Skip to main content
SpringerLink
Log in

Anti-Jaynes–Cummings interaction of a two-level atom with squeezed light: photon statistics, atomic population inversion and entropy of entanglement

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We analyse the dynamics generated by the anti-Jaynes–Cummings (AJC) Hamiltonian when a two-level atom in an initial atomic ground state couples to a single mode of squeezed coherent light and provide a juxtaposition with the Jaynes–Cummings (JC) interaction for the same initial atom–field states. In the AJC resonant atom–field interaction condition, we noted robust anti-bunching of the squeezed coherent cavity field mode within regions of strong coupling of the atom and the squeezed coherent cavity field mode. In addition, bunching of the field mode occurs when frequency detuning present in the sum frequency is raised while still in the strong coupling region. However, the field mode in the corresponding JC process still displays an immutable anti-bunching. This marked difference is driven by a non-vanishing frequency detuning parameter present during the AJC process. Further, clear enhancement of squeezing effect manifested by an increase in the degree of mixedness and ringing revivals triggered by increase of the squeeze parameter, frequency detuning and sum frequency is observed. Despite similarity in pattern of the coextensive atomic population inversion curves at resonance, the AJC process provides a longer quiescent phase, of atomic population inversion. This feature changes at the respective off-resonance conditions, where at a specified squeeze parameter, the AJC, JC processes have equal revival time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data availability

All data required are available in this manuscript.

References

  1. Rabi, I.I.: On the process of space quantization. Phys. Rev. 49(4), 324 (1936)

    Article  ADS  Google Scholar 

  2. Rabi, I.I.: Space quantization in a gyrating magnetic field. Phys. Rev. 51(8), 652 (1937)

    Article  ADS  Google Scholar 

  3. Braak, D.: Integrability of the Rabi model. Phys. Rev. Lett. 107(10), 100401 (2011)

    Article  ADS  Google Scholar 

  4. Braak, D., Chen, Q.-H., Batchelor, M.T., Solano, E.: Semi-classical and quantum Rabi models: in celebration of 80 years. J. Phys. A Math. Theor. 49(30), 300301 (2016)

    Article  MathSciNet  Google Scholar 

  5. Xie, Q., Zhong, H., Batchelor, M.T., Lee, C.: The quantum Rabi model: solution and dynamics. J. Phys. A Math. Theor. 50(11), 113001 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  6. Jaynes, E.T., Cummings, F.W.: Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51(1), 89–109 (1963)

    Article  Google Scholar 

  7. Shore, B.W., Knight, P.L.: The Jaynes–Cummings model. J. Mod. Opt. 40(7), 1195–1238 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  8. Shore, B.W., Knight, P.L.: The Jaynes-Cummings Revival. In: Grandy, W.T., Jr., Milonni, P.W. (eds.) Physics and Probability: Essays in Honour of Edwin T. Jaynes, pp. 15–32. Cambridge University Press, Cambridge (1993)

    Chapter  Google Scholar 

  9. Omolo, J.A.: The anti-Jaynes–Cummings model is solvable: quantum Rabi model in rotating and counter-rotating frames; following the experiments. arXiv preprint arXiv:2103.09546 (2021)

  10. Omolo, J.A.: Conserved excitation number and U(1)-symmetry operator for the anti-rotating (anti-Jaynes–Cummings) term of the Rabi Hamiltonian. arXiv preprint arXiv:2103.06577 (2021)

  11. Rossatto, D.Z., Villas-Bôas, C.J., Sanz, M., Solano, E.: Spectral classification of coupling regimes in the quantum Rabi model. Phys. Rev. A 96(1), 013849 (2017)

    Article  ADS  Google Scholar 

  12. Gerry, C., Knight, P.L.: Introductory Quantum Optics, p. 332. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  13. Loudon, R., Knight, P.L.: Squeezed light. J. Mod. Opt. 34(6–7), 709–759 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  14. Knight, P.L., Bužek, V.: Squeezed states: basic principles. In: Drummond, P.D., Ficek, Z. (eds.) Quantum Squeezing, pp. 3–32. Springer, Berlin (2004)

    Chapter  Google Scholar 

  15. Mandel, L.: Non-classical states of the electromagnetic field. Phys. Scr. 1986(T12), 34 (1986)

    Article  Google Scholar 

  16. Zaheer, K., Zubairy, M.S.: Advances in Atomic, Molecular and Optical Physics, vol. 28, p. 143. Academic Press, New York (1987)

    Google Scholar 

  17. Gea-Banacloche, J.: Collapse and revival of the state vector in the Jaynes–Cummings model: an example of state preparation by a quantum apparatus. Phys. Rev. Lett. 65(27), 3385 (1990)

