## Curvature effects on the interaction of nonlinear sphere coherent states with a three-level atom |

JOSA B, Vol. 30, Issue 11, pp. 2952-2959 (2013)

http://dx.doi.org/10.1364/JOSAB.30.002952

Enhanced HTML Acrobat PDF (889 KB)

### Abstract

In this paper, we consider the interaction of the nonlinear coherent states (CSs) on a sphere with a three-level atom. Since these generalized CSs depend on the curvature of the sphere, this model enables us to investigate the curvature effects of the physical space. By using the time-dependent state of the atom-field system, we first study the curvature effects on the occupation probabilities of the atomic levels. We especially study the relation between the revival time of the atomic occupation probabilities and the curvature. Then, to study the curvature effects on the dynamical properties of the cavity field, we consider photon distributions, correlation functions, and Mandel parameters of the field. The cavity field in this atom-field system exhibits nonclassical features which depend on the curvature of the physical space.

© 2013 Optical Society of America

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5290) Quantum optics : Photon statistics

(270.5580) Quantum optics : Quantum electrodynamics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: June 27, 2013

Revised Manuscript: August 19, 2013

Manuscript Accepted: September 7, 2013

Published: October 24, 2013

**Citation**

A. Mahdifar, M. Jamshidi Farsani, and M. Bagheri Harouni, "Curvature effects on the interaction of nonlinear sphere coherent states with a three-level atom," J. Opt. Soc. Am. B **30**, 2952-2959 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-11-2952

