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arXiv:0912.1300 · Physical Review A

Interplay of vacuum-mediated inter- and intra-atomic couplings in a pair of atoms

Sandra Isabelle Schmid, Jörg Evers

Published Jun 4, 2010• 22 citations
arXivHTMLPDF

Abstract

The resonance fluorescence emitted by a system of two dipole-dipole interacting nearby four-level atoms in a $J=1/2\ensuremath{\leftrightarrow}J=1/2$ configuration is studied. This setup is the simplest realistic model system which provides a complete description of the (inter-atomic) dipole-dipole interaction for arbitrary orientation of the inter-atomic distance vector, and at the same time allows for intra-atomic spontaneously generated coherences. Our main interest is the interplay of both these different coupling mechanisms. We discuss different methods to analyze the contribution of the various vacuum-induced coupling constants to the total resonance fluorescence spectrum. These allow us to find a dressed state interpretation of the contribution of the different inter-atomic dipole-dipole couplings to the total spectrum. We further study the role of the spontaneously generated coherences, and identify two different contributions to the single-particle vacuum-induced couplings. We show that they have a noticeable impact on the total resonance fluorescence spectrum down to small inter-atomic distances, even though the dipole-dipole coupling constants then are much larger in magnitude than the the single-particle coupling constants. Interestingly, we find that the inter-atomic couplings can induce an effect of the intra-atomic spontaneously generated coherences on the observed spectra which is not present in single-atom systems.

DOI
10.1103/physreva.81.063805

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The resonance fluorescence emitted by a system of two dipole-dipole interacting nearby four-level atoms in a J=1/2\ensuremath↔J=1/2J=1/2\ensuremath{\leftrightarrow}J=1/2J=1/2\ensuremath↔J=1/2 configuration is studied. This setup is the simplest realistic model system which provides a complete description of the (inter-atomic) dipole-dipole interaction for arbitrary orientation of the inter-atomic distance vector, and at the same time allows for intra-atomic spontaneously generated coherences. Our main interest is the interplay of both these different coupling mechanisms. We discuss different methods to analyze the contribution of the various vacuum-induced coupling constants to the total resonance fluorescence spectrum. These allow us to find a dressed state interpretation of the contribution of the different inter-atomic dipole-dipole couplings to the total spectrum. We further study the role of the spontaneously generated coherences, and identify two different contributions to the single-particle vacuum-induced couplings. We show that they have a noticeable impact on the total resonance fluorescence spectrum down to small inter-atomic distances, even though the dipole-dipole coupling constants then are much larger in magnitude than the the single-particle coupling constants. Interestingly, we find that the inter-atomic couplings can induce an effect of the intra-atomic spontaneously generated coherences on the observed spectra which is not present in single-atom systems.
Quantum interference and coherence effects in the interaction of atoms with the quantized electromagnetic field are investigated theoretically. A general master equation for the description of atom-field interactions is introduced. The interplay of the concepts of complementarity and interference in the time-energy domain are studied on the basis of the fluorescence light emitted by a single laser-driven atom, where the coherence of spontaneous processes gives rise to quantum interference in the spectrum of resonance fluorescence. The vacuum-induced dipole-dipole interaction in pairs of multi-level atoms is analyzed. It is shown that the interaction between orthogonal transition dipole moments of different atoms does not only influence the system dynamics crucially, but implies that the few-level approximation in general cannot be applied to near-degenerate Zeeman sublevels of the atomic level scheme. Potential applications of dipole-dipole interacting multi-level atoms for the implementation of decoherence-free subspaces and the generation of entanglement between atomic states are examined. The generation of an entangled state of the radiation field with a macroscopic number of photons is discussed on the basis of a single-atom laser.
The dynamics of a pair of atoms can significantly differ from the single-atom dynamics if the distance of the two atoms is small on a scale given by the relevant transition wavelengths. Here, we discuss two nearby three-level atoms in $\ensuremath{\Lambda}$ configuration, and focus on the dependence of the optical properties on the geometry of the setup. We find that in general transitions in the two atoms can be dipole-dipole coupled by interactions via the vacuum field even if their transition dipole moments are orthogonal. We give an interpretation of this effect and show that it may crucially influence the system dynamics. In particular, for a fixed setup of driving fields and detectors, the spatial orientation of the two-atom pair decides if the system reaches a true constant steady state or if it exhibits periodic oscillations in the long-time limit. As an example observable, we study the resonance fluorescence intensity, which is either constant or is modulated periodically in the long-time limit.
We discuss various aspects of the incoherent spontaneous emission in atomic few-level systems arising from the coupling of the atom to the surrounding vacuum. First, we consider systems where the decoherence due to spontaneous emission acts as a limiting factor. Here, we combine collective effects in larger samples of atoms with control mechanisms known from single-atom schemes, or modify the system dynamics by externally inducing multiphoton quantum interference effects. In the second part, we discuss ground-state laser cooling of trapped atoms and ions. Here, the momentum transfer in the spontaneous emission events is required to cool the particles, but needs to be controlled in order to achieve a low cooling limit. In our scheme, we make use of double electromagnetically induced transparency in order to design the absorption spectrum of the trapped particle. In the final part, we show that the incoherent part of the resonance fluorescence spectrum of a two-level system may serve as an interesting candidate for high-precision spectroscopy. For this, we discuss relativistic and radiative corrections to the resonance fluorescence spectra of laser-driven few-level systems.
Abstract The resonance fluorescence of a four-level atom in J = 1/2 to J = 1/2 transition driven by two coherent fields is studied. We find that the incoherent fluorescence spectrum shows a direct indication of vacuum-induced coherence in the atomic system. We show that such coherence manifests itself via an enhancement or suppression of the spectral peaks in the π -polarized fluorescence. The effect of the relative phase of the driving fields on the spectral features is also investigated. We show that phase-dependent enhancement or suppression of the fluorescence peaks appears in the incoherent spectrum emitted along the σ transitions. It is found that this phase dependence occurs because of the polarization-detection scheme employed for the observation of the fluorescence light. We present an analytical explanation, based on dressed-states of the atom-field system, to interpret the numerical results.
We investigate the effect of strong interaction in the dressed energy levels of the two level emitters. Strong dipole-dipole interactions give rise to new sidebands in the fluorescence spectrum due to specific couplings among the collective dressed levels which in turn depends on the spatial configuration of atoms. These couplings are the main responsible for the frequencies and variety of sidebands. We explain the general method for finding the dressed energy levels for a system of any number of strongly coupled atoms and we solve this problem for two different spatial configurations of three coupled two-level emitters. We show that the coupling among dressed levels and consequently energies and number of sidebands in the fluorescence spectrum are different for each configuration. Thus the fluorescence spectrum of strongly interacting atoms contains information about the number and configuration of atoms.
We study the resonance fluorescence from a coherently driven four-level atom in the Y-type configuration. The effects of quantum interference induced by spontaneous emission on the fluorescence properties of the atom are investigated. It is found that the quantum interference resulting from cascade emission decays of the atom leads to a splitting of resonances in the excited-level populations calculated as a function of light detuning. For some parameters, interference-assisted enhancement of inner sidebands and narrowing of central peaks may also occur in the fluorescence spectrum. We present a physical understanding of our numerical results using the dressed-state description of the atom-light interaction.