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arXiv:1809.11070

Non-classical properties of the e.m. near field of an atom in spontaneous light emission

Vincent Debierre, Brian Stout, Thomas Durt

Published Sep 28, 2018• 0 citations
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Abstract

We use Glauber's correlation function as well as the Green functions formalism to investigate, in the case of a dipolar atomic transition, the causal behaviour of the spontaneously emitted electromagnetic field, in the A.p coupling. This brings us to examine the role played by the longitudinal electric field, which is not described in terms of photonic (transverse) degrees of freedom.

DOI
10.48550/arxiv.1809.11070

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We investigate, in the case of the 2p−1s2\mathrm{p}-1\mathrm{s}2p−1s transition in atomic Hydrogen, the behaviour of the spontaneously emitted electromagnetic field in spacetime. We focus on Glauber's wave function for the emitted photon, a quantity which we find is nonzero outside the lightcone at all times after the start of the emission. We identify the uncertainty on the position of the decaying electron as a source of departure from causality in the naive sense of the term. We carry out a detailed study of the emitted electric field in the mid- and far-field regions, through analytical and numerical computations as well as asymptotic arguments.
The time-dependent electric energy density surrounding a two-level atom fixed at r = 0 is studied, the atom being taken in its excited state at t = 0 and the field being initially in the vacuum state. The atom-field coupling includes both rotating and counter-rotating terms. The energy density of the spontaneously emitted field in the rotating wave approximation is shown to behave non-causally, while in the presence of the complete coupling it is shown to vanish outside a sphere of radius r = ct centred on the atom. The deviations of atomic dynamics from the exponential Wigner-Weisskopf behaviour during spontaneous decay are shown to be deeply influenced by the counter-rotating terms. It is concluded that the virtual photons induced by the counter-rotating terms in the atom-field coupling are essential in order to ensure causality and cannot be neglected in any accurate treatment of spontaneous emission.
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We investigate (non-relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two-level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal-coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra-type equation which governs the time evolution of the amplitude of the excited state. The two-point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.
Abstract We investigate (non‐relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two‐level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal‐coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra‐type equation which governs the time evolution of the amplitude of the excited state. The two‐point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.