Photon antibunching in sixth harmonic generation
https://doi.org/10.17586/2220-8054-2024-15-2-170-183
Abstract
We studied photon antibunching in the pump and the harmonic modes of the sixth harmonic generation process. The generalized interaction Hamiltonian is solved for several particular cases in the Heisenberg picture, and the possibility of observing photon antibunching is investigated using the short-time approximation technique. It is shown that the photon antibunching in the pump field depends on the number of pump photons, the interaction time, and the coupling of the field between the modes. With the same amount of pump photons, we deduced that third-order photon antibunching is more nonclassical than second- and first-order photon antibunching. In this process, the effect of photon antibunching is not seen in the harmonic mode over pump mode. It is shown that photon antibunching is more noticeable with shorter interaction times as the depth of nonclassicality increases and the second-order correlation function decreases. The first-order Hamiltonian interaction, which stimulates both pump and harmonic fields, is demonstrated to be more nonclassical than the second-order Hamiltonian interaction. It is clear that the coherent state, or vacuum state, of a pump field with a nonzero harmonic field creates photon clusters because the pump field causes interaction, which leads to bunching effects. It is interpreted that the degree of photon antibunching is maximum in the regions where the second correlation function is minimum. Photon antibunching has been shown to be one of the quantum properties of light.
Keywords
photon antibunching,
higher-order antibunching,
sixth harmonic generation,
photon number operator,
short-time approximation
Supporting agencies: We would like to thank the referee for his comments and valuable suggestions.
About the Authors
Rupesh Singh
Department of Physics, D.A.V. Public School
India
India
Koylanagar, Dhanbad, Jharkhand
Dilip Kumar Giri
University Department of Physics, Binod Bihari Mahto Koyalanchal University
India
India
Dhanbad, Jharkhand
References
1. Stoler D. Photon antibunching and possible ways to observe it. Phys. Rev. Lett., 1974, 33(23), P. 1397–1400.
2. Tanas R. On nonlinear optical activity and photon statistics. Optik, 1974, 40, P. 109.
3. Loudon R. Photon bunching and antibunching. Phys. Bull., 1976, 27(1), P. 21–23.
4. Kimble H.J., et al. Photon antibunching in resonance fluorescence. Phys. Rev. Lett., 1977, 39(11), P. 691–695.
5. Paul H. Photon antibunching. Rev. Mod. Phys., 1982, 54(4), P. 1061–1102.
6. Mandel L. Squeezing and photon antibunching in harmonic generation. Opt. Commun., 1982, 42(6), P. 437–439.
7. Kielich S., et al. Photon antibunching and squeezing- Two non-trivial effects of the nonlinear interaction of laser photon with matter. Optica Acta, 1985, 32, P. 1023.
8. Zou X.T., Mandel L. Photon-antibunching and sub-Poissonian photon statistics. Phys. Rev. A, 1990, 41(1), P. 475–476.
9. Pathak A., Mandal S. Photon-bunching, photon-antibunching and nonclassical photon statistics of coherent photon coupled to a cubic nonlinear medium. Mod. Phys. Lett. B, 2003, 17(5-6), P. 225–233.
10. Fox M. Quantum Optics: An Introduction, Chapter 6. New York: Oxford University Press, 2006.
11. Kozierowski M., R. Tanas´. Quantum fluctuations in second-harmonic photon generation. Opt. Commun., 1977, 21(2), P. 229–231.
12. Loudon R., Knight P.L. Squeezed light. J. Mod. Opt., 1987, 34(6-7), P. 709–759.
13. Meystre P., Sargent M. III. Elements of Quantum Optics, 4th ed. Berlin: Springer-Verlag, 1991.
14. Dodonov V.V. Nonclassical states in quantum optics: A squeezed review of the first 75 years. J. Opt. B: Quantum Semiclass. Opt., 2002, 4(1), P. R1-R33.
15. Bennett C.H. et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 1993, 70(13), P. 1895–1899.
16. Furusawa A. et al., Unconditional quantum teleportation. Science, 1998, 282(5389), P. 706–709.
17. Gottesman D., Chuang I.L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 1999, 402(6760), P. 390–393.
18. Benioff P. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J. Stat. Phys., 1980, 22(5), P. 563–591.
19. Feynman R.P. Simulating physics with computers. Int. J. Theor. Phys., 1982, 21(6-7), P. 467–488.
20. Deutsch D. Quantum theory, The Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A, 1985, 400(1818), P. 97–117.
21. Raginsky M., Kumar P. Generation and manipulation of squeezed states of photon in optical networks for quantum communication and computation. J. Opt. B: Quantum Semiclass. Opt., 2001, 3(4), P. L1-L4.
22. Bennett C.H., Brassard G. Quantum public key distribution system. IBM Tech. Discl. Bull., 1985, 28, P. 3153.
23. Ekert A.K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett., 1991, 67(6), P. 661–663.
24. Hillery M. Quantum cryptography with squeezed states. Phys. Rev. A, 2000, 61(2), P. 022309.
25. Matsuoka M., Hirano T. Quantum key distribution with a single photon from a squeezed coherent state. Phys. Rev. A, 2003, 67(4), P. 042307.
