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arXiv:hep-th/0307134 · Nuclear Physics B

Novel multi-band quantum soliton states for a derivative nonlinear Schrödinger model

B. Basu-Mallick, Tanaya Bhattacharyya, Diptiman Sen

Published Oct 17, 2003• 8 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2003.09.048

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We return to the notion of optical solitons as these were first introduced—namely as exact soliton and multi-soliton solutions of the semi-classical self-induced transparency (SIT) equations. The SIT equations, even in their most general inhomogeneously broadened forms, are infinite dimensional, completely integrable Hamiltonian systems, and thus display much mathematical structure, yet their exact soliton solutions display well the nonlinear (self-induced) transparency features of the physical phenomenon. The mathematical feature of complete integrability is handed down from the SIT equations to the nonlinear Schrödinger equations and from this point of view the nonlinear Schrödinger (NLS) equations equations are studied first of all at classical level and then at quantum level. The ‘quantum soliton’ of the quantum attractive NLS model is defined and its properties investigated in detail, particularly in a comparison with the particular properties ascribed to the ‘quantum soliton’ as described in a recently published article (Abraham 1999 Phys. World (February) 21) with this title; as suggested in that article, the quantum NLS soliton is seen as a qubit for quantum information purposes. The covariant form of the quantum attractive NLS model is the quantum sine-Gordon model and this is briefly studied in the context of quantum information also; new results for large area Josephson junctions are reported in this context. The quantum soliton of the one dimensional attractive NLS model has apparently been observed in 2002 in a Bose condensed metal vapour ( 7 Li, (Khaykovich et al 2002 Science 296 1290)) and a detailed calculation suggests that the condensate undergoes a ‘collapse’ from three to one space dimensions thus forming an exact soliton solution of the one dimensional quantum attractive NLS model.