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Spectroscopy of systems of two identical atoms: effects of quantum interference

A.A. Makarov, Vladimir I. Yudson

Published Dec 13, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1051/epjconf/201713202023

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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.
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.
The possibility of realization of collective resonance fluorescence of extended systems of atoms in the strong travel and standing laser waves it is demonstrated. The influence of regular arrangement of the atoms in interaction with the laser pulls on the fluorescence intensity is analyzed. Taking in to account that such interference can be realize in two distant atomic ensembles we analyzed the collective interference phenomena between the fluorescent fields in the farther field detection region. These effects depend on the exchange integrals between systems of atoms through vacuum fluorescence field. The fluorescence spectrum of these atoms is found. About similar coherence interference experiment of spontaneous emission of light from two distant solid-state ensembles of atoms that are coherently excited by a short laser pulse it is reported in the papers [1,2]. For example, in paper [1] it is observed the entanglement between two distant atomic ensembles located in distinct apparatuses on different tables. Quantum interference in the detection of a photon emitted by one of the samples projects the otherwise independent ensembles into an entangled state with one joint excitation stored remotely in 105 atoms at each site. The experiment [2] relate about the ensembles of erbium ions doped into two LiNbO3 crystals with channel wave guides, which are placed in the two arms of a Mach-Zehnder interferometer. The light that is spontaneously emitted after the excitation pulse shows first-order interference. By a strong collective enhancement of the emission, the atoms behave as ideal two-level quantum systems and no which-path information is left in the atomic ensembles after emission of a photon. Influence of geometry of the sample on the coherent phenomena between two distant systems of atoms in this report is presented.
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.
We investigate the interaction between a single photon and a chain of NNN equally spaced two-level atoms inside a one-dimensional waveguide. By solving the eigenvectors of the Hamiltonian in the subspace with a single excitation, we address quantum interference effects in two physical processes. First, we analyze the scattering of a single photon when atoms are all initially at their ground states. We discover a set of transmission peaks determined by NNN. These transmission peaks are narrow and sensitive to the relative position between atoms. Second, we examine the spontaneous emission of a photon from an excited atom in the chain in vacuum. The characteristic atomic decay rates are found to be enhanced and reduced by increasing the number of atoms. In particular, the slowest decay rate scales approximately as ${N}^{\ensuremath{-}3}$.
Spectroscopic measurements of transition frequencies in various atomic systems are a significant part of modern physics. They enable the testing of fundamental interactions, the determination of physical constants, and the study of fundamental symmetries that occur in nature with unprecedented accuracy. Studies based on two-photon spectroscopy of simple atoms represent some of the most accurate experiments to date. The verification of precision experimental results is largely supported by theoretical analysis, which is most rigorous for light, nonrelativistic atoms and ions. In the last decade, much attention in the literature has been paid to the study of the quantum interference effect (QIE) in hydrogen and hydrogenlike atomic systems. This has made it possible to significantly reduce the experimental error in determining the appropriate transition frequency. The theoretical description of the QIE corresponds to the consideration of similar pathways arising for close-lying resonant states into which the transition frequency is measured. In the present work, the influence of the emission process on the absorption profile formation is investigated. The results of the studies carried out in this work show the need to take into account the effect of quantum interference in cascade radiation for the precise determination of the absorption transition frequency to highly excited states in two-photon spectroscopic experiments.
It is shown that when a monochromatic laser couples a single atomic ground level to two closely spaced excited levels the system can be driven into a state in which quantum interference prevents any fluorescence from the excited levels, regardless of the intensity of the exciting field. This steady-state interference occurs only at a particular excitation frequency which depends on the separation of the excited states and the relative size of the two transition dipole matrix elements. The results are derived from the density matrix equations of motion. It is shown that a correct description of the effect requires the inclusion of generalised Einstein A coefficients which are usually neglected in phenomenological damping theories. A dressed-state analysis is introduced to simplify the generalisation to atoms having more complex manifolds of excited states. Analogous interferences in multiphoton absorption and ionisation are also discussed briefly.