Skip to main content Accessibility help
  • Print publication year: 2011
  • Online publication date: January 2012

2 - Theory of laser–atom interactions


In this chapter, we shall discuss the theory of laser–atom interactions, using a semi-classical method in which the laser field is treated classically, while the atom is studied by using quantum mechanics. This semi-classical approach constitutes an excellent approximation for intense laser fields, since in that case the number of photons per laser mode is very large [1, 2]. In addition, spontaneous emission can be neglected. We begin therefore by giving in Section 2.1 a classical description of the laser field in terms of electric- and magnetic-field vectors satisfying Maxwell's equations. We start by considering plane wave solutions of these equations. Then general solutions describing laser pulses are introduced. The dynamics of a classical electron in the laser field, and in particular the ponderomotive energy and force, are discussed in Section 2.2. Neglecting first relativistic effects, we write down in Section 2.3 the time-dependent Schrödinger equation (TDSE), which is the starting point of the theoretical study of atoms in intense laser fields, and introduce the dipole approximation. In the subsequent two sections, we study the behavior of the TDSE under gauge transformations and the Kramers frame transformation. In view of the central role that the time evolution operator plays in the development of the theory of laser–atom interactions, some general properties of this operator are reviewed in Section 2.6.

[1] Mittleman, M. H., Introduction to the Theory of Laser–Atom Interactions, 2nd edn. (New York: Plenum Press, 1993).
[2] Joachain, C. J., Theory of laser-atom interactions. In More, R. M., ed., Laser Interactions with Atoms, Solids and Plasmas (New York: Plenum Press, 1994), p. 39.
[3] Glauber, R. J., Phys. Rev. 130, 2529 (1963).
[4] Glauber, R. J., Phys. Rev. 131, 2766 (1963).
[5] Mandel, L. and Wolf, E., Optical Coherence and Quantum Optics (Cambridge: Cambridge University Press, 1995).
[6] Parker, J. and Stroud, C. R., Phys. Rev. Lett. 56, 716 (1986).
[7] Král, P., Thanopoulos, I. and Shapiro, M., Rev. Mod. Phys. 79, 53 (2007).
[8] Geissler, M., Tempea, G., Scrinzi, A., Schnürer, M., Krausz, F. and Brabec, T., Phys. Rev. Lett. 83, 2930 (1999).
[9] Siegmann, A. E., Lasers, (Mill Valley, Calif.: University Science, 1986).
[10] Gouy, L. G., Comptes Rendus Acad. Sci. Paris 110, 1251 (1890).
[11] Lindner, F., Paulus, G. G., Walther, al., Phys. Rev. Lett. 92, 113001 (2004).
[12] Bharucha-Reid, A. T., Elements of the Theory of Markov Processes and their Applications, 3rd edn (New York: McGraw Hill, 1960).
[13] Daniele, R., Ferrante, G., Morales, F. and Trombetta, F., Fundamentals of Laser Interactions, Lecture Notes in Physics, 229 (Berlin: Springer-Verlag, 1985).
[14] Bivona, S., Burlon, R., Zangara, R. and Ferrante, G., J. Phys. B 18, 3149 (1985).
[15] Francken, P. and Joachain, C. J., J. Opt. Soc. Am. B 7, 554 (1990).
[16] Zoller, P., J. Phys. B 13, L249 (1980).
