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quantum solitons (Topic)

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.

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.

Bibliography

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.



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See Also: qubit and qudit

Also defines:  quantum soliton, SIT equations, NLS equations
Keywords:  quanta, quantum physics, solitons, waves, quantum solitons, nonlinear Schrödinger equations

Cross-references: Josephson junctions, qubit, systems, hamiltonian, representations, solitons

This is version 20 of quantum solitons, born on 2009-09-08, modified 2009-09-23.
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Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )
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