Coherence and Photons

  • Ingolf V. Hertel
  • Claus-Peter Schulz
Part of the Graduate Texts in Physics book series (GTP)


After the previous extensive exploration into the wave character of light, the present chapter focuses on its particle properties and on the statistical properties of photons. In Sect. 2.1 concepts such as “quasi-monochromatic” and “partially coherent” light will be defined and exemplified by simple models for a laser and a classical light source. We shall familiarize ourselves with the fundamental experiments, beginning with the famous “Hanbury Brown-Twiss experiment”. In Sect. 2.2 we shall try to find a pragmatic approach to the quantum mechanical description of photon states – giving an introduction for “pedestrians” so to say. Finally, we shall in Sect. 2.3 apply the new tools to the theory of absorption and emission of light – this time with explicit consideration of the quantum nature of photons. This will allow us for the first time to derive the basic formulas for spontaneous emission – as opposed to the previous, hand waving introduction of this inherently quantum mechanical phenomenon.


Spontaneous Emission Coherence Time Photon State Temporal Coherence Angular Diameter 
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Acronyms and Terminology


‘In statistical thermodynamics defined as the amount of energy or work that is necessary to change the number of particles of a system (by 1) without disturbing the equilibrium of the system’, see μ in Sect.  1.3.4, Vol. 1.


‘Continuous wave’, (as opposed to pulsed) light beam, laser radiation etc.


‘Electric dipole’, transitions induced by the interaction of an electric dipole with the electric field component of electromagnetic radiation.


‘Electric quadrupole’, transitions induced by the interaction of a quadrupolar charge distribution with the electromagnetic radiation field.


‘Electron paramagnetic resonance’, spectroscopy, also called electron spin resonance ESR (see Sect.  9.5.2 in Vol. 1).


‘European southern observatory’, in Chile, hosting four of today’s largest telescopes of the world, with 8.5 m diameter each.


‘electrostatic units’, old system of unities, equivalent to the Gauss system for electric quantities (see Appendix A.3 in Vol. 1).


Fabry-Pérot interferometer’, for high precision spectroscopy and laser resonators (see Sect.  6.1.2 in Vol. 1).


‘Full width at half maximum’.


‘Hanbury Brown and Twiss’, experiment, to determine the lateral correlation of light by a second-order interferometric measurement (see Sect. 2.1.6).


‘Infrared’, spectral range of electromagnetic radiation. Wavelengths between \(760\operatorname{nm}\) and \(1\operatorname{mm}\) according to ISO 21348 (2007).


‘Magnetic dipole’, transitions induced by the interaction of a magnetic dipole with the magnetic field component of electromagnetic radiation.


‘Near infrared’, spectral range of electromagnetic radiation. Wavelengths between \(760\operatorname{nm}\) and Open image in new window according to ISO 21348 (2007).


‘Nuclear magnetic resonance’, spectroscopy, a rather universal spectroscopic method for identifying molecules (see Sect.  9.5.3 in Vol. 1).


‘Quantum electrodynamics’, combines quantum theory with classical electrodynamics and special relativity. It gives a complete description of light-matter interaction.


‘Radio frequency’, range of the electromagnetic spectrum. Technically, one includes frequencies from \(3\operatorname{kHz}\) up to \(300\operatorname{GHz}\) or wavelengths from \(100\operatorname{km}\) to \(1\operatorname{mm}\); ISO 21348 (2007) defines the RF wavelengths from \(100\operatorname{m}\) to \(0.1\operatorname{mm}\); in spectroscopy RF usually refers to \(100\operatorname{kHz}\) up to some \(\operatorname{GHz}\).


‘Rotating wave approximation’, allows to solve the coupled equations for a two level system in a strong electromagnetic field in closed analytical form (see Sect.  10.2.3).


‘Second harmonic generation’, doubling of a fundamental frequency, for infrared or visible light typically by methods of nonlinear optics.


