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arXiv:1307.3866 · Condensed Matter Physics

A new exactly solvable spatially one-dimensional quantum superradiance fermi-medium model and properties of its quantum solitonic states

Blackmore, Prykarpatsky

Published Jan 1, 2013• 0 citations
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Abstract

A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with an external electromagnetic field is proposed.The infinite hierarchy of quantum conservation laws and many-particle Bethe eigenstates that model quantum solitonic impulse structures are constructed.The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related to the thermodynamical equilibrity of the model, are discussed.

DOI
10.5488/cmp.16.23701

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A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with an external electromagnetic field is proposed.The infinite hierarchy of quantum conservation laws and many-particle Bethe eigenstates that model quantum solitonic impulse structures are constructed.The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related to the thermodynamical equilibrity of the model, are discussed.
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Abstract Solitons are ubiquitous phenomena that appear, among others, in the description of tsunami waves, fiber-optic communication and ultracold atomic gases. The latter systems turned out to be an excellent playground for investigations of matter-wave solitons in a quantum world. This tutorial provides a general overview of the ultracold contact interacting Bose and Fermi systems in a one-dimensional space that can be described by the renowned Lieb–Liniger and Yang–Gaudin models. Both the quantum many-body systems are exactly solvable by means of the Bethe ansatz technique, granting us a possibility for investigations of quantum nature of solitonic excitations. We discuss in details a specific class of quantum many-body excited eigenstates called yrast states and show that they are strictly related to quantum dark solitons in the both considered Bose and Fermi systems.
The excitation spectrum in several models of the one-dimensional electron gas is calculated. The models studied are the backward scattering model, charge transfer model, and strong-coupling spinless fermion model, with no restrictions on the interaction strengths. All can exhibit new types of elementary excitations which are identified as quantum solitons and bound solitons. These excitations can participate in transport, and are exponentially activated at low temperatures. The gap energy is calculated for arbitrary coupling strengths in the various models, using a procedure which exactly solves the quantum sine-Gordon equation in one dimension.
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Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirms that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.