dorsal/arxiv
View SchemaCollective excitations in circular atomic configurations, and single-photon traps
| Authors | Hanno Hammer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402065 |
| URL | https://arxiv.org/abs/quant-ph/0402065 |
| DOI | 10.1103/PhysRevA.70.023803 |
| Journal | Phys. Rev. A 70, 023803 (2004) |
Abstract
Correlated excitations in a plane circular configuration of identical atoms with parallel dipole moments are investigated. The collective energy eigenstates, their level shifts and decay rates are computed utilizing a decomposition of the atomic state space into carrier spaces for the irreducible representations of the symmetry group $\ZZ_N$ of the circle. It is shown that the index $p$ of these representations can be used as a quantum number analogously to the orbital angular momentum quantum number $l$ in hydrogen-like systems. Just as the hydrogen s-states are the only electronic wave functions which can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the atoms in the circle can occupy the central atom only for vanishing $\ZZ_N$ quantum number $p$. If a central atom is present, the $p=0$ state splits into two and shows level-crossing at certain radii; in the regions between these radii, damped Rabi oscillations between two "extreme" $p=0$ configurations occur. The physical mechanisms behind super- and subradiance at a given radius and the divergence of the level shifts at small interatomic distances are discussed. It is shown that, beyond a certain critical number of atoms in the circle, the lifetime of the maximally subradiant state increases exponentially with the number of atoms in the configuration, making the system a natural candidate for a {\it single-photon trap}.
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"abstract": "Correlated excitations in a plane circular configuration of identical atoms\nwith parallel dipole moments are investigated. The collective energy\neigenstates, their level shifts and decay rates are computed utilizing a\ndecomposition of the atomic state space into carrier spaces for the irreducible\nrepresentations of the symmetry group $\\ZZ_N$ of the circle. It is shown that\nthe index $p$ of these representations can be used as a quantum number\nanalogously to the orbital angular momentum quantum number $l$ in hydrogen-like\nsystems. Just as the hydrogen s-states are the only electronic wave functions\nwhich can occupy the central region of the Coulomb potential, the\nquasi-particle corresponding to a collective excitation of the atoms in the\ncircle can occupy the central atom only for vanishing $\\ZZ_N$ quantum number\n$p$. If a central atom is present, the $p=0$ state splits into two and shows\nlevel-crossing at certain radii; in the regions between these radii, damped\nRabi oscillations between two \"extreme\" $p=0$ configurations occur. The\nphysical mechanisms behind super- and subradiance at a given radius and the\ndivergence of the level shifts at small interatomic distances are discussed. It\nis shown that, beyond a certain critical number of atoms in the circle, the\nlifetime of the maximally subradiant state increases exponentially with the\nnumber of atoms in the configuration, making the system a natural candidate for\na {\\it single-photon trap}.",
"arxiv_id": "quant-ph/0402065",
"authors": [
"Hanno Hammer"
],
"categories": [
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"physics.atm-clus"
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"doi": "10.1103/PhysRevA.70.023803",
"journal_ref": "Phys. Rev. A 70, 023803 (2004)",
"title": "Collective excitations in circular atomic configurations, and single-photon traps",
"url": "https://arxiv.org/abs/quant-ph/0402065"
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