Quantum Bright Soliton in a Disorder Potential

K. Sachaa,b, D. Delande b and J. Zakrzewskia,b a Instytut Fizyki im. Mariana Smoluchowskiego and Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński, Reymonta 4, PL-30-059 Kraków, Poland b Laboratoire Kastler Brossel, UPMC, ENS, CNRS; 4 Place Jussieu, F-75005 Paris, France

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At very low temperature, a quasi one dimensional ensemble of atoms with attractive interactions tend to form: a bright soliton. When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected. We develop in detail the Bogoliubov approach for the problem, treating, in a non perturbative way, the motion of the center of mass of the soliton. Quantization of this motion allows us to discuss its long time properties. In particular, in the presence of a disordered potential, the quantum motion of the center of mass of a bright soliton may exhibit Anderson localization, on a localization length which may be much larger than the soliton size and could be observed experimentally.

DOI: 10.12693/APhysPolA.116.772 PACS numbers: 03.75.Lm, 72.15.Rn, 05.30.Jp