Control of Open Quantum Systems

Abstract

Spontaneous emission in atomic tunneling has been virtually unexplored before our recent work [1]. Since tunneling is a distinct manifestation of wave-like properties, it is important to raise the basic questions: can spontaneous decay of internal excitations in tunneling atoms be viewed as a decoherence process that is analogous to its counterpart in diffracted atoms? and if so, how would such decoherence manifest itself? We have put forward a theory of spontaneous emission from a two-level atom as it tunnels through a square potential barrier [1]. Our theory demonstrates that the emission process is describable as loss of coherence between interfering classical trajectories in space-time, which constitute the atom tunneling motion. The emitted photon at each frequency is correlated to particular atomic classical trajectories, in a way which makes them measurably distinguishable. This distinguishability destroys their interference [2], as does which-way (Welcher-Weg) information, which is obtainable from spontaneous emission in diffracted atoms [3, 4]. The ensuing analysis rests on two observations. (i) The overall duration of the decay process is much longer than the inverse transition frequency ω (see below). This allows us to resort to the rotating wave approximation (RWA), which is used in the Wigner—Weisskopf (WW) treatment of spontaneous emission [5]. (ii) Nearly all of the cavity-enhanced spontaneous emission is funneled into the continuum of nearly resonant modes with wave-vectors q (ω/c)ź, which are aligned with the cavity axis z, perpendicular to the atomic incidence axis x. This allows us to use the dipole approximation, since q . x 0, and neglect off-axis photon recoil effects on the atomic wave packet. Hence, the RWA interaction Hamiltonian of the atom with the cavity-mode continuum becomes effectively one-dimensional,