Quantum electrodynamics effects in atoms and molecules

Abstract

Quantum electrodynamics (QED) is the fundamental theory describing the interaction of electrons and photons. Its characteristic feature is that both radiation and matter are treated quantum mechanically. For almost all atomic and molecular systems, which contain bound electrons moving at velocities considerably less than that of light, a non-relativistic formulation of QED is appropriate. Termed molecular QED, its Hamiltonian operator can be constructed by starting from the classical Lagrangian function for the interaction of a charged particle with a radiation field on applying the variational calculus and carrying out the canonical quantization procedure. It is shown how the minimal-coupling Lagrangian can be transformed to the chemically advantageous multipolar Hamiltonian in which matter couples to radiation directly through molecular multipole moments, with the ensuing interaction strictly causal. Applications include evaluation of transition rates for one-and two-photon absorption, spontaneous and stimulated emission, and signal intensities for second-and third-harmonic generation. Fundamental intermolecular interactions examined include resonance energy transfer, the van der Waals dispersion potential, and the change in energy shift of the pair induced by intense external radiation. The non-relativistic contribution to the Lamb shift is also extracted. It is shown how a number of the above mentioned processes may be attributed to fluctuations of the vacuum electromagnetic field, which possesses zero-point energy, a signature QED effect that has widespread implications for the structural and dynamical properties of atoms and molecules.

Perspective: Quantum Hamiltonians for optical interactions

“…As such, the quanta of the radiation field are correctly regarded as 'transverse' photons. All interactions between material particles are therefore mediated by the exchange of virtual photons with this specific transverse character [21], [87], [88]. Indeed, this feature is the origin of the widespread application of the multipolar PZW development to intermolecular interactions [10].…”

“…Another apparent misconception arises in the view that only if one goes to the electric dipole approximation does the interaction operator reduce to a term linear in the field variables and proportional to the electric charge e. [11] As has been seen, expansions of the second and third terms of equation (47) yield the electric and magnetic multipole series, from which the prominence of the electric dipole coupling term readily follows on making the long wavelength approximation. The third interaction term in the PZW Hamiltonian is proportional to the square of the electronic charge and depends bilinearly on the magnetic field, giving rise to the diamagnetic coupling term [1], [3], [9], [10], [21], [20]. Only the interaction terms that are linear in the Maxwell fields are employed in first-order processes such as one-photon absorption.…”

“…Obviously it is not a gauge transformation since S commutes with the Coulomb gauge vector potential, A; since it is unitary the commutation relation between A and its conjugate π is unchanged. S also commutes with Gauss's Law (21); the form of the Hamiltonian is modified however. It may be written…”

“…This is a surprising claim, since over its close to sixty year history there has been a host of applications to which the PZW Hamiltonian has been applied, which have agreed with, or led to predictions borne out by experiment. There are many hundreds of papers in the established literature citing the original work, bearing testimony to its efficacy and success; numerous significant applications and advances have built upon it, even over the last decade [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37]. Indeed we know of no cases where the theory has been faulted by experimental studywhich would usually be the condition to invite reappraisal of a previously successful theory.…”

Virtual photon exchange, intermolecular interactions and optical response functions

“…Apart from the fundamental nature of QED, and the rigour of its approach when applied to specific problems involving an electron-photon coupling [44], a powerful and versatile aspect of the theory is that it is able to treat the radiationmatter and particle-particle interactions within a single unified framework. Hence, spectroscopic processes and intermolecular forces are described accurately and consistently in terms of the emission and absorption of photons.…”