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arXiv:0804.3674 · Journal of Physics Conference Series

Entanglement production with Bose atoms in optical lattices

Vyacheslav I. Yukalov, Elizaveta P. Yukalova

Published Mar 1, 2008• 9 citations
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Abstract

A method of entanglement production is suggested, based on the resonant generation of topological modes in systems with Bose-Einstein condensates trapped in optical or magnetic lattices. The method makes it possible to regulate the strength of entanglement production as well as to govern its time variation. This method can serve as a practical tool for quantum information processing and quantum computing.

DOI
10.1088/1742-6596/104/1/012003

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A method of entanglement production is suggested, based on the resonant generation of topological modes in systems with Bose-Einstein condensates trapped in optical or magnetic lattices. The method makes it possible to regulate the strength of entanglement production as well as to govern its time variation. This method can serve as a practical tool for quantum information processing and quantum computing.
A system of traps is considered, each containing a large number of Bose-condensed atoms. This ensemble of traps is subject to the action of an external modulating field generating nonequilibrium non-ground-state condensates. When the frequency of the modulating field is in resonance with the transition frequency between two different topological coherent modes, each trap becomes an analog of a finite-level resonant atom. Similarly to the case of atoms in an electromagnetic resonant field, one can create entanglement between atomic traps subject to a common resonant modulating field generating higher coherent modes in each of the traps. A method is suggested for regulating entanglement production in such a system of multitrap and multimode Bose-Einstein condensates coupled through a common resonant modulating field. Several regimes of evolutional entanglement production, regulated by manipulating the external field, are illustrated by numerical calculations.
Abstract By pumping energy into a trapped Bose-Einstein condensate it is possible to generate nonlinear coherent modes representing non-ground-state condensates. A Bose-condensed system of trapped atoms with nonlinear coherent modes is analogous to a finite-level atom considered in optics which can be excited by applying external fields. The excitation of finite-level atoms produces a variety of optical phenomena. In the similar way, the generation of nonlinear coherent modes in a trapped condensate results in many phenomena studied in what is termed atom optics. For example, there occur such effects as interference patterns, interference current, Rabi oscillations, harmonic generation, parametric conversion, Ramsey fringes, mode locking, and a dynamic transition between Rabi and Josephson regimes. The possibility of creating mesoscopic entangled states of trapped atoms and entanglement production by atomic states in optical lattices are studied.
The report reviews the problem of topological coherent modes, which are nonlinear collective states of Bose-condensed atoms. Such modes can be generated by means of alternating external fields, whose frequencies are in resonance with the transition frequencies between the related modes. The Bose gas with generated topological coherent modes is a collective nonlinear analog of a resonant atom. Such systems exhibit a variety of nontrivial effects, e.g.: interference fringes, interference current, mode locking, dynamic transitions, critical phenomena, chaotic motion, harmonic generation, parametric conversion, atomic squeezing, and entanglement production. 1
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.
The report reviews the problem of topological coherent modes, which are nonlinear collective states of Bose‐condensed atoms. Such modes can be generated by means of alternating external fields, whose frequencies are in resonance with the transition frequencies between the related modes. The Bose gas with generated topological coherent modes is a collective nonlinear analog of a resonant atom. Such systems exhibit a variety of nontrivial effects, e.g.: interference fringes, interference current, mode locking, dynamic transitions, critical phenomena, chaotic motion, harmonic generation, parametric conversion, atomic squeezing, and entanglement production.