‘Ultraviolet’, spectral range of electromagnetic radiation. Wavelengths between \(100\operatorname{nm}\) and \(400\operatorname{nm}\) according to ISO 21348 (2007).


‘Visible’, spectral range of electromagnetic radiation. Wavelengths between \(380\operatorname{nm}\) and \(760\operatorname{nm}\) according to ISO 21348 (2007).


‘Very long baseline interferometry’, worldwide network of radio telescopes for interferometry.


  1. Baym, G.: 1998. ‘The physics of Hanbury Brown-Twiss intensity interferometry: From stars to nuclear collisions’. Acta Phys. Pol. B, 29, 1839–1884. ADSGoogle Scholar
  2. Beth, R. A.: 1936. ‘Mechanical detection and measurement of the angular momentum of light’. Phys. Rev., 50, 115–125. CrossRefADSGoogle Scholar
  3. Born, M. and E. Wolf: 2006. Principles of Optics. Cambridge: Cambridge University Press, 7th (expanded) edn. Google Scholar
  4. Boyajian, T. S. et al.: 2012. ‘Stellar diameters and temperatures. I. Main-sequence A, F, and G stars’. Astrophys. J., 746, 101 (26 pages). CrossRefADSGoogle Scholar
  5. Brown, R. H. and R. Q. Twiss: 1954. ‘A new type of interferometer for use in radio astronomy’. Philos. Mag., 45, 663–682. Google Scholar
  6. Brown, R. H. and R. Q. Twiss: 1956a. ‘Correlation between photons in 2 coherent beams of light’. Nature, 177, 27–29. CrossRefADSGoogle Scholar
  7. Brown, R. H. and R. Q. Twiss: 1956b. ‘A test of a new type of stellar interferometer on Sirius’. Nature, 178, 1046–1048. CrossRefADSGoogle Scholar
  8. Brown, R. H. and R. Q. Twiss: 1958. ‘Interferometry of the intensity fluctuations in light II. An experimental test of the theory for partially coherent light’. Proc. R. Soc. A 243, 291–319. CrossRefADSGoogle Scholar
  9. ten Brummelaar, T. A. et al.: 2005. ‘First results from the Chara array. II. A description of the instrument’. Astrophys. J., 628, 453–465. CrossRefADSGoogle Scholar
  10. Davis, J. and B. Lovell: 2003. ‘Robert Hanbury Brown, 1916–2002’, Australian Academy of Science., accessed: 9 Jan 2014.
  11. Glauber, R. J.: 1963. ‘Coherent and incoherent states of radiation field’. Phys. Rev., 131, 2766–2788. MathSciNetCrossRefADSGoogle Scholar
  12. Glauber, R. J.: 2005. ‘The Nobel prize in physics: for his contribution to the quantum theory of optical coherence’, Stockholm.
  13. Glauber, R. J.: 2006. ‘Nobel lecture: 100 years of light quanta’. Rev. Mod. Phys., 78, 1267–1278. CrossRefADSGoogle Scholar
  14. Glauber, R. J.: 2007. Quantum Theory of Optical Coherence, Selected Papers and Lectures. New York: Wiley-VCH Verlag, 643 pages. Google Scholar
  15. Goy, P., J. M. Raimond, M. Gross and S. Haroche: 1983. ‘Observation of cavity-enhanced single-atom spontaneous emission’. Phys. Rev. Lett., 50, 1903–1906. CrossRefADSGoogle Scholar
  16. Grangier, P., G. Roger and A. Aspect: 1986. ‘Experimental-evidence for a photon anticorrelation effect on a beam splitter – a new light on single-photon interferences’. Europhys. Lett., 1, 173–179. CrossRefADSGoogle Scholar
  17. Grynberg, G., A. Aspect and C. Fabre: 2010. Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light. Cambridge: Cambridge University Press, 665 pages. CrossRefGoogle Scholar
