Boundary effects influencing single-atom spontaneous emission in a linear atomic chain

Abstract

As a contribution to quantum optics in the vicinity of surfaces we study the single atom spontaneous emission in a linear chain of two-level atoms. The electromagnetic field is thereby treated with the help of integro-differential equations which take into account the interaction with the other atoms in the chain. The life time of the excited atom, the frequency shift of the atomic transition and the angular distribution of emitted photons are worked out. They depend on the position of the emitting atom. As compared with the single atom in free space, considerable modifications occur for atoms a few interatomic distances away from the ends of the chain. * Permanent address:

Spontaneous decay of an excited atom in an absorbing dielectric

“…In other words, the electromagnetic field inside and outside the cavity exactly solves Maxwell's equations (12) - (15) together with the standard boundary conditions at the surface of the cavity. In contrast to the virtual cavity approach, in the real cavity approach the field inside the cavity exactly satisfies the fundamental QED equal-time commutation relations (24) and (25), and the Green tensor does not lead to a singular contribution to the decay rate. The Green tensor for an inhomogeneous problem of that type can always be written as a sum of the Green tensor for a homogeneous problem and some tensor that obeys a source-free wave equation and ensures the boundary conditions to be satisfied [22].…”

“…Hence a refined treatment of the medium should also allow for the presence in the cavity of nearest-neighboring medium species whose interaction with the guest atom is considered separately. The enlarged cavity can then be chosen such that the guest atom cannot "resolve" the discrete structure of the medium outside the cavity and the continuous description applies [23,24].…”