Radial quantum number of Laguerre-Gauss modes
| dc.contributor.author | Karimi, E. | |
| dc.contributor.author | Boyd, R.W. | |
| dc.contributor.author | Hoz Iglesias, Pablo de la | |
| dc.contributor.author | de Guise, H. | |
| dc.contributor.author | Řeháček, J. | |
| dc.contributor.author | Hradil, Z. | |
| dc.contributor.author | Aiello, A. | |
| dc.contributor.author | Leuchs, Gerd | |
| dc.contributor.author | Sánchez Soto, Luis Lorenzo | |
| dc.date.accessioned | 2023-06-19T13:32:27Z | |
| dc.date.available | 2023-06-19T13:32:27Z | |
| dc.date.issued | 2014-06-16 | |
| dc.description | © 2014 American Physical Society. E.K. and R.W.B. acknowledge the support of the Canada Excellence Research Chairs (CERC) Program. The work of H.G. is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. J.R. and Z.H. are grateful for the financial assistance of the Technology Agency of the Czech Republic (Grant No. TE01020229) and the Czech Ministry of Industry and Trade (Grant No. FR-TI1/364). G.L. is partially funded by EU FP7 (Grant Q-ESSENCE). Finally, P.H. and L.L.S.S. acknowledge the support from the Spanish MINECO (Grant No. FIS2011-26786). | |
| dc.description.abstract | We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes. | |
| dc.description.department | Depto. de Óptica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Canada Excellence Research Chairs (CERC) Program | |
| dc.description.sponsorship | Natural Sciences and Engineering Research Council (NSERC) of Canada | |
| dc.description.sponsorship | Technology Agency of the Czech Republic | |
| dc.description.sponsorship | Czech Ministry of Industry and Trade | |
| dc.description.sponsorship | EU FP7 | |
| dc.description.sponsorship | Spanish MINECO | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/29498 | |
| dc.identifier.doi | 10.1103/PhysRevA.89.063813 | |
| dc.identifier.issn | 1050-2947 | |
| dc.identifier.officialurl | http://dx.doi.org/ 10.1103/PhysRevA.89.063813 | |
| dc.identifier.relatedurl | http://journals.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33972 | |
| dc.issue.number | 6 | |
| dc.journal.title | Physical review A | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | TE01020229 | |
| dc.relation.projectID | FR-TI1/364 | |
| dc.relation.projectID | Q-ESSENCE | |
| dc.relation.projectID | FIS2011-26786 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 535 | |
| dc.subject.keyword | Orbital angular-momentum | |
| dc.subject.keyword | Minimum uncertainty states | |
| dc.subject.keyword | Electron vortex beams | |
| dc.subject.keyword | Coherent states | |
| dc.subject.keyword | Intelligent states | |
| dc.subject.keyword | SU(1 | |
| dc.subject.keyword | 1) | |
| dc.subject.keyword | Vortices | |
| dc.subject.keyword | Light | |
| dc.subject.keyword | SU(2) | |
| dc.subject.keyword | Representations. | |
| dc.subject.ucm | Óptica (Física) | |
| dc.subject.unesco | 2209.19 Óptica Física | |
| dc.title | Radial quantum number of Laguerre-Gauss modes | |
| dc.type | journal article | |
| dc.volume.number | 89 | |
| dcterms.references | [1] Twisted Photons: Applications of Light with Orbital Angular Momentum, edited by J. Torres and L. Torner (Wiley-VCH, Weinheim, 2011). [2] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A, 45, 8185 (1992). [3] Optical Tweezers, edited by M. J. Padgett, J. Molloy, and D. McGloin (Chapman and Hall, London, 2010). [4] C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Laser Photon. Rev., 5, 81 (2011). [5] N. Uribe-Patarroyo, A. Fraine, D. S. Simon, O. Minaeva, and A. V. Sergienko, Phys. Rev. Lett., 110, 043601 (2013). [6] N. M. Elias, II, Astron. Astrophys., 492, 883 (2008). [7] F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, Nat. Phys., 7, 195 (2011). [8] J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photon., 6, 488 (2012). [9] M. Uchida and A. Tonomura, Nature (London), 464, 737 (2010). [10] J. Verbeeck, H. Tian, and P. Schattschneider, Nature (London), 467, 301 (2010). [11] B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, Science, 331, 192 (2011). [12] E. Karimi, L. Marrucci, V. Grillo, and E. Santamato, Phys. Rev. Lett., 108, 044801 (2012). [13] A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, and I. McNulty, Opt. Lett., 27, 1752 (2002). [14] K. A. Nugent, Adv. Phys., 59, 1 (2009). [15] E. Hemsing, A. Knyazik, M. Dunning, D. Xiang, A. Marinelli, C. Hast, and J. B. Rosenzweig, Nat. Phys., 9, 549 (2013). [16] B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, Phys. Rev. Lett., 99, 087701 (2007). [17] S. M. Mohammadi, L. K. S. Daldorff, K. Forozesh, B. Thidé, J. E. S. Bergman, B. Isham, R. Karlsson, and T. D. Carozzi, Radio Sci., 45, RS4007 (2010). [18] F. Tamburini, E. Mari, A. Sponselli, B. T. A. Bianchini, and F. Romanato, New J. Phys., 14, 033001 (2012). [19] A. Mair, A. Vaziri, G.Weihs, and A. Zeilinger, Nature (London), 412, 313 (2001). [20] G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett., 92, 167903 (2004). [21] S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett., 92, 217901 (2004). [22] L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, J. Opt., 13, 064001 (2011). [23] G. Molina-Terriza, L. Rebane, J. P. Torres, L. Torner, and S. Carrasco, J. Eur. Opt. Soc., 2, 07014 (2007). [24] R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science, 338, 640 (2012). [25] E. Karimi and E. Santamato, Opt. Lett., 37, 2484 (2012). [26] W. N. Plick, R. Lapkiewicz, S. Ramelow, and A. Zeilinger, arXiv:1306.6517. [27] G. Nienhuis and J. Visser, J. Opt. A, 6, S248 (2004). [28] A. B. Mikhailovskii, V. P. Lakhin, G. D. Aburdzhaniya, L. A. Mikhailovskaya, O.G.Onishchenko, and A. I. Smolyakov, Plasma Phys. Controlled Fusion, 29, 1 (1987). [29] M. M. Salomaa and G. E. Volovik, Rev. Mod. Phys., 59, 533 (1987). [30] V. V. Dodonov and V. I. Mank’o, Invariants and the Evolution of Nonstationary Quantum Systems (Nova Science, New York, 1989). [31] C. Cohen-Tannoudji, B. Diu, and F. Lalöe, Quantum Mechanics (Wiley, New York, 2006). [32] L. L. Sánchez-Soto, A. B. Klimov, P. de la Hoz, I. Rigas, J. Řeháček, Z. Hradil, and G. Leuchs, Phys. Rev. A, 88, 053839 (2013). [33] H. S. Yi, H. R. Lee, and K. S. Sohn, Phys. Rev. A, 49, 3277 (1994). [34] R. Lynch, Phys. Rep., 256, 367 (1995). [35] L. C. Biedenharn, J. Nuyts, and N. Straumann, Ann. Inst. Henri Poincaré, Section A, tome 3, 13 (1965). [36] C. C. Gerry, Phys. Rev. A, 31, 2721 (1985). [37] B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A, 33, 4033 (1986). [38] V. Bužek, Phys. Rev. A, 39, 3196 (1989). [39] A. Vourdas, Phys. Rev. A, 45, 1943 (1992). [40] M. Ban, Phys. Rev. A, 47, 5093 (1993). [41] C. Brif and A. Mann, Phys. Rev. A, 54, 4505 (1996). [42] C. C. Gerry, S. C. Gou, and J. Steinbach, Phys. Rev. A, 55, 630 (1997). [43] G. S. Agarwal and J. Banerji, Phys. Rev. A, 64, 023815 (2001). [44] G. I. Mias, N. R. Cooper, and S. M. Girvin, Phys. Rev. A, 77, 023616 (2008). [45] A. M. Marino, N. V. Corzo Trejo, and P. D. Lett, Phys. Rev. A, 86, 023844 (2012). [46] A. Perelomov, Generalized Coherent States and their Applications (Springer, Berlin, 1986). [47] E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, Opt. Lett., 32, 3053 (2007). [48] A. O. Barut and L. Girardello, Commun. Math. Phys., 21, 41 (1971). [49] K. Wókiewicz and J. H. Eberly, J. Opt. Soc. Am. B, 2, 458 (1985). [50] R. Jackiw, J. Math. Phys., 9, 339 (1968). [51] J. A. Bergou, M. Hillery, and D. Yu, Phys. Rev. A, 43, 515 (1991). [52] C. C. Gerry and R. Grobe, Phys. Rev. A, 51, 4123 (1995). [53] R. R. Puri and G. S. Agarwal, Int. J. Mod. Phys. B, 10, 1563 (1996). [54] P. Joanis, D. H. Mahler, and H. de Guise, J. Phys. A 43, 385304 (2010). [55] H. Ui, Prog. Theor. Phys., 44, 689 (1970). [56] D. J. Rowe, H. de Guise, and B. C. Sanders, J. Math. Phys., 42, 2315 (2001). [57] E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. M. Miatto, M. J. Padgett, and R. W. Boyd, Phys. Rev. A, 89, 013829 (2014). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 88b797ff-cbd7-4498-a9c7-4e39f4fa4776 | |
| relation.isAuthorOfPublication.latestForDiscovery | 88b797ff-cbd7-4498-a9c7-4e39f4fa4776 |
Download
Original bundle
1 - 1 of 1
