Modelling of quantum memories based on atomic external degrees of freedom

Abstract

In this work, we present some fundamental tools in the modelling of quantum networks. We intend to develop theoretical tools such as the usage of the mixed variables density matrix formalism to model from first principles atomic experiments where external degrees of free- dom play an important role, and entanglement quantification in atom-photon systems where entanglement is present in the continuous variables of the system. Namely, we first perform a detailed theoretical and experimental investigation of an atomic memory based on recoil- induced resonance in cold cesium atoms. We consider the interaction of a nearly degenerated pump and probe beams with an ensemble of two-level atoms. A full theoretical density ma- trix calculation in the extended Hilbert space of the internal and external atomic degrees of freedom allows us to obtain, from first principles, the transient and stationary responses de- termining the probe transmission and the forward four-wave mixing spectra. These two signals are generated together at the same order of perturbation with respect to the intensities of pump and probe beams. Moreover, we have investigated the storage of optical information on the spatial modes of light beams in the atomic external degrees of freedom, which provided a simple interpretation for the previously-reported non-volatile character of this memory. The retrieved signals after storage reveal the equivalent role of probe transmission and four-wave mixing, as the two signals have similar amplitudes. Probe transmission and forward four-wave- mixing spectra were then experimentally measured for both continuous excitation and after storage. The experimental observations are in good agreement with the developed theory and open a new pathway for the reversible exchange of optical information with atomic systems. Next, we review the Weisskopf-Wigner formalism for spontaneous emission considering the spatial modes of light as well as external atomic degrees of freedom which we introduce in the theory by modelling the atom as a wavepacket in momentum space with a given initial uncertainty, and perform a purity calculation in order to quantify the entanglement encoded in the momentum variables of the atom-photon system. Our purity calculations reveal two high entanglement regimes depending on the initial atomic momentum uncertainty: the Recoil entanglement regime (which arises in the small momentum uncertainty region), where recoil effects dominate the mechanisms that originate entanglement and the Doppler entanglement regime (in the large momentum uncertainty region) where homogeneous Doppler shifts in the emitted photon’s frequency play the fundamental part in the build up of quantum correlations in the system. Simplified expressions for the system’s wavefunction are found for each of the entanglement regimes and physical considerations are made to explain their nature. Finally, we briefly investigate the role of entanglement in the distinguishability of two physically different quantum states that arise naturally from the theory, where we note that entanglement in the system leads to a better resolution of the two quantum states.