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arXiv:quant-ph/0005093 · Physical Review Letters

Anisotropic Vacuum-Induced Interference in Decay Channels

G. S. Agarwal

Published Jun 12, 2000• 214 citations
arXivHTMLPDF

Abstract

We demonstrate how the anisotropy of the vacuum of the electromagnetic field can lead to quantum interferences among the decay channels of close lying states. Our key result is that interferences are given by the scalar formed from the antinormally ordered electric field correlation tensor for the anisotropic vacuum and the dipole matrix elements for the two transitions. We present results for emission between two conducting plates as well as for a two photon process involving fluorescence produced under coherent cw excitation.

DOI
10.1103/physrevlett.84.5500

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We demonstrate how the anisotropy of the vacuum of the electromagnetic field can lead to quantum interferences among the decay channels of close lying states. Our key result is that interferences are given by the scalar formed from the antinormally ordered electric field correlation tensor for the anisotropic vacuum and the dipole matrix elements for the two transitions. We present results for emission between two conducting plates as well as for a two photon process involving fluorescence produced under coherent cw excitation.
Spontaneous emission of an atom with two close upper levels and one lower level in a multilayer dielectric medium, and quantum interference between transitions from the upper levels to the lower one, are considered. Since the medium is inhomogeneous along the direction normal to the interfaces of the dielectric layers, the vacuum has an anisotropic spatial structure, and quantum intereference between the two decay channels can appear even if the two dipole matrix elements are orthogonal to each other. If the atom is placed in a three-layer dielectric plate cavity, a strong quantum interference similar to that for an atom with two nearly parallel dipole moments in free space arises due to the influence of anisotropic vacuum. Putting the atom in a three-layer dielectric waveguide and a one-dimensional photonic crystal, there appears a strong quantum interference similar to that for an atom with nearly antiparallel dipole moments.
We investigate the generation of quantum interference induced by spontaneous emission from two transitions of a V-type three-level atom embedded between two parallel plates (one or both the plates have infinite permeability, i.e. μ→ ∞ ). The result shows that, due to the anisotropy of vacuum, quantum interference still exists although the two dipole matrix elements of the atom are orthogonal to each other. When the atom is located very close to one of the plates, the quantum interference effect is particularly prominent. The strength of quantum interference displays oscillating behaviour with the position of the atom. With the increase of the distance between the plates, the oscillation becomes dense.
The interference pattern of coherent electrons is effected by coupling to the quantized electromagnetic field. The amplitudes of the interference maxima are changed by a factor which depends upon a double line integral of the photon two-point function around the closed path of the electrons. The interference pattern is sensitive to shifts in the vacuum fluctuations in regions from which the electrons are excluded. Thus this effect combines aspects of both the Casimir and the Aharonov-Bohm effects. The coupling to the quantized electromagnetic field tends to decrease the amplitude of the interference oscillations, and hence is a form of decoherence. The contributions due to photon emission and to vacuum fluctuations may be separately identified. It is to be expected that photon emission leads to decoherence, as it can reveal which path an electron takes. It is less obvious that vacuum fluctuations also can cause decoherence. What is directly observable is a shift in the fluctuations due, for example, to the presence of a conducting plate. In the case of electrons moving parallel to conducting boundaries, the dominant decohering influence is that of the vacuum fluctuations. The shift in the interference amplitudes can be of the order of a few percent, so experimental verification of this effect may be possible. The possibility of using this effect to probe the interior of matter, e.g., to determine the electrical conductivity of a rod by means of electrons encircling it is discussed. (Presented at the Conference on Fundamental Problems in Quantum Theory, University of Maryland, Baltimore County, June 18-22, 1994.)
An anisotropic quantum vacuum (AQV) has been predicted to induce quantum interferences during the spontaneous emission process in an atomic VVV transition [G. S. Agarwal, Phys. Rev. Lett. 84, 5500 (2000)]. Nevertheless, the finite lifetime of the excited states is expected to strongly limit the observability of this phenomenon. In this paper, we predict that an AQV can induce a long-lifetime coherence in an atomic $\mathrm{\ensuremath{\Lambda}}$ transition from the process of spontaneous emission, which has an additional advantage of removing the need for coherent laser excitation. We also carry out two metasurface designs and compare their respective efficiencies for creating an AQV over remote distances. The detection of this coherence induced by a metasurface, in addition to being yet another vindication of quantum electrodynamics, could pave the way towards the remote distance control of coherent coupling between quantum emitters, which is a key requirement to produce entanglement in quantum technology applications.
We show that radiative coupling between two multilevel atoms having near-degenerate states can produce new interference effects in spontaneous emission. We explicitly demonstrate this possibility by considering two identical V systems each having a pair of transition dipole matrix elements that are orthogonal to each other. We discuss in detail the origin of the new interference terms and their consequences. Such terms lead to the evolution of certain coherences and excitations that would not occur otherwise. The special choice of the orientation of the transition dipole matrix elements enables us to illustrate the significance of vacuum-induced coherence in multiatom multilevel systems. These coherences can be significant in energy transfer studies.
The coupling of the quantized electromagnetic field to coherent electrons is investigated. The effects both of photon emission and of the electromagnetic vacuum fluctuations upon electron interference are analyzed. The modifications of the vacuum fluctuations due to a conducting plate lead to a decrease in the amplitude of the interference oscillations. The possibility of observing this effect is discussed. It is also shown that there is an analogue of the Aharonov-Bohm effect in which electron interference is sensitive to vacuum fluctuations in regions from which the electrons are excluded.