaming operators. These algorithms are suitable for a Type-II quantum computers, with wave function collapse induced by quantum measurements required to determine the coupling potentials.
- Electrical and Electronic Equipment
- Quantum Theory and Relativity