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Journal of Experimental and Theoretical Physics

Spontaneous decay in a system of two spatially separated atoms (One-dimensional case)

A. A. Makarov, Vladilen S Letokhov

Published Oct 1, 2003• 18 citations
Publisher

Abstract

The problem of the dynamics and the spectrum of spontaneous radiation is solved for a system of two atoms in one-dimensional space. In order to single out, to the maximum possible degree, phenomena associated with the influence of spatially separated atoms on each other via the radiation field, the present analysis is performed precisely for the one-dimensional case. As a result, two effects are revealed and considered in detail: (i) the existence of stable (metastable) entangled superposition states at specific distances between the atoms and (ii) a considerable distinction between the spectra of photons emitted in two opposite directions from the system where only one of the atoms is initially excited. The possibilities of observing these effects are discussed.

DOI
10.1134/1.1625059

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EPJ Web of Conferences•Jan 1, 2015•0 citations
The problem of the dynamics and the spectrum of spontaneous radiation is solved for a system of two atoms in one-dimensional space. In order to single out, to the maximum possible degree, phenomena associated with the influence of spatially separated atoms on each other via the radiation field, the present analysis is performed precisely for the one-dimensional case. As a result, two effects are revealed and considered in detail: (i) the existence of stable (metastable) entangled superposition states at specific distances between the atoms and (ii) a considerable distinction between the spectra of photons emitted in two opposite directions from the system where only one of the atoms is initially excited. The possibilities of observing these effects are discussed.
Dynamics of spontaneous decay and corresponding emission spectrum areexactly treated for a system of two identical two-level atoms in 1D.Just a one-dimensional case is considered in order to maximally extractan information on mutual influence of spatially remote atoms through theradiation field. As a result, an effect is revealed and considered indetail that there exist stable (metastable) entangled states at definitedistances between the atoms. That state is supported by a(quasi)stationary field bounded between the atoms. Also, acorrespondence is established between the lifetime and emissionspectrum, and possibilities for observing the effect are discussed.
Several effects of quantum interference in spectroscopy of a system of two atoms are discussed. (i) In the system of spatially separated atoms in a one-dimensional (1D) geometry (a single-mode waveguide or photon crystal), a (meta)stable excited entangled state can be formed, its decay being very sensitive to the distance between the atoms and to perturbations which cause a difference between their resonance frequencies. (ii) In a system of closely located atoms in 3D space, the extreme sensitivity of absorption and fluorescence spectra to the direction of the applied magnetic field is demonstrated. These theoretical predictions can be useful for the quantum information processing and ultrasensitive measurements.
Sub- and superradiant dynamics of spontaneously decaying atoms are manifestations of collective many-body systems. We study the internal dynamics and the radiation properties of two atoms in free space. Interesting results are obtained when the atoms are separated by less than half a wavelength of the atomic transition, where the dipole-dipole interaction gives rise to new coherent effects, such as (a) coherence between two intermediate collective states, (b) oscillations in the two-photon correlation G(2){G}^{(2)}G(2), (c) emission of two photons by one atom, and (d) the loss of directional correlation. We compare the population dynamics during the two-photon emission process with the dynamics of single-photon emission in the cases of a $\ensuremath{\Lambda}$ and a V scheme. We compute the temporal correlation and angular correlation of two successively emitted photons using the G(2){G}^{(2)}G(2) for different values of atomic separation. We find antibunching when the atomic separation is a quarter wavelength $\ensuremath{\lambda}∕4$. Oscillations in the temporal correlation provide a useful feature for measuring subwavelength atomic separation. Strong directional correlation between two emitted photons is found for atomic separation larger than a wavelength. We also compare the directionality of a photon spontaneously emitted by the two atoms prepared in phased-symmetric and phased-antisymmetric entangled states ${\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}⟩}_{{\mathbf{k}}_{0}}={e}^{i{\mathbf{k}}_{0}∙{\mathbf{r}}_{1}}\ensuremath{\mid}{a}_{1},{b}_{2}⟩\ifmmode\pm\else\textpm\fi{}{e}^{i{\mathbf{k}}_{0}∙{\mathbf{r}}_{2}}\ensuremath{\mid}{b}_{1},{a}_{2}⟩$ by a laser pulse with wave vector k0{\mathbf{k}}_{0}k0​. Photon emission is directionally suppressed along k0{\mathbf{k}}_{0}k0​ for the phased-antisymmetric state. The directionality ceases for interatomic distances less than $\ensuremath{\lambda}∕2$.
A model radiating system consisting of two atoms in close proximity is analyzed. This system demonstrates the influence of spatial coherence on the spectrum of the radiation field. Explicit expressions for the degree of coherence, the source spectrum, and the spectrum of the radiation field are derived. The results are discussed in terms of Wolf's work [Phys. Rev. Lett. 56, 1370 (1986)] on this effect, which can be considered in terms of a multiple-atom analog of the effects of radiation reaction on a single atom, i.e., spontaneous decay and the Lamb shift.
Second-order interference effects in the spontaneous emission by two identical two-level atoms, separated a distance apart and both initially excited, are considered. On the basis of the analysis in our previous paper published in 2004, within fourth-order perturbation, detailed analysis of the second-order quantum interference in the emitted field is made. The interference arises both from single-photon states and two-photon states owing to interferences between different decaying sequences. By detailed analysis we have found some cancellations between single-photon and two-photon interference terms, and an interpretation of this is given. The contributions from the single- and the two-photon states as well as the total interference are analysed numerically for various interatomic distances and times. The contribution from a two-photon state is mostly larger than that from a single-photon state except when the atomic electric dipole is large, in which case the two contributions can be comparable. It is shown that the emission patterns from the two interacting atoms provide more information on atom–atom correlations than the decay time evolution of the atomic states population does. The number of interference fringes and the distance between them depend on the interatomic distance in a similar fashion to Young's interference fringes.
The light-matter interaction effects are especially important in one-dimentional (1D) systems, where there is no spatial spreading of emitted radiation. We study Such metastable states of a singly excited pair of resonant atoms arise when the distance between the atoms takes special values We have calculated their decay rate when the interatomic distance deviates from the special values or when the transition frequencies of the two atoms do not coincide (inhomogeneous detuning). Also, we have found that the doubly excited state of two resonant atoms located at the special positions does not completely decay, but with a finite probability can evolve to one of the metastable singly-excited states. Dark states of pairs of qubits may serve as memory elements or sensitive detectors of external perturbations.