Algebraic dynamics of Bloch oscillations of ultra - cold atoms in optical lattice

Pahlavani, H; Zamani, A

doi:10.18869/acadpub.ijpr.16.2.139

Algebraic dynamics of Bloch oscillations of ultra - cold atoms in optical lattice

Authors

H Pahlavani

A Zamani

https://doi.org/10.18869/acadpub.ijpr.16.2.139

Abstract

The dynamic of a charged quantum particle in a system of arrays of quantum well in tight-binding model, under the effect an external field, in one and two dimension, is studied by algebraic approach. The persistent‎ (quantum confinement) and ‎transmission ‎(quantum teleportaion) probabilities of this quantum particle in terms of infinite-variable Bessel functions is calculated and the results is discussed by numerical method.

Keywords

tight-binding model

Lie algebra

persistent probability

transmission probability

1. D H Dunlap and V M Kenkre, Phys. Rev. B 34 (1986) 3625.
2. A R Kolovsky and H J Korsch, Phys. Rev. A 67 (2003) 063601.
3. B P Anderson and M A Kasevich, “Macroscopic Quantum Interference from Atomic Tunnel Arrays”, Science 27 (1998) 1686.
4. R Walters, “Ultra-cold Atoms in Optical Lattices: Simulating Quantum Spin Systems”, Ph.D. ‎Thesis, Oxford University (2012).
5. B P Anderson and M A Kasevich, Science 282 (1998) 1686.
6. .A R Kolovsky and H J Korsch, International J. Mod. Phys. 18 (2004) 1235.
7. S Whitlock, R Gerritsma, T Fernholz, and R J C Spreeuw, New Journal of Physics 11 (2009) 023021.
8. H J Korsch and S Mossmann, Phys. Lett. A 317 (2003) 54.
9. S Mossmann, A Schulze, D Witthaut, and H J Korsch,‎ J. Phys. A: Math. Gen. 38 (2005) 3381.
10. T Hartman, F Keck, H J Korsch, and S Mossmann, New J. Phys. 6 (2004) 2.
11. L Galue, H G Khajah, S L Kalla, J. Computational and Applied Mathematics 118 (2000) 143.
12. ‎F Keck and ‎H J Korsch, J. Phys. A: Math. ‎Gen. 3‎5‎‎ (2002)‎ L105.