    Article  ADS  Google Scholar 

  18. Gea-Banacloche, J.: Atom- and field-state evolution in the Jaynes–Cummings model for large initial fields. Phys. Rev. A 44(9), 5913 (1991)

    Article  ADS  Google Scholar 

  19. Abo-Kahla, D.A.M., Farouk, A.: Entanglement and entropy of a three-qubit system interacting with a quantum spin environment. Appl. Sci. 9(23), 5222 (2019)

    Article  Google Scholar 

  20. Messinger, A., Ritboon, A., Crimin, F., Croke, S., Barnett, S.M.: Coherence and catalysis in the Jaynes–Cummings model. New J. Phys. 22(4), 043008 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  21. Abo-Kahla, D.A.M.: Long-lived quantum coherence in a two-level semiconductor quantum dot. Pramana 94, 1–14 (2020)

    Article  ADS  Google Scholar 

  22. Goldberg, A.Z., Steinberg, A.M.: Transcoherent states: optical states for maximal generation of atomic coherence. PRX Quantum 1(2), 020306 (2020)

    Article  Google Scholar 

  23. Abo-Kahla, D.A.M., Abdel-Aty, M.: Information entropy of multi-qubit Rabi system. Int. J. Quantum Inf. 13(06), 1550042 (2015)

    Article  MathSciNet  Google Scholar 

  24. Abo-Kahla, D.A.M.: Information entropies of multi-qubit Rabi model beyond the rotating wave approximation. Nonlinear Dyn. 94, 1689–1701 (2018)

    Article  Google Scholar 

  25. Moya-Cessa, H., Vidiella-Barranco, A.: Interaction of squeezed light with two-level atoms. J. Mod. Opt. 39(12), 2481–2499 (1992)

    Article  ADS  Google Scholar 

  26. Abo-Kahla, D.A.M., Abdel-Aty, M., Farouk, A.: The population inversion and the entropy of a moving two-level atom in interaction with a quantized field. Int. J. Theor. Phys. 57, 2319–2329 (2018)

    Article  MathSciNet  Google Scholar 

  27. Furusawa, A., van Loock, P.: Quantum Teleportation and Entanglement: A Hybrid Approach to Optical Quantum Information Processing. Wiley, Hoboken (2011)

    Book  Google Scholar 

  28. Mandel, L.: Sub-Poissonian photon statistics in resonance fluorescence. Opt. Lett. 4(7), 205–207 (1979)

    Article  ADS  Google Scholar 

  29. Teich, M.C., Saleh, B.E.A.: I photon bunching and antibunching. In: Progress in Optics, vol. 26, pp. 1–104. Elsevier, Amsterdam (1988)

    Google Scholar 

  30. Teich, M.C., Saleh, B.E.A.: Squeezed state of light. Quant. Opt. 1(2), 153 (1989)

    Article  ADS  Google Scholar 

  31. Mandel, L., Wolf, E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  32. Mayero, C.: Photon statistics and quantum field entropy in the anti-Jaynes–Cummings model: a comparison with the Jaynes–Cummings interaction. Quantum Inf. Process 22(5), 182 (2023)

    Article  ADS  MathSciNet  Google Scholar 

  33. Satyanarayana, M.V., Rice, P., Vyas, R., Carmichael, H.J.: Ringing revivals in the interaction of a two-level atom with squeezed light. JOSA B 6(2), 228–237 (1989)

    Article  ADS  Google Scholar 

  34. Seke, J.: Squeezing and Rabi oscillations in the Dicke model within and without rotating-wave approximation. Phys. A Stat. Mech. Appl. 213(4), 587–596 (1995)

    Article  Google Scholar 

  35. 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(11), 1796 (1996)

    Article  ADS  Google Scholar 

  36. Brune, M., Schmidt-Kaler, F., Maali, A., Dreyer, J., Hagley, E., Raimond, J.M., Haroche, S.: Quantum Rabi oscillation: a direct test of field quantization in a cavity. Phys. Rev. Lett. 76(11), 1800 (1996)

    Article  ADS  Google Scholar 

  37. Chuang, Y.-T., Hsu, L.-Y.: Quantum dynamics of molecular ensembles coupled with quantum light: counter-rotating interactions as an essential component. Phys. Rev. A 109(1), 013717 (2024)

    Article  ADS  MathSciNet  Google Scholar 

  38. Klimov, A.B., Chumakov, S.M.: A Group-Theoretical Approach to Quantum Optics: Models of Atom–Field Interactions. Wiley, Hoboken (2009)

    Book  Google Scholar 

  39. Le Boité, A.: Theoretical methods for ultrastrong light-matter interactions. Adv. Quantum Technol. 3(7), 1900140 (2020)

