Collective states in highly symmetric atomic configurations and singlephoton traps
Abstract
Abbreviated Abstract: We study correlated states in a circular and linearchain configuration of identical twolevel atoms containing the energy of a single quasiresonant 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 hydrogenlike system. Just as the hydrogen sstates are the only electronic wave functions which can occupy the central region of the Coulomb potential, the quasiparticle 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 linearchain and the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jumplike "critical" behaviour for nextneighbour distances close to a halfwavelength. Furthermore, both the linearchain and the circular configuration exhibit exponential photon trapping once the nextneighbour distance becomes less than a halfwavelength, 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 singlephoton traps}.
 Publication:

Optics and Spectroscopy
 Pub Date:
 August 2005
 DOI:
 10.1134/1.2034622
 arXiv:
 arXiv:quantph/0407094
 Bibcode:
 2005OptSp..99..320H
 Keywords:

 Quantum Physics;
 Condensed Matter  Other
 EPrint:
 Invited contribution to "Xth International Conference on Quantum Optics ICQO 2004" in Minsk, Belarus. To be published in Optics and Spectroscopy