dorsal/arxiv
View SchemaCollective states in highly symmetric atomic configurations, and single-photon traps
| Authors | Hanno Hammer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407094 |
| URL | https://arxiv.org/abs/quant-ph/0407094 |
| DOI | 10.1134/1.2034622 |
| Journal | Optics and Spectroscopy -- August 2005 -- Volume 99, Issue 2, pp. 320--337 |
Abstract
Abbreviated Abstract: We study correlated states in a circular and linear-chain configuration of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behaviour is mediated by exchange of transverse photons between the atoms. For a circular configuration of atoms the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. In this case, the radiationless energy eigenstates carry a $\mathbb{Z}_N$ quantum number $p=0,1, ..., N$ which is analogous to the angular momentum quantum number $l= 0, 1, ...$, carried by particles propagating in a central potential, such as a hydrogen-like system. 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 circular atomic sample can occupy the central atom only for vanishing $\mathbb{Z}_N$ quantum number $p$. For large numbers of atoms in a maximally subradiant state, a critical interatomic distance of $\lambda/2$ emerges both in the linear-chain and the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jump-like "critical" behaviour for next-neighbour distances close to a half-wavelength. Furthermore, both the linear-chain and the circular configuration exhibit exponential photon trapping once the next-neighbour distance becomes less than a half-wavelength, with the suppression of spontaneous decay being particularly pronounced in the circular system. In this way, circular configurations containing sufficiently many atoms may be natural candidates for {\it single-photon traps}.
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"abstract": "Abbreviated Abstract: We study correlated states in a circular and\nlinear-chain configuration of identical two-level atoms containing the energy\nof a single quasi-resonant photon in the form of a collective excitation, where\nthe collective behaviour is mediated by exchange of transverse photons between\nthe atoms. For a circular configuration of atoms the effective Hamiltonian on\nthe radiationless subspace of the system can be diagonalized analytically. In\nthis case, the radiationless energy eigenstates carry a $\\mathbb{Z}_N$ quantum\nnumber $p=0,1, ..., N$ which is analogous to the angular momentum quantum\nnumber $l= 0, 1, ...$, carried by particles propagating in a central potential,\nsuch as a hydrogen-like system. Just as the hydrogen s-states are the only\nelectronic wave functions which can occupy the central region of the Coulomb\npotential, the quasi-particle corresponding to a collective excitation of the\ncircular atomic sample can occupy the central atom only for vanishing\n$\\mathbb{Z}_N$ quantum number $p$. For large numbers of atoms in a maximally\nsubradiant state, a critical interatomic distance of $\\lambda/2$ emerges both\nin the linear-chain and the circular configuration of atoms. The spontaneous\ndecay rate of the linear configuration exhibits a jump-like \"critical\"\nbehaviour for next-neighbour distances close to a half-wavelength. Furthermore,\nboth the linear-chain and the circular configuration exhibit exponential photon\ntrapping once the next-neighbour distance becomes less than a half-wavelength,\nwith the suppression of spontaneous decay being particularly pronounced in the\ncircular system. In this way, circular configurations containing sufficiently\nmany atoms may be natural candidates for {\\it single-photon traps}.",
"arxiv_id": "quant-ph/0407094",
"authors": [
"Hanno Hammer"
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"doi": "10.1134/1.2034622",
"journal_ref": "Optics and Spectroscopy -- August 2005 -- Volume 99, Issue 2, pp.\n 320--337",
"title": "Collective states in highly symmetric atomic configurations, and single-photon traps",
"url": "https://arxiv.org/abs/quant-ph/0407094"
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