    Article  Google Scholar 

  40. Omolo, J.A.: Conserved excitation number and U(1)-symmetry operators for the antirotating (anti-Jaynes–Cummings) term of the Rabi Hamiltonian. Preprint Research Gate. https://doi.org/10.13140/RG.2.2.30936.80647 (2017)

  41. Omolo, J.A.: Polariton and anti-polariton qubits in the Rabi model. preprint Research Gate. https://doi.org/10.13140/RG.2.2.11833.67683 (2017)

  42. Mayero, C., Omolo, J.A., Okeyo, O.S.: Rabi oscillations, entanglement and teleportation in the anti-Jaynes–Cummings model. J. Mod. Phys. 12(4), 408–432 (2021)

    Article  Google Scholar 

  43. Omolo, J.A.: On atomic state purity operator, degree of state purity and concurrence in the JC and anti-JC models. arXiv preprint arXiv:2207.02730 (2022)

  44. Omolo, J.A.: Symmetry conjugates and dynamical properties of the quantum Rabi model. arXiv preprint arXiv:2112.12514 (2021)

  45. Liu, K.-L., Goan, H.-S.: Non-Markovian entanglement dynamics of quantum continuous variable systems in thermal environments. Phys. Rev. A 76(2), 022312 (2007)

    Article  ADS  Google Scholar 

  46. Li, G.-X., Sun, L.-H., Ficek, Z.: Multi-mode entanglement of n harmonic oscillators coupled to a non-Markovian reservoir. J. Phys. B At. Mol. Opt. Phys. 43(13), 135501 (2010)

    Article  ADS  Google Scholar 

  47. Phoenix, S.J.D., Knight, P.L.: Fluctuations and entropy in models of quantum optical resonance. Ann. Phys. 186(2), 381–407 (1988)

    Article  ADS  Google Scholar 

  48. Phoenix, S.J.D., Knight, P.L.: Comment on “Collapse and revival of the state vector in the Jaynes–Cummings model: an example of state preparation by a quantum apparatus’’. Phys. Rev. Lett. 66(21), 2833 (1991)

    Article  ADS  Google Scholar 

  49. Scully, M.O., Zubairy, M.S., et al.: Quantum Optics. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  50. Jaeger, G.: Entanglement, Information, and the Interpretation of Quantum Mechanics. Springer, Berlin (2009)

    Book  Google Scholar 

  51. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2011)

    Google Scholar 

  52. Dung, H.T., Shumovsky, A.S., Bogolubov, N.N., Jr.: Antibunching and sub-Poissonian photon statistics in the Jaynes-Cummings model. Opt. Commun. 90(4–6), 322–328 (1992)

    Article  ADS  Google Scholar 

  53. Cohen-Tannoudji, C., Reynaud, S.: Atoms in strong light-fields: photon antibunching in single atom fluorescence. Philos. Trans. R Soc. Lond. Ser. A 293(1402), 223–237 (1979)

    Article  ADS  Google Scholar 

  54. Cresser, J.D., Häger, J., Leuchs, G., Rateike, M., Walther, H.: Dissipative systems in quantum optics. In: Bonifacio, R. (ed.) Topics in Current Physics, vol. 27. Springer, Berlin (1982)

    Google Scholar 

  55. Leuchs, G., Rateike, M., Walther, H.: cited by Walls, D.F. Nature 280, 451 (1979)

  56. Kimble, H.J., Dagenais, M., Mandel, L.: Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39(11), 691 (1977)

    Article  ADS  Google Scholar 

  57. Kimble, H.J., Mandel, L.: Theory of resonance fluorescence. Phys. Rev. A 13(6), 2123 (1976)

    Article  ADS  Google Scholar 

  58. Carmichael, H.J., Walls, D.F.: A quantum-mechanical master equation treatment of the dynamical stark effect. J. Phys. B 9(8), 1199 (1976)

    Article  ADS  Google Scholar 

  59. Carmichael, H.J., Walls, D.F.: Proposal for the measurement of the resonant stark effect by photon correlation techniques. J. Phys. B 9(4), 43 (1976)

    Article  ADS  Google Scholar 

  60. Forn-Díaz, P., Lisenfeld, J., Marcos, D., Garcia-Ripoll, J., Solano, E., Harmans, C.J.P.M., Mooij, J.E.: Observation of the Bloch–Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime. Phys. Rev. Lett. 105(23), 237001 (2010)

    Article  ADS  Google Scholar 

  61. Pradhan, P., Cardoso, G.C., Morzinski, J., Shahriar, M.S.: Effects of the Bloch–Siegert oscillation on the precision of qubit rotations: direct two-level vs. off-resonant Raman excitation. arXiv preprint quant-ph/0402122 (2004)

