1 Quantum Solitons
Intitially, optical solitons were introduced as exact soliton and multi-soliton solutions of
the semi-classical self-induced transparency (SIT) equations; the SIT equations are
defined as descriptions or representations of infinite dimensional, completely integrable
hamiltonian systems [1]. The exact solutions of SIT equations have nonlinear (self-induced)
transparency features. The complete integrability leads to nonlinear (NLS) Schrödinger
equations.
Definition 1.1. Quantum solitons are defined as solutions of the quantum attractive NLS
model that exhibit the physical properties described in ref. [2]. Therefore, the quantum NLS
soliton can be regarded as a qubit of quantum information.
1.1 Remarks
The covariant form of the quantum attractive NLS model is the quantum sine-Gordon model. The
latter model is also relevant in the context of quantum information and new results have been
reported already for large area Josephson junctions. The quantum soliton of the one
dimensional attractive NLS model has been claimed to have been observed in a Bose
condensed metal vapour (7Li, ref.[3]). Detailed calculations seem to suggest that the Bose
condensate undergoes a ’collapse’ from three to one space dimensions, thus yielding an exact
soliton (“quantum soliton solution”) of the one dimensional quantum attractive NLS
model.
References
[1] R. K. Bullough and Miki Wadati. 2004. J. Opt. B: Quantum Semiclass. Opt. 6:
S205–S216.
[2] A. Abraham et al. 1999. Quantum Solitons. Phys. World, February 21, 1999 issue.
[3] Khaykovich, et al. 2002. Science. 296: 1290.
