# Quantum theory of radiation of an excited atom placed near a microresonator containing a single-photon wavepacket: Photon correlation properties

- 54 Downloads
- 2 Citations

## Abstract

The strong resonance interaction of a two-level atom with the continuum of quantized electromagnetic modes falling within the contour of a resonance mode of a dielectric microsphere is considered within the framework of quantum electrodynamics. Analytical solutions are derived. As an initial condition, we consider the case when, at time *t* = 0, the atom is excited and the resonance modes of the microsphere contain a single-photon wavepacket. It is shown that the properties of the emitted photon pair depend crucially on space-time properties of the photon wavepacket contained in the resonator. When the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is close to the vacuum value, the radiation of an atom is similar to a spontaneous one and the emitted photon pair has no correlations. On the contrary, if the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is substantially greater than the vacuum value, the radiation of an atom has a stimulated nature and the emitted photon pair has very complicated strong correlations. The relationship between the results obtained and the predictions of the dressed states theory are briefly discussed. The results obtained are of a general character and can be applied to the description of the resonant interaction of an excited atom and an excited resonator of an arbitrary shape.

## PACS numbers

32.50.+d 42.50.Pq## Preview

Unable to display preview. Download preview PDF.

## References

- 1.D. N. Klyshko, “The Nonclassical Light,” Phys. Usp.
**39**, 573 (1996).CrossRefADSGoogle Scholar - 2.M. Lipeles, R. Novick, and N. Tolk, “Direct Detection of Two-Photon Emission from the Metastable State of Singly Ionized Helium,” Phys. Rev. Lett.
**15**, 690 (1965).CrossRefADSGoogle Scholar - 3.R. D. Kaul, J. Opt. Soc. Am.
**56**, 1262 (1966).CrossRefGoogle Scholar - 4.C. A. Kocher and E. D. Commins, “Polarization Correlation of Photons Emitted in an Atomic Cascade,” Phys. Rev. Lett.
**18**, 575 (1967).CrossRefADSGoogle Scholar - 5.S. A. Akhmanov et al., “Quantum Noise in Parametric Application of Light,” JETP Lett.
**6**, 85 (1967).ADSGoogle Scholar - 6.S. E. Harris, M. K. Oshman, and R. Byer, “Observation of Tunable Optical Parametric Fluorescence,” Phys. Rev. Lett.
**18**, 732 (1967).CrossRefADSGoogle Scholar - 7.D. Magde and H. Mahr, “Study in Ammonium Dihydrogen Phosphate of Spontaneous Parametric Interaction Tunable from 4400 to 16 000 Å,” Phys. Rev. Lett.
**18**, 905 (1967).CrossRefADSGoogle Scholar - 8.S. Machida, Y. Yamamoto, and Y. Itaya, “Observation of Amplitude Squeezing in a Constant-Current-Driven Semiconductor Laser,” Phys. Rev. Lett.
**58**, 1000 (1987).CrossRefADSGoogle Scholar - 9.W. H. Richardson and R. M. Shelby, “Nonclassical Light from a Semiconductor Laser Operating at 4 K,” Phys. Rev. Lett.
**64**, 400 (1990).CrossRefADSGoogle Scholar - 10.H. Wang, M. J. Freeman, and D. G. Steel, “Squeezed Light from Injection-Locked Quantum Well Lasers,” Phys. Rev. Lett.
**71**, 3951 (1993).CrossRefADSGoogle Scholar - 11.A. M. Fox et al., “Squeezed Light Generation in Semiconductors,” Phys. Rev. Lett.
**74**, 1728 (1995).CrossRefADSGoogle Scholar - 12.S. F. Pereira et al., “Generation of Squeezed Light by Intracavity Frequency Doubling,” Phys. Rev. A
**38**, 4931 (1998).CrossRefADSMathSciNetGoogle Scholar - 13.R. Paschotta et al., “Bright Squeezed Light from a Singly Resonant Frequency Doubler,” Phys. Rev. Lett.
**72**, 3807 (1994).CrossRefADSGoogle Scholar - 14.T. C. Ralph et al., “Squeezed Light from Second Harmonic Generation: Experiment versus Theory,” Opt. Lett.
**20**, 1316 (1995).ADSGoogle Scholar - 15.
*Cavity Quantum Electrodynamics*, Ed. by P. Berman (Academic, New York, 1994).Google Scholar - 16.P. N. Prasad,
*Nanophotonics*(Wiley-Interscience, New York, 2004).Google Scholar - 17.V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-Factor and Nonlinear Properties of Optical Whispering-Gallery Modes,” Phys. Lett. A
**137**, 393 (1989).CrossRefADSGoogle Scholar - 18.L. Collot, V. Lefevre, M. Brune, et al., “Very Higher Whispering-Gallery Mode Resonances Observed in Fused Silica Microspheres,” Eur. Phys. Lett.
**23**, 327 (1993).ADSGoogle Scholar - 19.M. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “On the Ultimate Q of Optical Microsphere. Resonators,” Opt. Lett.
**21**, 453 (1996).ADSGoogle Scholar - 20.V. V. Klimov and V. S. Letokhov, “Resonance Fluorescence in an Atom Plusdielectric Microsphere System Excited by a Single Photon,” JETP Lett.
**68**, 124–130 (1998).CrossRefADSGoogle Scholar - 21.V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Strong Interaction of Two-Level Atom with Whispering Gallery Modes of Dielectric Microsphere: Quantum Consideration,” Phys. Rev. A.
**59**, 2996 (1999).CrossRefADSGoogle Scholar - 22.A. S. Davydov,
*Quantum Mechanics*(Nauka, Moscow, 1973; Pergamon, Oxford, 1976).Google Scholar - 23.S. C. Ching, H. M. Lai, and K. J. Young, “Dielectric Microspheres as Optical Cavities: Einstein A and B Coefficients and Level Shift,” Opt. Soc. Am. B
**4**, 1995 (1987); Opt. Soc. Am. B**4**, 2004 (1987).ADSGoogle Scholar - 24.D. P. Craig and T. Thirunamachandran,
*Molecular Quantum Electrodynamics*(Academic, New York, 1984).Google Scholar - 25.G. S. Agarwal., “Spectroscopy of Strongly Coupled Atom-Cavity Systems: a Topical Review,” J. Mod. Opt.
**45**, 449–470 (1998).ADSGoogle Scholar - 26.M. Löffler, G. M. Meyer, and H. Walther, “Spectral Properties of the One-Atom Laser,” Phys. Rev. A
**55**, 3923–3930 (1997).CrossRefADSGoogle Scholar - 27.E. T. Jaynes and F. W. Cummings, “Comparison of Quantum and Semiclassical Radiation Theory with Application to the Beam Maser,” Proc. IEEE
**51**, 89 (1963).CrossRefGoogle Scholar - 28.M. O. Scully and M. S. Zubairy,
*Quantum Optics*(Cambridge Univ. Press, Cambridge, 1997).Google Scholar