Joseph Akeyo Omolo^*

Show more
Department of Physics, Maseno University, Maseno, Kenya.
Show less

Abstract: An exact quantum treatment reveals that signal and idler photon number operators are not well-behaved dynamical operators for studying photon statistics in parametric amplification/down-conversion processes. Contrary to expectations, the mean signal-idler photon number difference varies with time, while the corresponding signal-idler photon number cross-correlation function is complex and experiences an interference phenomenon driven by the interaction parameters. The intensity operators and related polarization operators of the polarized signal-idler photon pair in positive and negative helicity states are identified as the appropriate operators specifying a conservation law and the dynamical symmetry group (SU(1, 1)) of the parametric amplification process. The conservation of the mean positive and negative helicity photon intensity difference and the purely real positive-negative helicity intensity cross-correlation function correctly account for the simultaneous production of polarized signal and idler photons in positive and negative helicity states.

Keywords: Quantized Parametric Amplification, Jaynes-Cummings Interaction, Fluctuation State Vectors, Fractional Revivals, Interference, Positive-Negative Helicity Intensity/Polarization Operators, SU(1, 1) Symmetry Group

Cite this paper: Omolo, J. (2014) Some New Features of Photon Statistics in a Fully Quantized Parametric Amplification Process. Journal of Modern Physics, 5, 706-723. doi: 10.4236/jmp.2014.58082.

References

[1]   Mandel, L. (1986) Quantum Effects in Spontaneous Parametric Down Conversion of light. In: Pike, E.R. and Sarkar, S., Eds., Frontiers in Quantum Optics, Adam Hilger, Bristol and Boston, 318.

[2]   Nation, P.D. and Blencowe, M.P. (2010) New Journal of Physics, 12, Article ID: 09013.
http://dx.doi.org/10.1088/1367-2630/12/9/095013

[3]   Omolo, J.A. (2013) Journal of Modern Optics, 60, 578.
http://dx.doi.org/10.1080/09500340.2013.798039

[4]   Jaynes, E.T. and Cummings, F.W. (1963) Proceedings of the IEEE, 51, 89.
http://dx.doi.org/10.1109/PROC.1963.1664

[5]   Knight, P.L. and Radmore, P.M. (1982) Physical Review A, 26, 676.
http://dx.doi.org/10.1103/PhysRevA.26.676

[6]   Shore, B.W. and Knight, P.L. (1993) Journal of Modern Optics, 40, 195.
http://dx.doi.org/10.1080/09500349314551321

[7]   Meystre, P. and Sargent III, M. (1991) Elements of Quantum Optics. Springer-Verlag, Berlin Heidelberg New York.
http://dx.doi.org/10.1007/978-3-662-11654-8

[8]   Averbukh, I.Sh. (1992) Physical Review A, 46, R2205.
http://dx.doi.org/10.1103/PhysRevA.46.R2205

[9]   Azuma, H. (2009) Application of Abel-Abner Formula for Collapse and Revival of Rabi Oscillations in Jaynes-Cummings Model.

[10]   El-Orany, F.A.A. (2009) Revival-Collapse Phenomenon in the Quadrature Squeezing of the Multiphoton Intensity-Dependent Jaynes-Cummings Model.

[11]   Glauber, R.J. (1986) Amplifiers, Attenuators, and the Quantum Theory of Measurement. In: Pike, E.R. and Sarkar, S., Eds., Frontiers in Quantum Optics, Malvern Physics Series, Adam Hilger, Bristol and Boston, 534.

[12]   Jyotsna, I.V. and Agarwal, G.S. (1997) Journal of Modern Optics, 44, 305-312.
http://dx.doi.org/10.1080/09500349708241872

[13]   Drobny, G. and Jex, I. (1992) Physical Review A, 46, 499; (1992) Physical Review A, 45, 1816.
http://dx.doi.org/10.1103/PhysRevA.46.499
http://dx.doi.org/10.1103/PhysRevA.45.1816

[14]   Walls, D.F. and Barakat, R. (1970) Physical Review A, 1, 446; Walls, D.F. and Tindle, C. (1972) Physical Review A: General Physics, 5, 534.
http://dx.doi.org/10.1103/PhysRevA.1.446
http://dx.doi.org/10.1088/0305-4470/5/4/010

[15]   Hillery, M. (2009) Acta Physica Slovaca, 59, 1-80.
http://dx.doi.org/10.2478/v10155-010-0094-8

[16]   Omolo, J.A. (2008) PRAMANA-Journal of Physics, 71, 1311.

[17]   Dell’Anno, F., et al. (2006) Physics Reports, 428, 53-168.
http://dx.doi.org/10.1016/j.physrep.2006.01.004

[18]   Joanis, P. (2010) Journal of Physics A: Mathematical and Theoretical, 43, Article ID: 385304.
http://dx.doi.org/10.1088/1751-8113/43/38/385304

[19]   Bjork, G., et al. (2012) Physical Review A, 85, Article ID: 053835.
http://dx.doi.org/10.1103/PhysRevA.85.053835

[20]   Soderholm, J., et al. (2012) New Journal of Physics, 14, Article ID: 115014.
http://dx.doi.org/10.1088/1367-2630/14/11/115014

[21]   Schilling, U., et al. (2010) Physical Review A, 81, Article ID: 013826.
http://dx.doi.org/10.1103/PhysRevA.81.013826

[22]   Wolf, E. (2008) Optics Letters, 33, 642.
http://dx.doi.org/10.1364/OL.33.000642