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4
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84926909711
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see also R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford University Press, London, 1983).
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17
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84926890899
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132, 397 (1985);
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25
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84926909710
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The second paper shows how Fermi's results are obtained with some ancillary approximations.
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27
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84926948028
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See, for instance, P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics
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28
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84926909709
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The field operator E vec here actually corresponds to the electric displacement vector, but for our purposes it will not be essential to distinguish between E vec and D vec. For a discussion of this point see E. A. Power, in Physics and Probability, edited by W. T. Grandy, Jr. and P. W. Milonni (Cambridge University Press, Cambridge, 1993). It should also be noted that all our results follow also from the minimal coupling form of the atom-field interaction involving the vector potential: in the Coulomb gauge the static, unretarded dipole-dipole interaction between two atoms is exactly canceled by a static coupling arising from the A vec cdot p vec coupling. We intend to discuss these points in more detail in a future paper dealing with dispersive dielectric media.
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30
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84926948027
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That causality is an exact consequence of the retarded nature of the Heisenberg field operators has been emphasized by E. A. Power (private communication). See E. A. Power, Ref. [8].
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31
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84926909708
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E vec1(+)( x vec2, t ) also has a (non-RWA) term involving σ1dag, but this term plays no role in the present discussion.
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33
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84926909707
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We follow a standard notation where V is a quantization volume, eventually allowed to become infinite, and e veck vec λ is a unit polarization vector. The field is quantized in free space, but quantization in terms of any other complete set of mode functions does not affect our conclusions.
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34
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84926928991
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See, for instance, Ref. [7] or W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Oxford University Press, London, 1960), p. 183.
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35
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84926923471
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In this connection the reason for Dirac's preference for the Heisenberg picture [, ] is worth recalling: ``.if one starts with zero in the Heisenberg picture, it remains zero, while if one starts with vacuum in the Schrödinger picture, it does not remain the vacuum. In that way the Heisenberg picture avoids the worst difficulties of the Schrödinger picture.''
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(1965)
P. A. M. Dirac, Phys. Rev.
, vol.139
, pp. B684
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37
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84926909704
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The shortest sampling times in photon counting that we know of, roughly 260 fs, have been reported by M. Munroe, D. Boggavarapu, M. E. Anderson, and M. G. Raymer, Phys. Rev. A (to be published); M. G. Raymer (unpublished).
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