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arXiv:0706.0477 · Physical Review A

Polarization rotation of slow light with orbital angular momentum in ultracold atomic gases

Julius Ruseckas, Gediminas Juzeliūnas, Patrik Öhberg, Stephen Mark Barnett

Published Nov 16, 2007• 59 citations
arXivHTMLPDF

Abstract

We consider the propagation of slow light with an orbital angular momentum (OAM) in a moving atomic medium. We have derived a general equation of motion and applied it in analyzing propagation of slow light with an OAM in a rotating medium, such as a vortex lattice. We have shown that the OAM of slow light manifests itself in a rotation of the polarization plane of linearly polarized light. To extract a pure rotational phase shift, we suggest to measure a difference in the angle of the polarization plane rotation by two consecutive light beams with opposite OAM. The differential angle $\ensuremath{\Delta}{\ensuremath{\alpha}}_{l}$ is proportional to the rotation frequency of the medium ${\ensuremath{\omega}}_{\text{rot}}$ and the winding number $l$ of light, and is inversely proportional to the group velocity of light. For slow light the angle $\ensuremath{\Delta}{\ensuremath{\alpha}}_{l}$ should be large enough to be detectable. The effect can be used as a tool for measuring the rotation frequency ${\ensuremath{\omega}}_{\text{rot}}$ of the medium.

DOI
10.1103/physreva.76.053822

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We consider the propagation of slow light with an orbital angular momentum (OAM) in a moving atomic medium. We have derived a general equation of motion and applied it in analyzing propagation of slow light with an OAM in a rotating medium, such as a vortex lattice. We have shown that the OAM of slow light manifests itself in a rotation of the polarization plane of linearly polarized light. To extract a pure rotational phase shift, we suggest to measure a difference in the angle of the polarization plane rotation by two consecutive light beams with opposite OAM. The differential angle \ensuremathΔ\ensuremathαl\ensuremath{\Delta}{\ensuremath{\alpha}}_{l}\ensuremathΔ\ensuremathαl​ is proportional to the rotation frequency of the medium \ensuremathωrot{\ensuremath{\omega}}_{\text{rot}}\ensuremathωrot​ and the winding number lll of light, and is inversely proportional to the group velocity of light. For slow light the angle \ensuremathΔ\ensuremathαl\ensuremath{\Delta}{\ensuremath{\alpha}}_{l}\ensuremathΔ\ensuremathαl​ should be large enough to be detectable. The effect can be used as a tool for measuring the rotation frequency \ensuremathωrot{\ensuremath{\omega}}_{\text{rot}}\ensuremathωrot​ of the medium.
We investigate the propagation of optical vector vortices of slow light in a coherently prepared four-level tripod atomic system. The vector vortex consists of superposed pulse pairs with opposite circular polarizations and orbital angular momentum (OAM) charges ±l\pm l±l, weakly interacting with an atomic medium initially prepared in a coherent superposition of two ground states. A third unoccupied state is coupled to a stronger control laser without OAM, creating a phase-dependent configuration. In the linear regime, the vortex OAM is mapped onto the medium, producing symmetrical azimuthally structured absorption patterns, with losses significantly reduced by the control field. For small detunings, complementary spatially dependent amplification and absorption occur for the two circular polarization components. This OAM-structured coherence induces a dynamical anisotropy, affecting both the intensity and polarization of the slow-light vortex. Polarization states evolve periodically between left-circular, linear, and right-circular polarizations during propagation. Once the beam reaches a stationary regime, the ring-shaped intensity transforms into a petal-like structure, and the final polarization states stabilize according to the initial superposition. The rate of polarization transitions is tunable via the control field strength, demonstrating flexible control over slow-light vector vortex dynamics.
We consider the optical rotation of the polarization of a linearly polarized probe field passing through an M-type atomic system by using the interaction between two vortex control fields and optical transitions. We investigate theoretically to generate the spatially dependent structured light with the atoms acting as a spatially varying circular birefringent medium. We show that the polarization and intensity distributions of the vector beam spatially vary by changing the orbital angular momentum (OAM) of the vortex control field.
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 phase 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.
We study the manipulation of slow light with an orbital angular momentum propagating in a cloud of cold atoms. Atoms are affected by four co-propagating control laser beams in a double tripod configuration of the atomic energy levels involved, allowing us to minimize the losses at the vortex core of the control beams. In such a situation the atomic medium is transparent for a pair of co-propagating probe fields, leading to the creation of two-component (spinor) slow light. We study the interaction between the probe fields when two control beams carry optical vortices of opposite helicity. As a result, a transfer of the optical vortex takes place from the control to the probe fields without switching off and on the control beams. This feature is missing in a single tripod scheme where the optical vortex can be transferred from the control to the probe field only during either the storage or retrieval of light.
We consider propagation, storing and retrieval of slow light (probe beam) in a resonant atomic medium illuminated by two control laser beams of larger intensity. The probe and two control beams act on atoms in a tripod configuration of light–matter coupling. The first control beam is allowed to have an orbital angular momentum (OAM). Application of the second vortex-free control laser ensures the adiabatic (lossless) propagation of the probe beam at the vortex core where the intensity of the first control laser goes to zero. Storing and release of the probe beam is accomplished by switching off and on the control laser beams leading to the transfer of the optical vortex from the first control beam to the regenerated probe field. A part of the stored probe beam remains frozen in the medium in the form of atomic spin excitations, the number of which increases with increasing intensity of the second control laser. We analyze such losses in the regenerated probe beam and provide conditions for the optical vortex of the control beam to be transferred efficiently to the restored probe beam.
Optical vortex orbital angular momentum modes, namely the twists number of the light does in one wavelength, play a critical role in quantum-information coding, super-resolution imaging, and high-precision optical measurement. Here, we present the identification of the orbital angular momentum modes based on spatial self-phase modulation in rubidium atomic vapor. The refractive index of atomic medium is spatially modulated by the focused vortex laser beam, and the resulted nonlinear phase shift of beam directly related to the orbital angular momentum modes. The output diffraction pattern carries clearly distinguishable tails, whose number and rotation direction correspond to the magnitude and sign of the input beam orbital angular momentum, respectively. Furthermore, the visualization degree of orbital angular momentums identification is adjusted on-demand in the terms of incident power and frequency detuning. These results show that the spatial self-phase modulation of atomic vapor can provide a feasible and effective way to rapidly readout the orbital angular momentum modes of vortex beam.