We analyze the interaction of arbitrary quantum states of light with a single atom in free space using a local interaction with a single mode and a discrete model of light field propagation.
Today the interaction of light and matter on the single quantum level is a wide research field. Strong coupling between a single photon and a single atom has already been achieved with optical cavities. Here, we treat strong interaction in free space, i.e. strong interaction whilst maintaining the free space density of states of the electromagnetic field. We pursue the coupling of a properly designed single photon wave packet to a single ion aiming at an excitation probability close to unity. For this purpose a linear dipole transition of an ion localized in the focal point of a deep parabolic mirror is addressed by a collimated laser beam focused onto the ion from nearly the full solid angle. In order to reach the highest possible coupling strength, the incident vectorial light field must be matched to the radiation pattern of the corresponding atomic transition both in the spatial and in the temporal domain. Here the generation of such an incident light mode is presented.
We study the dynamics of a one-dimensional array of the Jaynes–Cummings–Hubbard system of arbitrary number of coupled cavities, each containing a two-level atom that interacts with a field mode. In particular, we consider the propagation of a single-excitation quantum state for two different couplings between the localized photonic modes of the adjacent cavities, namely a translation invariant uniform coupling on a closed chain of cavities, and also a nonuniform parabolically varying intercavity coupling on a linear chain where the interaction Hamiltonian is associated with the Jacobi matrix of the relevant Krawtchouk polynomial. Using a description via the delocalized atomic and field modes, we observe that for a large detuning of these two degrees of freedom, atomic excitations propagate without populating the field modes, and vice versa. For the near-resonance scenario between these modes, the atomic excitations, say, while propagating mix with the photonic states. In the context of the parabolic coupling between photons of adjacent cavities, the time-dependent correlation function describing the propagation of the quantum state between two arbitrary sites may be expressed in closed form for dominant values of the detuning parameter, when an exact transmission of the quantum state at pre-specified times is realized.