Nonrelativistic limit in the 2+1 Dirac oscillator: A Ramsey-interferometry effect

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 3, 2008, Pages

  Bermudez, A ^a   Martin Delgado, M A ^a   Luis, A ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

INTERFEROMETRY; MACH-ZEHNDER INTERFEROMETERS; MATHEMATICAL MODELS; PARTICLE OPTICS; QUANTUM THEORY; SPIN DYNAMICS; TWO DIMENSIONAL;

2+1 DIRAC OSCILLATORS; RAMSEY INTERFEROMETRIC PHENOMENON; RAMSEY INTERFEROMETRY EFFECTS; SPIN ORBIT ZITTERBEWEGUNG;

QUANTUM OPTICS;

EID: 41149097653     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.033832     Document Type: Article

References (27)

1. M. Moshinsky and A. Szczepaniak, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/22/17/002 22, L817 (1989).
2. D. Ito, K. Mori, and E. Carrieri, Nuovo Cimento A NCIAAT 0369-3546 10.1007/BF02721775 51, 1119 (1967).
3. P. A. Cook, Lett. Nuovo Cimento Soc. Ital. Fis. LNUCAE 0375-930X 10, 419 (1971).
4. C. Quesne and M. Moshinsky, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/23/12/011 23, 2263 (1990).
5. M. Moreno and A. Zentella, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/22/17/003 22, L821 (1989).
6. J. Benitez, R. P. Martinez, H. N. Nuñez-Yepez, and A. L. Salas-Brito, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1643 64, 1643 (1990).
7. R. P. Martinez, M. Moreno, and A. Zentella, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.43.2036 43, 2036 (1991).
8. E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963). 0018-9219
9. P. Rozmej and R. Arvieu, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 32/28/314 32, 5367 (1999).
10. R. Arvieu and P. Rozmej, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.50.4376 50, 4376 (1994).
11. R. Arvieu and P. Rozmej, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.51.104 51, 104 (1995).
12. P. Rozmej and R. Arvieu, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/ 29/7/015 29, 1339 (1996).
13. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.281 75, 281 (2003).
14. A. Bermudez, M. A. Martin-Delgado, and E. Solano, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.041801 76, 041801 (R) (2007).
15. N. F. Ramsey, Molecular Beams (Oxford University Press, New York, 1985)
16. N. F. Ramsey, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.62.541 62, 541 (1990).
17. W. Greiner, Relativistic Quantum Mechanics: Wave Equations (Springer, Berlin, 2000).
18. V. Villalba, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.49.586 49, 586 (1994).
19. There are two possible situations where the relativistic system is mapped onto the usual Jaynes-Cummings modelIn an active procedure, the substitution ω→-ω in Eq. 3 leads to the chiral partner Hamiltonian of the Dirac oscillator which can be directly mapped onto a Jaynes-Cummings interactionConversely, we may regard | χ as the ground state and | χ as the excited state, with a simultaneous change of sign in the detuning δ. This passive procedure is of no consequence since quantum optical detunings can experimentally attain both positive and negative values.
20. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications (Wiley-VCH, Weinheim, 2004).
21. P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin, 1999).
22. A. E. Siegman, Lasers (University Science Books, Sausalito, California, 1986).
23. M. Brune, S. Haroche, V. Lefevre, J. M. Raimond, and N. Zagury, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.976 65, 976 (1990)
24. M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4887 77, 4887 (1996).
25. A. B. Klimov and L. L. Sánchez-Soto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.063802 61, 063802 (2000).
26. B. W. Shore and P. L. Knight, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500349314551321 40, 1195 (1993).
27. W. Vogel and R. L. de Matos Filho, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.4214 52, 4214 (1995).