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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 2 — Feb. 1, 2014
  • pp: 270–276

On the generation of number states, their single- and two-mode superpositions, and two-mode binomial state in a cavity

Seyedeh Robabeh Miry, Mohammad Kazem Tavassoly, and Rasoul Roknizadeh  »View Author Affiliations

JOSA B, Vol. 31, Issue 2, pp. 270-276 (2014)

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The proposed schemes in this paper involve the interaction of a two-level atom with single- or two-mode quantized cavity fields (for different purposes) in the presence of a classical field. Indeed, following the path of Solano et al. in [Phys. Rev. Lett. 90, 027903 (2003)], the behavior of the entire atom-field system may be described by the Jaynes–Cummings (JC)- and anti-Jaynes–Cummings (anti-JC)-like models. It is illustrated that, under specific conditions, the effective Hamiltonian of the system can be switched from a JC- to an anti-JC-like model. During the process, the two-level atom in the cavity is alternately affected by the above two effective interactions. Ultimately, after the occurrence of the desired interactions in appropriate setups, the cavity field will arrive at a specific superposition of number states, a fixed number state, and in particular, two-mode binomial field states. Moreover, the entanglement property of the two-mode binomial state is investigated by evaluating the entropy criterion. While there exist various proposals for preparation of number states and their superpositions in the literature, our scheme has the advantage that it is independent of the detection of the atomic state after the interaction occurs.

© 2014 Optical Society of America

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

Original Manuscript: October 9, 2013
Revised Manuscript: December 4, 2013
Manuscript Accepted: December 5, 2013
Published: January 15, 2014

Seyedeh Robabeh Miry, Mohammad Kazem Tavassoly, and Rasoul Roknizadeh, "On the generation of number states, their single- and two-mode superpositions, and two-mode binomial state in a cavity," J. Opt. Soc. Am. B 31, 270-276 (2014)