  62. Cardoso, G.C., Pradhan, P., Morzinski, J., Shahriar, M.S.: In situ detection of the temporal and initial phase of the second harmonic of a microwave field via incoherent fluorescence. Phys. Rev. A 71(6), 063408 (2005)

    Article  ADS  Google Scholar 

  63. Eberly, J.H., Narozhny, N.B., Sanchez-Mondragon, J.J.: Periodic spontaneous collapse and revival in a simple quantum model. Phys. Rev. Lett. 44(20), 1323–1325 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  64. Bužek, V., Moya-Cessa, H., Knight, P.L., Phoenix, S.J.D.: Schrödinger-cat states in the resonant Jaynes–Cummings model: collapse and revival of oscillations of the photon-number distribution. Phys. Rev. A 45(11), 8190 (1992)

    Article  ADS  Google Scholar 

  65. Kukliński, J.R., Madajczyk, J.L.: Strong squeezing in the Jaynes–Cummings model. Phys. Rev. A 37(8), 3175 (1988)

    Article  ADS  Google Scholar 

  66. Abo-Kahla, D.A.M.: Information entropy and population inversion of a three-level semiconductor quantum dot. Indian J. Phys. 95, 1295–1304 (2021)

    Article  ADS  Google Scholar 

  67. Abo-Kahla, D.A.M.: The atomic inversion and the purity of a quantum dot two-level systems. Appl. Math. Inf. Sci. 10(4), 1–5 (2016)

    Article  MathSciNet  Google Scholar 

  68. Subeesh, T., Sudhir, V., Ahmed, A.B.M., Satyanarayana, M.V.: Effect of squeezing on the atomic and the entanglement dynamics in the Jaynes–Cummings model. Nonlinear Opt. Quantum Opt. 44(4) (2012)

  69. Leibfried, D., Blatt, R., Monroe, C., Wineland, D.: Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75(1), 281 (2003)

    Article  ADS  Google Scholar 

  70. Beige, A., Knight, P.L., Vitiello, G.: Cooling many particles at once. New J. Phys. 7(1), 96 (2005)

    Article  ADS  Google Scholar 

  71. Sacolick, L.I., Wiesinger, F., Hancu, I., Vogel, M.W.: B1 mapping by Bloch–Siegert shift. Magn. Reson. Med. 63(5), 1315–1322 (2010)

    Article  Google Scholar 

  72. Zhang, Z.-Z., Wu, W.: Effects of counter-rotating-wave terms on the noisy frequency estimation. Phys. Rev. A 105(4), 043706 (2022)

    Article  ADS  Google Scholar 

  73. Compagno, G., Palma, G.M., Passante, R., Persico, F.: Virtual field, causal photon absorption and photodetectors. Europhys. Lett. 9(3), 215 (1989)

    Article  ADS  Google Scholar 

  74. Drummond, P.D.: Unifying the pA and dE interactions in photodetector theory. Phys. Rev. A 35(10), 4253 (1987)

    Article  ADS  Google Scholar 

  75. Deng, W.-W., Li, G.-X.: Influences of counter-rotating wave terms on the trace distance of quantum states in the Rabi model. J. Phys. B At. Mol. Opt. Phys. 46(3), 035505 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  76. Werlang, T., Dodonov, A.V., Duzzioni, E.I., Villas-Bôas, C.J.: Rabi model beyond the rotating-wave approximation: generation of photons from vacuum through decoherence. Phys. Rev. A 78(5), 053805 (2008)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank Tom Mboya University and Maseno University for providing conducive environment to carry out this study.

Funding

Not funded.

Author information

Authors and Affiliations

  1. Department of Physics, Tom Mboya University, C19, P.O. Box, 199-40300, Homabay, Kenya

    Christopher Mayero

  2. Department of Physics and Material Science, Maseno University, Busia Road, Private Bag-40105, Maseno, Kenya

    Christopher Mayero & Joseph Akeyo Omolo

Authors
  1. Christopher Mayero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph Akeyo Omolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Christopher Mayero wrote and analysed each section of this article as presented. Joseph Akeyo Omolo developed the theoretical model applied in this article and reviewed the manuscript before submission for Journal review.

Corresponding author

Correspondence to Christopher Mayero.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest towards publication of this work.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mayero, C., Omolo, J.A. Anti-Jaynes–Cummings interaction of a two-level atom with squeezed light: photon statistics, atomic population inversion and entropy of entanglement. Quantum Inf Process 23, 182 (2024). https://doi.org/10.1007/s11128-024-04390-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-024-04390-1

Keywords

Search

Navigation