@article{SIGMA_2006_2_a49,
author = {Benedetto Militello and Paolo Aniello and Antonino Messina},
title = {Perturbative {Treatment} of the {Evolution} {Operator} {Associated} with {Raman} {Couplings}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2006},
volume = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a49/}
}
TY - JOUR AU - Benedetto Militello AU - Paolo Aniello AU - Antonino Messina TI - Perturbative Treatment of the Evolution Operator Associated with Raman Couplings JO - Symmetry, integrability and geometry: methods and applications PY - 2006 VL - 2 UR - http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a49/ LA - en ID - SIGMA_2006_2_a49 ER -
%0 Journal Article %A Benedetto Militello %A Paolo Aniello %A Antonino Messina %T Perturbative Treatment of the Evolution Operator Associated with Raman Couplings %J Symmetry, integrability and geometry: methods and applications %D 2006 %V 2 %U http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a49/ %G en %F SIGMA_2006_2_a49
Benedetto Militello; Paolo Aniello; Antonino Messina. Perturbative Treatment of the Evolution Operator Associated with Raman Couplings. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a49/
[1] Wineland D. J., Monroe C., Itano W. M., Leibfried D., King B. E., Meekhof D. M., “Experimental issues in coherent quantum-state manipulation of trapped atomic ions”, J. Res. Natl. Inst. Stand. Tech., 103 (1998), 259–328; arXiv:quant-ph/9710025
[2] Leibfried D., Blatt R., Monroe C., Wineland D., “Quantum dynamics of single trapped ions”, Rev. Modern Phys., 75 (2003), 281–324 | DOI
[3] Ghosh P. K., Ion traps, Clarendon Press, Oxford, 1995
[4] Steinbach J., Twamley J., Knight P. L., “Generation of nonclassical motional states of a trapped atom”, Phys. Rev. A, 56 (1997), 4815–4825 | DOI
[5] Aniello P., “A new perturbative expansion of the time evolution operator associated with a quantum system”, J. Opt. B Quantum Semiclass. Opt., 7 (2005), S507–S522 ; arXiv:quant-ph/0508017 | DOI | MR
[6] Aniello P., Man'ko V. I., Marmo G., Porzio A., Solimeno S., Zaccaria F., “Trapped ions interacting with laser fields: a perturbative analysis without the rotating wave approximation”, J. Russ. Las. Res., 25 (2004), 30–53 ; arXiv:quant-ph/0301138 | DOI
[7] Aniello P., Man'ko V., Marmo G., Porzio A., Solimeno S., Zaccaria F., “Ion traps in interaction with laser fields: a RWA-free perturbative approach”, Proceedings of the 8-th ICSSUR, eds. H. Moya-Cessa, R. Járengui R., S. Hacyan and O. Castaños, Rinton Press, Princeton, 2003, 17–22
[8] Aniello P., “Perturbative solutions of differential equations in Lie groups”, Int. J. Geom. Methods Mod. Phys., 2 (2005), 111–126 | DOI | MR
[9] Militello B., Aniello P., Messina A., “Coarse grained and fine dynamics in trapped ion Raman schemes”, J. Phys. A: Math. Gen., 37 (2004), 8177–8187 ; arXiv:quant-ph/0310162 | DOI | MR | Zbl
[10] Magnus W., “On the exponential solution of differential equations for a linear operator”, Comm. Pure Appl. Math., 7 (1954), 649–673 | DOI | MR | Zbl
[11] Amerio L., Prouse G., Almost periodic functions and functional equations, Van Nostrand Reinhold, 1971 | MR | Zbl
[12] Wilcox R. M., “Exponential operators and parameter differentiation in quantum physics”, J. Math. Phys., 8 (1967), 962–982 | DOI | MR | Zbl
[13] Meekhof D. M., Monroe C., King B. E., Itano W. M., Wineland D. J., “Generation of nonclassical motional states of a trapped atom”, Phys. Rev. Lett., 76 (1996), 1796–1799 | DOI
[14] Leibfried D., Meekhof D. M., King B. E., Monroe C., Itano W. M., Wineland D. J., “Experimental preparation and measurement of the state of motion of a trapped atom”, J. Modern Opt., 44 (1997), 2485–2505
[15] Di Fidio C., Vogel W., “Damped Rabi oscillations of a cold trapped ion”, Phys. Rev. A, 62 (2000), 031802, 4 pp., ages | DOI
[16] Militello B., Aniello P., Messina A., Trapped ion Raman schemes: a novel time-dependent perturbative approach, in preparation