QED with a parabolic mirror

Abstract

We investigate the quantum electrodynamics of a single two-level atom located at the focus of a parabolic cavity. We first work out the modifications of the spontaneous emission induced by the presence of this boundary in the optical regime, where the dipole and the rotating-wave approximations apply. Furthermore, the single-photon state that leaves the cavity asymptotically is determined. The corresponding time-reversed single-photon quantum state is capable of exciting the atom in this extreme multimode scenario with near-unit probability. Using semiclassical methods, we derive a photon-path representation for the relevant transition amplitudes and show that it constitutes a satisfactory approximation for a wide range of wavelengths

Spectral properties of spontaneous photon emission by a material twolevel system in a parabolic cavity

“…In the long-time limit, i.e. t 1/Γ 0 with Γ 0 denoting the spontaneous decay rate of state |e , one obtains the result [10]:…”

“…In this paper we generalize previous investigations into the interaction of a trapped approximately motionless material two-level system with a single photon inside a parabolic cavity [10] and explore the spectral properties of a spontaneously emitted photon inside this cavity. For this purpose, we apply our recently developed classical path representation of photonic transition amplitudes to the description of the electric field correlation function of a single photon and to the corresponding spectrum.…”

“…As a consequence, the mode functions g ω,n (x) solving Eq. (4) and capable of coupling to this atomic dipole can be written in the form [10]:…”

“…The Hamiltonian describing the dynamics of its interaction with the quantized radiation field is given by [10]:Ĥ…”

“…Contrary to the case of extreme mode selection, in this scenario this half open cavity supports a continuum of photonic modes which can couple to the trapped material two-level system. This continuum of modes, however, is structured by the presence of the parabolic cavity so that interesting dynamical modifications take place, which range from modifications of the spontaneous decay rate of the trapped two-level system in comparison with the free-space scenario by the Purcell effect [8] to intricate recurrence effects observable in the time evolution of the trapped two-level system originating from photonic reflections at the boundary of the cavity [9,10].…”