Non-collinear retrieving of stored orbital angular momentum of light in cold atoms

Summary form only given. Light beams carrying orbital angular momentum (OAM) have attracted a great interest owing to their several applications ranging from the mechanical manipulation of macroscopic particles to the encoding of quantum information [1]. A well-known family of these beams is constituted by Laguerre-Gaussian modes specified by a topological charge ℓ, which gives to the mode a hélicoïdal phase structure and a corresponding OAM per photon equal to ℓħ. The nonlinear interaction of these beams with atomic systems has been investigated via four-wave mixing processes and the corresponding conservation of OAM demonstrated both in cold and thermal atoms [2]. The storage of OAM in cold and thermal atomic ensembles was also previously demonstrated [3].Differently from the previous observations, in this work we demonstrate that the stored OAM of a light beam can be retrieved along a nearly non-collinear direction with a reasonable fidelity. The experiment is performed in cold cesium atoms obtained from a MOT, using a delayed FWM configuration. Light beams with topological charges ℓ=0,1,2,3, produced by a spatial light modulator (SLM) are incident into the medium along the z direction, as shown in the simplified experimental scheme depicted in Fig. 1 (A). The frequency of the beams is resonant with the transition 6S1/2, F=3 - 6P3/2, F=2. The phase structure of the beam carrying OAM is stored into the Zeeman coherence grating induced by the incident writing beams W and W´ that form a small angle (~ή between them and have opposite circular polarization. The writing beams are kept on for a period long enough to create a stationary Zeeman coherence grating and then are switched off. After the storage time, a reading beam R, counter-propagating and with opposite circular polarization to the writing beam W, is turned on and the retrieved beam (C), whose propagation direction is determined by the phas- matching condition is monitored by a CCD camera. In Fig. 1(B) (a, b) we show images of the incident beams (W) intensity for the cases ℓ=1,2. In Fig. 1B (c, d) the corresponding images of the retrieved C beams. In order to determine the topological charges of the beams we create interference with a reference Gaussian beam. Fig 1(B) (e,f) and (g,h), show the interferograms for the incident (W) and the retrieved (C) beams respectively. Considering the detection geometry we conclude that the incident and retrieved beams carry the same OAM. These results clearly demonstrate that for small angles between W and W´ beams, the OAM stored along the z direction can ben retrieved along the non-collinear direction z´. Additional results concerning the conservationof OAM as well as the manipulation of the stored OAM by a magnetic field will also be presented.