[17] Daniele, R., Faisal, F. H. M. and Ferrante, G., J. Phys. B 16, 3831 (1983).
[18] Zoller, P., J. Phys. B 11, 805 (1978).
[19] Trombetta, F., Ferrante, G., Wodkiewicz, K. and Zoller, P., J. Phys. B 18, 2915 (1985).
[20] Francken, P. and Joachain, C. J., Europhys. Lett. 3, 11 (1987).
[21] Francken, P. and Joachain, C. J., Europhys. Lett. 9, 517 (1989).
[22] Shore, B. W., J. Opt. Soc. Am. B 1, 176 (1984).
[23] Brissaud, A. and Frisch, U., J. Math. Phys. 15, 524 (1974).
[24] Wodkiewicz, K., Shore, B. W. and Eberly, J. H., J. Opt. Soc. Am. B 1, 398 (1984).
[25] Kampen, N. G., Stochastic Processes in Physics and Chemistry (Amsterdam: North Holland, 1981).
[26] Trombetta, F., Ferrante, G. and Zoller, P., Opt. Commun. 60, 213 (1986).
[27] Jackson, J. D., Classical Electrodynamics, 3rd edn (New York: Wiley, 1998).
[28] Salamin, Y. I., Hu, S. X., Hatsagortsyan, K. Z. and Keitel, C. H., Phys. Rep. 427, 41 (2006).
[29] Pauli, W. and Fierz, M., Nuovo Cimento 15, 1167 (1938).
[30] Kramers, H. A., Collected Scientific Papers (Amsterdam: North Holland, 1956), p. 272.
[31] Henneberger, W. C., Phys. Rev. Lett. 21, 838 (1968).
[32] Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions (New York: Dover, 1970).
[33] Joachain, C. J., Quantum Collision Theory, 3rd edn (Amsterdam: North Holland, 1983).
[34] Gordon, W., Z. Phys. 40, 117 (1926).
[35] Volkov, D. M., Z. Phys. 94, 250 (1935).
[36] Bransden, B. H. and Joachain, C. J., Physics of Atoms and Molecules, 2nd edn (Harlow, UK: Prentice Hall-Pearson, 2003).
[37] Joachain, C. J. and Kylstra, N. J., Laser Phys. 11, 212 (2001).
[38] Joachain, C. J., Kylstra, N. J. and Potvliege, R. M., J. Mod. Opt. 50, 313 (2003).
[39] Maquet, A., Taïeb, R. and Véniard, V., Relativistic laser–atom physics. In Brabec, T., ed. Strong Field Laser Physics, Springer Series in Optical Sciences 134, (New York: Springer, 2009), p. 477.
[40] Kylstra, N. J., Potvliege, R. M. and Joachain, C. J., J. Phys. B 34, L55 (2001).
[41] Bransden, B. H. and Joachain, C. J., Quantum Mechanics 2nd edn (Harlow, UK: Prentice Hall-Pearson, 2000).
[42] Hartemann, F. V. and Kerman, A. K., Phys. Rev. Lett. 76, 624 (1996).
[43] Pauli, W. and Weisskopf, V., Helv. Phys. Acta 7, 709 (1934).
[44] Brown, L. S. and Kibble, T. W. B., Phys. Rev. 133A, 705 (1964).
[45] Foldy, L. L. and Wouthuysen, S. A., Phys. Rev. 78, 29 (1950).
[46] Messiah, A., Quantum Mechanics (Amsterdam: North Holland, 1968).
[47] Bjorken, J. D. and Drell, S. D., Relativistic Quantum Mechanics (New York: McGraw Hill, 1964).
[48] Hu, S. X. and Keitel, C. H., Phys. Rev. Lett. 83, 4709 (1999).
[49] Sauter, F., Z. Phys. 69, 742 (1931).
[50] Schwinger, J., Phys. Rev. 82, 664 (1951).
[51] Schwinger, J., Phys. Rev. 93, 615 (1954).
[52] Brezin, E. and Itzykson, C., Phys. Rev. D 2, 1191 (1970).
[53] Perelomov, A. M., Popov, V. S. and Terent'ev, M. V., Sov. Phys. JETP 23, 924 (1966).
[54] Perelomov, A. M., Popov, V. S. and Terent'ev, M. V., Sov. Phys. JETP 24, 207 (1967).
[55] Bethe, H. A. and Heitler, W., Proc. R. Soc. London A 146, 83 (1934).
[56] Müller, C., Voitkiv, A. B. and Grün, N., Phys. Rev. A 67, 063407 (2003).