Coupling Dressed Photons and Phonons
This chapter presents theoretical formulations of the coupling between dressed-photons (DPs) and phonons based on the physical picture of DPs reviewed in Chap. 2 . After showing some novel phenomena involving photo-dissociation of molecules, a theoretica
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Coupling Dressed Photons and Phonons
Mihi contuenti semper suasit rerum natura nihil incredibile existimare de ea. Caius Plinius Secundus Major, Naturalis Historya, XI, 2
This chapter presents theoretical formulations of the coupling between dressed photons (DPs) and phonons based on the physical picture of DPs reviewed in Chap. 2. After showing some novel phenomena involving photo-dissociation of molecules, a theoretical model for the interaction between DPs and phonons is described.
4.1 Novel Molecular Dissociation and the Need for a Theoretical Model 4.1.1 Unique Phenomena of Molecular Dissociation by Dressed Photons First, conventional molecular dissociation is discussed by taking a diatomic molecule as the simplest example. Comparing a nucleus and an electron in an atom, the nucleus moves more slowly than the electron because of its larger mass. In other words, the electron shifts its position instantaneously by following the movement of the nucleus, whereas the nucleus is almost independent of the electron movement. Therefore, one can use the approximation that the inter-nuclear distance R of the diatomic molecule is maintained constant, while only the electron moves, which is called the Born–Oppenheimer approximation [1]. This is also called the adiabatic approximation because the state of the nucleus remains unchanged. The inter-nuclear force is repulsive or attractive depending on R. As is shown in Fig. 4.1, the coupling length between the two atoms corresponds to the inter-nuclear distance R0 at which the potential energy of the inter-atomic interaction takes the minimum. In the limit
M. Ohtsu, Dressed Photons, Nano-Optics and Nanophotonics, DOI: 10.1007/978-3-642-39569-7_4, © Springer-Verlag Berlin Heidelberg 2014
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4 Coupling Dressed Photons and Phonons
Fig. 4.1 Relation between the inter-nuclear distance in a molecule and the energies of the electron states and the molecular vibration states Energy
Bonding excited state
Anti-bonding excited state Excitation energy by optical absorption Eex Dissociation energy Edis Molecular vibration states Electronic ground state R0
Inter-nuclear distance
of infinite distance (R → ∞), the two atoms do not interact any more, which corresponds to dissociation. The difference between the interaction energies at R = ∞ and at R0 corresponds to the dissociation energy Rdis . The adiabatic approximation is effective also in the case of molecular dissociation induced by propagating light because the nucleus does not respond to the propagating light. Therefore, the molecule does not dissociate even if it is illuminated with propagating light whose photon energy is as high as Rdis . However, if propagating light with much higher photon energy is applied to the molecule, it is absorbed by the electron, and the electron is excited to the binding excited state shown in Fig. 4.1. This transition is represented by an upward arrow in Fig. 4.1. The energy of this binding excited state takes the minimum at a value of R that is larger than R0 of the ground state because
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