Nonlocality of the energy density of a spontaneously emitted single-photon from a Hydrogen atom

Abstract We analyze through the expectation value of the energy density the spatial nonlocality of single photons emitted by the spontaneous decay of a Hydrogen atom. By using a minimal coupling between the quantized electromagnetic field and the atom, we compute the state of the photon under the assumption that only a single-photon is produced. The calculations are thus performed in the subspace of single-photon states which is essentially equivalent to the rotating wave approximation. We obtain a characterization of the spatial decay of the energy density. We compute the asymptotic limit of large distances from the atom at each given time, and find an algebraic behavior of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msup> <mml:mi>r</mml:mi> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> . This result confirms that the energy density of single-photon states is nonlocal and the algebraic decay is far from the maximal quasiexponential localization predicted by the theory.