Sort: Year | Journal | Reset

### References

- S. Haroche and J.-M. Raimond, Exploring the Quantum, Atoms, Cavities, and Photons (Oxford University, 2006).
- H. Stephani, General Relativity (Cambridge, 1996).
- F. W. Dyson, A. S. Eddington, and C. Davidson, “A determination of the deflection of light by the Sun’s gravitational field, from observations made at the total eclipse of 29 May 1919,” Philos. Trans. R. Soc. Lond. A 220, 291–333 (1920). [CrossRef]
- D. Walsh, R. F. Carswell, and R. J. Weymann, “0957 + 561 A, B: twin quasistellar objects or gravitational lens?” Nature 279, 381–384 (1979). [CrossRef]
- R. V. Pound and G. A. Rebka, “Apparent weight of photons,” Phys. Rev. Lett. 4, 337–341 (1960). [CrossRef]
- I. Bloch, T. W. Hänsch, and T. Esslinger, “Measurement of the spatial coherence of a trapped Bose gas at the phase transition,” Nature 403, 166–170 (2000). [CrossRef]
- V. V. Nesvizhevsky, H. G. Börner, A. K. Petukhov, H. Abele, S. Baeler, F. J. Rue, Th. Stöferle, A. Westphal, A. M. Gagarski, G. A. Petrov, and A. V. Strelkov, “Quantum states of neutrons in the Earth’s gravitational field,” Nature 415, 297–299 (2002). [CrossRef]
- M. Mohammadi, M. H. Naderi, and M. Soltanolkotabi, “Quantum statistical properties of the Jaynes–Cummings model in the presence of a classical homogeneous gravitational field,” J. Phys. A 40, 1377–1393 (2007). [CrossRef]
- Sh. Barzanjeh, M. H. Naderi, and M. Soltanolkotabi, “Dynamical behaviours of the nonlinear atom-field interaction in the presence of classical gravity: f-deformation approach,” J. Phys. A 43, 375304 (2010). [CrossRef]
- W. G. Unruh, “Experimental black-hole evaporation?” Phys. Rev. Lett. 46, 1351–1353 (1981). [CrossRef]
- R. Schutzhold and W. G. Unruh, “Gravity wave analogues of black holes,” Phys. Rev. D 66, 044019 (2002). [CrossRef]
- U. Leonhardt, “A laboratory analogue of the event horizon using slow light in an atomic medium,” Nature 415, 406–409 (2002). [CrossRef]
- R. Schutzhold and W. G. Unruh, “Hawking radiation in an electromagnetic waveguide?” Phys. Rev. Lett. 95, 031301 (2005). [CrossRef]
- T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008). [CrossRef]
- C. Barcelo, S. Liberati, and M. Visser, “Probing semiclassical analog gravity in Bose–Einstein condensates with widely tunable interactions,” Phys. Rev. A 68, 053613 (2003). [CrossRef]
- P. O. Fedichev and U. R. Fischer, “Gibbons–Hawking effect in the sonic de sitter space-time of an expanding Bose–Einstein-condensed gas,” Phys. Rev. Lett. 91, 240407 (2003). [CrossRef]
- S. Batz and U. Peschel, “Linear and nonlinear optics in curved space,” Phys. Rev. A 78, 043821 (2008). [CrossRef]
- V. H. Schultheiss, S. Batz, A. Szameit, F. Dreisow, S. Nolte, A. Tünnermann, S. Longhi, and U. Peschel, “Optics in curved space,” Phys. Rev. Lett. 105, 143901 (2010). [CrossRef]
- R. C. T. da Costa, “Quantum mechanics of a constrained particle,” Phys. Rev. A 23, 1982–1987 (1981). [CrossRef]
- M. Encinosa and B. Etemadi, “Energy shifts resulting from surface curvature of quantum nanostructures,” Phys. Rev. A 58, 77–81 (1998). [CrossRef]
- J. Gravesen, M. Willatzen, and L. L. Y. Voon, “Quantum-mechanical particle confined to surfaces of revolution—truncated cone and elliptic torus case studies,” Phys. Scr. 72, 105–111 (2005). [CrossRef]
- J. Gravesen, M. Willatzen, and L. L. Y. Voon, “Schrödinger problems for surfaces of revolution—the finite cylinder as a test example,” J. Math. Phys. 46, 012107 (2005). [CrossRef]
- R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963). [CrossRef]
- R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963). [CrossRef]
- R. J. Glauber, “Photon correlations,” Phys. Rev. Lett. 10, 84–86 (1963). [CrossRef]
- A. P. Perelomov, Generalized Coherent States and their Applications (Springer, 1986).
- J. R. Klauder and B. S. Skagerstam, Coherent States, Applications in Physics and Mathematical Physics (World Scientific, 1985).
- S. Twareqe Ali, J.-P. Antoine, and J.-P. Gazeau, Coherent States, Wavelets and Their Generalizations (Springer-Verlag, 2000).
- A. I. Solomon, “A characteristic functional for deformed photon phenomenology,” Phys. Lett. A 196, 29–34 (1994). [CrossRef]
- J. Katriel and A. I. Solomon, “Nonideal lasers, nonclassical light, and deformed photon states,” Phys. Rev. A 49, 5149–5151 (1994). [CrossRef]
- P. Shanta, S. Chaturvedi, V. Srinivasan, and R. Jagannathan, “Unified approach to the analogues of single-photon and multiphoton coherent states for generalized bosonic oscillators,” J. Phys. A 27, 6433–6442 (1994). [CrossRef]
- W. Vogel and R. L. de Matos Filho, “Nonlinear Jaynes–Cummings dynamics of a trapped ion,” Phys. Rev. A 52, 4214–4217 (1995). [CrossRef]
- R. L. de Matos Filho and W. Vogel, “Nonlinear coherent states,” Phys. Rev. A 54, 4560–4563 (1996). [CrossRef]
- V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, “f-oscillators and nonlinear coherent states,” Phys. Scr. 55, 528–541 (1997). [CrossRef]
- P. Aniello, V. I. Man’ko, G. Marmo, S. Solimeno, and F. Zaccaria, “On the coherent states, displacement operators and quasidistributions associated with deformed quantum oscillators,” J. Opt. B 2, 718–725 (2000). [CrossRef]
- A. Mahdifar, R. Roknizadeh, and M. H. Naderi, “Detection of the spatial curvature effects through physical phenomena: the nonlinear coherent states approach,” Int. J. Geom. Methods Mod. Phys. 9, 1250009 (2012). [CrossRef]
- H.-I. Yoo and J. H. Eberly, “Dynamical theory of an atom with two or three levels interacting with quantized cavity fields,” Phys. Rep. 118, 239–337 (1985). [CrossRef]
- W. K. Lai, V. Buzek, and P. L. Knight, “Interaction of a three-level atom with an SU(2) coherent state,” Phys. Rev. A 44, 2003–2012 (1991). [CrossRef]
- A. Mahdifar, R. Roknizadeh, and M. H. Naderi, “Geometric approach to nonlinear coherent states using the Higgs model for harmonic oscillator,” J. Phys. A 39, 7003–7014 (2006). [CrossRef]
- A. Mahdifar, “Coherent states for nonlinear two-boson realization of the isotropic oscillator algebra on a sphere,” Int. J. Geom. Methods Mod. Phys. 10, 1350028 (2013). [CrossRef]
- J. Schwinger, Quantum Theory of Angular Momentum (Academic, 1965).
- B. Deb, G. Gangopadhyay, and D. Sh. Ray, “Generation of a class of arbitrary two-mode field states in a cavity,” Phys. Rev. A 51, 2651–2653 (1995). [CrossRef]
- K. Vogel, V. M. Akulin, and W. P. Schleich, “Quantum state engineering of the radiation field,” Phys. Rev. Lett. 71, 1816–1819 (1993). [CrossRef]
- N. Ashby, “Relativity in the global positioning system,” Living Rev. Relativity 6, 1–45 (2003). [CrossRef]
- H. Müller, A. Peters, and S. Chu, “A precision measurement of the gravitational redshift by the interference of matter waves,” Nature 463, 926–929 (2010). [CrossRef]
- C. W. Chou, “Optical clocks and relativity,” Science 329, 1630–1633 (2010). [CrossRef]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.