26. Eisaman M.D. et al. Invited review article: Single-photon sources and detectors. Rev. Sci. Instrum., 2011, 82(7), P. 071101.
27. Stevens M.J. et al. Third-order antibunching from an imperfect single-photon source. Opt. Exp., 2014, 22(3), P. 3244–3260.
28. Meyer-Scott E. et al. Single-photon sources: Approaching the ideal through multiplexing. Rev. Sci. Instrum., 2020, 91(4), P. 041101.
29. Lee C.T. Higher-order criteria for nonclassical effects in photon statistics. Phys. Rev. A, 1990, 41(3), P. 1721–1723.
30. Lee C.T. Many-photon antibunching in generalized pair coherent states. Phys. Rev. A, 1990, 41(3), P. 1569–1575.
31. An N.B. Multimode higher-order antibunching and squeezing in trio coherent states. J. Opt. B: Quantum Semiclass. Opt., 2002, 4(3), P. 222–227.
32. Pathak A., Garcia M.E. Control of higher order antibunching. Appl. Phys. B, 2006, 84(3), P. 479–484.
33. Gupta P. et al., Higher order antibunching is not a rare phenomenon. J. Phys. B: At. Mol. Opt. Phys., 2006, 39(5), P. 1137–1143.
34. Grosse N.B. et al., Measuring photon anti-bunching from continuous variable side band squeezing. Phys. Rev. Lett., 2007, 98(15), P. 153603.
35. Mandal S. et al., Antibunching of photons in a coherent radiation field coupled to a non-degenerate parametric oscillator beyond rotating wave approximation. Pramana J. Phys., 2021, 95(2), P. 82.
36. Inui Y., Yamamoto Y. Entanglement and photon anti-bunching in coupled non-degenerate parametric oscillators. Entropy (Basel), 2021, 23(5), P. 624.
37. Bachor H.-A. A Guide to Experiments in Quantum Optics, 2nd ed. Weinheim: Wiley-VCH, 1998, Chapters 8 and 10.
38. Vogel W. et al., Chapter 6, Quantum Optics: An Introduction, 2nd ed. Berlin: Wiley-VCH, 2001.
39. Erenso D. et al., Higher-order sub-Poissonian photon statistics in terms of factorial moments. J. Opt. Soc. Am. B, 2002, 19(6), P. 1471.
40. Vyas R. and Singh S. Photon-counting statistics of the degenerate optical parametric oscillator. Phys. Rev. A Gen. Phys., 1989, 40(9), P. 5147–5159.
41. Verma A. et al., Higher order antibunching in intermediate states. Phys. Lett. A, 2008, 372(34), P. 5542–5551.
42. Sen B. et al., Squeezing and photon antibunching in second harmonic generation: An analytical approach. J. Mod. Opt., 2012, 59(6), P. 555–564.
43. Truong D.M. et al., Sum squeezing, difference squeezing, higher-order antibunching and entanglement of two-mode photon-added displaced squeezed states. Int. J. Theor. Phys., 2014, 53(3), P. 899–910.
44. Mukhopadhyay A. et al., Squeezing and antibunching in three-mode atom-molecule Bose-Einstein condensates. J. Physiol. Sci., 2017, 22, P. 151.
45. Nitu Sahu et al., Higher-order antibunching of light in seven-photon interaction process. J. Russ. Laser Res., 2022, 43(3), P. 290–306.
46. Dell’Anno F., De Siena S., Fabrizio Illuminati. Multiphoton Quantum Optics and Quantum State Engineering. Phys. Rep., 2006, 428, P. 53–168.
47. Tanas R. Squeezing from an anharmonic oscillator model: (a+)2a2 versus. (a+a)2 interaction Hamiltonians. Physics Letters A, 1989, 141, P. 217.
48. Tanas R. et al., Squeezing and its graphical representations in the anharmonic oscillator model. Phys. Rev. A, 1991, 43(7), P. 4014–4021.
49. Perina J. Quantum Statistics of Linear and Nonlinear Optical Phenomena, 2nd ed. Dordrecht, The Netherlands: Kluwer, 1991, Chapters 9 and 10.
50. Gerry C.C., Rodrigues S. Time evolution of squeezing and antibunching in an optically bistable two-photon medium. Phys. Rev. A Gen. Phys., 1987, 36(11), P. 5444–5447.
51. Giri D.K., Gupta P.S. Short-time fourth-order squeezing effects in spontaneous and stimulated four- and six-wave mixing processes. J. Opt. B: Quantum Semiclass. Opt., 2003, 5(2), P. 158–163.
52. Latha G.M. et al., Generation of nonclassical photon by unsaturated two-photon absorption. Opt. Photonics J., 2017, 7, P. 139–150.
Review
For citations:
Singh R., Giri D.K. Photon antibunching in sixth harmonic generation. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(2):170-183. https://doi.org/10.17586/2220-8054-2024-15-2-170-183
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