Virtual photon exchange, intermolecular interactions and optical response functions

Abstract

According to molecular quantum electrodynamics, coupling between material particles occurs due to an exchange of one or more virtual photons. In this work, the relationship between polarisability and hyperpolarisability tensors of atoms and molecules that feature in linear and nonlinear optical processes, and their analytically continued form in the complex frequency domain that appear in formulae describing fundamental inter-particle interactions, is studied. Examples involving a single virtual photon exchange, which are linearly proportional to electric dipole moments at each centre, include the electrostatic energy and the resonant transfer of excitation energy. The Casimir–Polder dispersion potential, and its discriminatory counterpart applicable to coupled chiral molecules, are used to illustrate response properties depending on the exchange of two virtual photons. Meanwhile, the energy shift between two hyperpolarisable species, a higher order discriminatory contribution to the dispersion potential, is employed to represent forces arising from the three virtual photon exchange. It is shown that for energy shifts that are quadratic or bilinear or cubic in the transition dipole moment, it is necessary to account for all two- and three-photon optical processes, such as absorption, emission and linear and nonlinear scattering of light in order to arrive at the correct form of the molecular response tensor.

Keywords:

• virtual photon exchange
• inter-particle interactions
• polarisability
• hyperpolarisability
• molecular quantum electrodynamics

Acknowledgements

Prof. Robert A. Harris of the University of California at Berkeley is acknowledged for an interesting communication during March, 2010 regarding discriminatory dispersion forces and their expression in terms of optical response properties. He is thanked for sending the author reference [15], from which this work grew, and his encouragement of it.

Disclosure statement

No potential conflict of interest was reported by the author.