  18. Haroche, S. and D. J. Wineland: 2012. ‘The Nobel prize in physics: for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems’, Stockholm.
  19. Hasselbach, F.: 2010. ‘Progress in electron- and ion-interferometry’. Rep. Prog. Phys., 73. Google Scholar
  20. Henny, M., S. Oberholzer, C. Strunk, T. Heinzel, K. Ensslin, M. Holland and C. Schonenberger: 1999. ‘The fermionic Hanbury Brown and Twiss experiment’. Science, 284, 296–298. CrossRefADSGoogle Scholar
  21. ISO 21348: 2007. ‘Space environment (natural and artificial) – Process for determining solar irradiances’. International Organization for Standardization, Geneva, Switzerland. Google Scholar
  22. Jeltes, T. et al.: 2007. ‘Comparison of the Hanbury Brown-Twiss effect for bosons and fermions’. Nature, 445, 402–405. CrossRefADSGoogle Scholar
  23. Kimble, H. J., M. Dagenais and L. Mandel: 1977. ‘Photon anti-bunching in resonance fluorescence’. Phys. Rev. Lett., 39, 691–695. CrossRefADSGoogle Scholar
  24. Kleppner, D.: 1981. ‘Inhibited spontaneous emission’. Phys. Rev. Lett., 47, 233–236. CrossRefADSGoogle Scholar
  25. Kleppner, D.: 2008. ‘Hanbury Brown’s steamroller’. Phys. Today, 61, 8–9. CrossRefGoogle Scholar
  26. Lambropoulos, P. and D. Petrosyan: 2007. Fundamentals of Quantum Optics and Quantum Information. Berlin, Heidelberg, New York: Springer Verlag, 325 pages. Google Scholar
  27. Loudon, R.: 2000. Quantum Theory of Light. Oxford, New York: Oxford University Press, 3rd edn. zbMATHGoogle Scholar
  28. Mandel, L. and E. Wolf: 1995. Optical Coherence and Quantum Optics. Cambridge: Cambridge University Press. CrossRefGoogle Scholar
  29. Michelson, A. A. and F. G. Pease: 1921. ‘Measurement of the diameter of a orionis with the interferometer’. Astrophys. J., 53, 249–259. CrossRefADSGoogle Scholar
  30. Milloni, P. W. and J. H. Eberly: 2010. Laser Physics. Hoboken: Wiley, 832 pages. CrossRefGoogle Scholar
  31. Monnier, J. D.: 2003. ‘Optical interferometry in astronomy’. Rep. Prog. Phys., 66, 789–857. CrossRefADSGoogle Scholar
  32. Mukamel, S.: 1999. Principles of Nonlinear Optical Spectroscopy. Oxford: Oxford University Press, 576 pages. Google Scholar
  33. Phillips, D. T., H. Kleiman and S. P. Davis: 1967. ‘Intensity-correlation linewidth measurement’. Phys. Rev., 153, 113–115. CrossRefADSGoogle Scholar
  34. Purcell, E. M.: 1946. ‘Spontaneous emission probabilities at radio frequencies’. Phys. Rev., 69, 681, Note B10. CrossRefGoogle Scholar
  35. Walther, H., B. T. H. Varcoe, B. G. Englert and T. Becker: 2006. ‘Cavity quantum electrodynamics’. Rep. Prog. Phys., 69, 1325–1382. CrossRefADSGoogle Scholar
  36. Weissbluth, M.: 1978. Atoms and Molecules. New York, London, Toronto, Sydney, San Francisco: Academic Press, Student Edition, 713 pages. Google Scholar
  37. Weissbluth, M.: 1989. Photon-Atom Interactions. New York, London, Toronto, Sydney, San Francisco: Academic Press, 407 pages. Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ingolf V. Hertel
    • 1
  • Claus-Peter Schulz
    • 1
  1. 1.Max-Born-Institut für Nichtlineare Optikund KurzzeitspektroskopieBerlinGermany

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