Entanglement in atomic systems interacting with single-photon pulses in free space

New technologies providing tightly focusing lenses and mirrors with large numerical apertures and electro-optic modulation of single photons are now available for the investigation of photon-atom interactions without a cavity. From the theoretical side, new models must be developed which take into account the intrinsic open system aspect of the problem as well as details about atomic relative positions and temporal (spectral) features of the pulses. In this paper, we investigate the generation of nonclassical correlations between two atoms in free space interacting with a quantized pulse containing just one single photon. For this purpose, we develop a general theoretical approach which allows us to find the equations of motion for single- and two-body atomic operators from which we obtained the system density operator. We show that one single photon is capable of promoting substantial entanglement between two initially ground-state atoms, and we analyze the dependence of these correlations on atomic relative positions (vacuum effects) and spectral features of the single-photon pulse.

Figure 1

Entanglement dynamics for initially unexcited atoms interacting with a single-photon pulse for different atomic separations and pulse shapes. In (a) the parameters used for the Gaussian pulse were $r_{12}/\lambda =0.2,\Omega /\gamma =2.55$ and for the rising exponential pulse $r_{12}/\lambda =0.2,\Omega /\gamma =1.77$. In (b) the parameters used for the Gaussian and rising pulse were $r_{12}=0.2,\Omega /\gamma =1.0$.

Figure 2

Maximal entanglement for several atomic distances as a function of the normalized pulse bandwidth $\Omega /\gamma$. (a) Rising exponential pulse (b) Gaussian pulse.