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  1. A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, “Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence,” Phys. Rev. Lett. 71, 3095–3098 (1993). [CrossRef]
  2. P. Domokos, M. Brune, J. M. Raimond, and S. Haroche, “Photon number state generation with a single two-level atom in a cavity: a proposal,” Euro. Phys. J. 1, 1–4 (1998). [CrossRef]
  3. S. Brattke, B. T. H. Varoce, and H. Walther, “Generation of photon number states on demand via cavity quantum electrodynamics,” Phys. Rev. Lett. 86, 3534–3537 (2001). [CrossRef]
  4. D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, “Generation of nonclassical motional states of a trapped atom,” Phys. Rev. Lett. 76, 1796–1799 (1996). [CrossRef]
  5. A. Benmoussa and C. C. Gerry, “Proposal for generating Fock states in traveling wave fields,” Phys. Lett. A 365, 258–261 (2007).
  6. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963). [CrossRef]
  7. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963). [CrossRef]
  8. J. R. Klauder, “Continuous-representation theory. I. Postulates of continuous-representation theory,” J. Math. Phys. 4, 1055 (1963). [CrossRef]
  9. V. V. Dodonov, I. A. Malkin, and V. I. Manko, “Even and odd coherent states and excitations of a singular oscillator,” Physica 72, 597–615 (1974). [CrossRef]
  10. D. Stoler, B. E. A. Saleh, and M. C. Teich, “Binomial states of the quantized radiation field,” Opt. Acta 32, 345–355 (1985). [CrossRef]
  11. D. Stoler, “Equivalence classes of minimum uncertainty packets,” Phys. Rev. D 1, 3217–3219 (1970). [CrossRef]
  12. H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226–2243 (1976). [CrossRef]
  13. S. R. Miry, M. Shahpari, and M. K. Tavassoly, “Nonlinear elliptical states: generation and nonclassical properties,” Opt. Commun. 306, 49–56 (2013).
  14. J. Janszky, P. Domokos, and P. Adam, “Coherent states on a circle and quantum interference,” Phys. Rev. A 48, 2213–2219 (1993). [CrossRef]
  15. Y. Wang, Q. Liao, Z. Liu, J. Wang, and S. Liu, “Nonclassical properties of odd and even elliptical states,” Opt. Commun. 284, 282–288 (2011). [CrossRef]
  16. S. J. van Enk and O. Hirota, “Entangled coherent states: teleportation and decoherence,” Phys. Rev. A 64, 022313 (2001). [CrossRef]
  17. X. Wang, “Quantum teleportation of entangled coherent states,” Phys. Rev. A 64, 022302 (2001). [CrossRef]
  18. N. B. An, “Teleportation of coherent-state superpositions within a network,” Phys. Rev. A 68, 022321 (2003). [CrossRef]
  19. J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Molmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006). [CrossRef]
  20. K. L. Pregnell and D. T. Pegg, “Single-shot measurement of quantum optical phase,” Phys. Rev. Lett. 89, 173601 (2002). [CrossRef]
  21. N. K. Tran and O. Pfister, “Quantum teleportation with close-to-maximal entanglement from a beam splitter,” Phys. Rev. A 65, 052313 (2002). [CrossRef]
  22. V. Buzek and T. Quang, “Generalized coherent state for bosonic realization of SU(2) Lie algebra,” J. Opt. Soc. Am. B 6, 2447–2449 (1989). [CrossRef]
  23. C. C. Gerry and R. Grobe, “Two-mode SU(2) and SU(2) Schrödinger cat states,” J. Mod. Opt. 44, 41–53 (1997). [CrossRef]
  24. C. J. Villas-Bas, Y. Guimares, M. H. Y. Moussa, and B. Baseia, “Recurrence formula for generalized optical state truncation by projection synthesis,” Phys. Rev. A 63, 055801 (2001). [CrossRef]
  25. J. Fiurasek, “Conditional generation of N-photon entangled states of light,” Phys. Rev. A 65, 053818 (2002). [CrossRef]
  26. X. Zou, K. Palhlke, and W. Mathis, “Phase measurement and generation of arbitrary superposition of Fock states,” Phys. Lett. A 323, 329–338 (2004). [CrossRef]
  27. S.-B. Zheng, “Preparation of superpositions of Fock states via the interaction of a multi-level atom with the field,” Opt. Commun. 154, 290–292 (1998). [CrossRef]
  28. B. I. Lev, A. A. Semenov, C. V. Usenko, and J. R. Klauder, “Relativistic coherent states and charge structure of the coordinate and momentum operators,” Phys. Rev. A 66, 022115 (2002). [CrossRef]
  29. J. R. Klauder, K. A. Penson, and J.-M. Sixdeniers, “Constructing coherent states through solutions of Stieltjes and Hausdorff moment problems,” Phys. Rev. A 64, 013817 (2001). [CrossRef]
  30. A. Mahdifar, W. Vogel, Th. Richter, R. Roknizadeh, and M. H. Naderi, “Coherent states of a harmonic oscillator on a sphere in the motion of a trapped ion,” Phys. Rev. A 78, 063814 (2008). [CrossRef]
  31. S. Sivakumar, “Photon-added coherent states in parametric down-conversion,” Phys. Rev. A 83, 035802 (2011). [CrossRef]
  32. M. S. Abdalla, A.-S. F. Obada, and M. Darwish, “Statistical properties of nonlinear intermediate states: binomial state,” J. Opt. B 7, S695–S704 (2005). [CrossRef]
  33. X.-G. Meng, J.-S. Wang, and B.-L. Liang, “The construction, properties and applications of a new bipartite coherent-entangled state in the two-mode Fock space,” Phys. Scr. 83, 025005 (2011). [CrossRef]
  34. P. M. Hernando and A. Luis, “Nonclassicality in phase-number uncertainty relations,” Phys. Rev. A 84, 063829 (2011). [CrossRef]
  35. E. Solano, G. S. Agarwal, and H. Walther, “Strong-driving-assisted multipartite entanglement in cavity QED,” Phys. Rev. Lett. 90, 027903 (2003). [CrossRef]
  36. S.-B. Zheng, “Generation of nonclassical states with a driven dispersive interaction,” Phys. Rev. A 74, 043803 (2006). [CrossRef]
  37. G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, “Generation of phase-coherent states,” Phys. Rev. A 57, 4894–4898 (1998). [CrossRef]
  38. R. L. de Mathos Filho and W. Vogel, “Even and odd coherent states of the motion of a trapped ion,” Phys. Rev. Lett. 76, 608–611 (1996). [CrossRef]
  39. M. J. Collett, “Generation of number-phase squeezed states,” Phys. Rev. Lett. 70, 3400–3403 (1993). [CrossRef]
  40. B. M. Rodriguez-Lara, H. Moya-Cessa, and A. B. Klimov, “Combining Jaynes-Cummings and anti-Jaynes-Cummings dynamics in a trapped-ion system driven by a laser,” Phys. Rev. A 71, 023811 (2005).
  41. S. Bose and V. Vedral, “Mixedness and teleportation,” Phys. Rev. A 61, 040101(R) (2000). [CrossRef]
  42. P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, “Simple cavity-QED two-bit universal quantum logmaic gate: the principle and expected performances,” Phys. Rev. A 52, 3554–3559 (1995). [CrossRef]
  43. A. Vidiella-Barranco and J. A. Roversi, “Statistical and phase properties of the binomial states of the electromagnetic field,” Phys. Rev. A 50, 5233–5241 (1994). [CrossRef]
  44. M. H. Y. Moussa and B. Baseia, “Generation of the reciprocal-binomial state,” Phys. Lett. A 238, 223–226 (1998). [CrossRef]
  45. R. Lo Franco, G. Compagno, A. Messina, and A. Napoli, “Single-shot generation and detection of a two-photon generalized binomial state in a cavity,” Phys. Rev. A 74, 045803 (2006). [CrossRef]
  46. H.-C. Fu and R. Sasaki, “Negative binomial and multinomial states: probability distributions and coherent states,” J. Math. Phys. 38, 3968–3987 (1997). [CrossRef]
  47. G. S. Agarwal and A. Biswas, “Quantitative measures of entanglement in pair-coherent states,” J. Opt. B 7, 350–354 (2005). [CrossRef]
  48. S. M. Barnett and S. J. D. Phoenix, “Entropy as a measure of quantum optical correlation,” Phys. Rev. A 40, 2404–2409 (1989). [CrossRef]
  49. S. J. D. Phoenix and P. L. Knight, “Establishment of an entangled atom-field state in the Jaynes-Cummings model,” Phys. Rev. A 44, 6023–6029 (1991). [CrossRef]
  50. R. Simon, “Peres-Horodecki separability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2726–2729 (2000). [CrossRef]
  51. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998). [CrossRef]

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