Polarization correlation in the two–photon decay of heavy ions

Since the early days of quantum mechanics, the two– photon transitions in hydrogen–like ions have been the subject of intense experimental and theoretical studies. For many years, these studies have mainly dealt with the two–photon decay rates, energy and angular distributions. More recently, moreover, interest was focused on the polarization–resolved analysis of the two–photon emission. For example, a number of experiments have been performed in order to analyze the polarization correlations between the photons emitted in the decay of neutral hydrogen or low–Z ions [1]. In contrast, much less attention has been previously paid to the high–Z domain. A first step towards the two–photon polarization studies with heavy, few–electron ions is likely to be carried at the GSI facility where significant progress has been recently achieved in development of x–ray polarization detectors [2]. By making use of these detectors it becomes possible today to measure both (i) the correlated spin state of two photons (polarization entanglement) and (ii) the polarization of only one of the photons measured in coincidence with the other one. To better understand the polarization effects in the two– photon emission from heavy ions we have recently re– investigated the decay of metastable hydrogenic states in view of the photon spin properties [3]. The theoretical analysis has been performed within the framework of the Dirac’s relativistic equation and the density matrix approach. By making use of such an approach we were able to obtain an “angle–polarization” correlation function which characterizes the linear polarization of one of the photons if measured in coincidence with the second one whose spin states remain unobserved. For the well–known 2s1/2 → 1s1/2 two–photon transition, for example, we found a simple analytical expression for the (degree of) linear polarization of the emitted radiation: