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Collaborators: Prof. A. Lezama (Inst. of Phys. Montevideo, Uruguay)

Quantum Optics II – Cozumel, Dec. 6-9, 2004. Coherent Spectroscopy of Cold Cesium Atoms Using Light Carrying Orbital Angular Momentum. J. W. Tabosa Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil tabosa@df.ufpe.br.

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Collaborators: Prof. A. Lezama (Inst. of Phys. Montevideo, Uruguay)

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  1. Quantum Optics II – Cozumel, Dec. 6-9, 2004 Coherent Spectroscopy of Cold Cesium Atoms Using Light Carrying Orbital Angular Momentum J. W. Tabosa Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Braziltabosa@df.ufpe.br Financial support: FINEP, CNPq: Pronex, Instituto do Milenio Collaborators: Prof. A. Lezama (Inst. of Phys. Montevideo, Uruguay) Students: George C. Cardoso (PhD, Post-doc/USA) Sergio Barreiro (PhD)

  2. First Part: • Introduction: The Orbital Angular Momentum (OAM) of Light(Entanglement of OAM states in Parametric Down Conversion) • Electromagnetically Induced Transparency (EIT)andElectromagnetically Induced Grating (EIG) • Coherent Four-Wave Mixing Using Light with OAM: Generation of Superposition of OAM states OUTLINE: • Second Part: • Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry • Coherence Grating Transfer in Cold Atoms. • Summary and Conclusions

  3. Dislocations are located in positions where: Intensity Screw dislocation (Vortex): Phase Phase Dislocation in an Optical Field

  4. Laguerre-Gaussian Mode: Topological charge Phase front: For Laguerre-Gauss Mode: Total Angular Momentum: Total Energy: Orbital Spin OAM per Photon: Orbital and Spin Angular Momentum of Light with Screw Phase Dislocation (L. Allen et al. PRA, (1992))

  5. Mode Converter: Computer-generated holograms: m=1 m=2 Generation of Vortex Beams

  6. Mask Vortex beam CCD Reference wave Interferograms for a single charged beam Noncollinear Collinear Measuring the topological charge:

  7. m Arbitrary mode selector: Mach-Zehnder Interferometer: mode selector m=even m=odd

  8. Spontaneous Parametric dow-conversion: w/2 w w/2 OAM Conservation: Emitted photon state: Nature (2002),Zeilinger et at.

  9. First Part: • Introduction: The Orbital Angular Momentum (OAM) of Light (Entanglement of OAM states in Parametric Down Conversion) • Electromagnetically Induced Transparency (EIT)andElectromagnetically Induced Grating (EIG) • Coherent Four-Wave Mixing Using Light with OAM: Generation of Superposition of OAM states OUTLINE: • Second Part: • Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry • Coherence Grating Transfer in Cold Atoms. • Summary and Conclusions

  10. d Coupling field WC Probe field WP D a Dw d=0(Raman resonance) Group Velocity: Transparency windowDn: ground states dephasing rateg Coherent Effects in Three-Level Systems:Electromagnetically Induced Transparency(EIT)Boller, Imamoglu, Harris, PRL (1991) - Light storage: C. Liu et al, Nature (2001); M.D. Lukin, Rev. Mod. Phys. (2003)

  11. Spatially Modulated Coherence: FWM Spatially Modulated EIT D d EIT grating EIT EIG EIG signal Absorption Spectrum -2 -1 0 1 2 -2 -1 0 1 2 d/G d/G Electromagnetically Induced Grating (EIG)Ling, Li, and Xial, PRA (1998)

  12. Coherent spectroscopy in Recife

  13. s+ The Magneto-Optical Trap (MOT)E. Raab, et al (1987) s+ I s- s+ s- I s- Repumping Cold Atoms:

  14. Beams polarization: B F S P Scanning frequency: wP wF Electromagnetically Induced gratings in degenerate two-level systemG.C.Cardoso and JWT, PRA (2002) DTLS of Cesium: Transition: 6S1/2 , Fg=4-6P3/2 , Fe=4

  15. First Part: • Introduction: The Orbital Angular Momentum (OAM) of Light (Entanglement of OAM states in Parametric Down Conversion) • Electromagnetically Induced Transparency (EIT) and Electromagnetically Induced Grating (EIG) • Coherent Four-Wave Mixing Using Light with OAM: Generation of Superposition of OAM states OUTLINE: • Second Part: • Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry • Coherence Grating Transfer in Cold Atoms. • Summary and Conclusions

  16. DTLS of Cesium: Fg=4 – Fe=5 Fe=5 d w w F B w-d P w+d Fg=4 S Two-level systems B F P S Zeeman coherence grating B F P S FWM in a closed degenerate two-level system

  17. DTLS Fe=2 Fg=1 Master equation: Theoretical Model

  18. Parallel polarization Orthogonal polarization Zeeman coherence grating Measured and Calculated FWM Spectra Lezama, Cardoso, JWT, PRA (2001) Narrow dip: quantuminterference of Zeeman pairs with different values of mi

  19. Experimental Scheme B S P (F||B) P F 200 KHz Generation of ligth with OAM via coherence induced grating S. Brarreiro and JWT, PRL (2003)

  20. Topological charge: m=1 out in Generated reference wave Coherently Generated Beam with OAM

  21. Energy and linear momentum conservation: OAM conservation: Topological charge: m=2 out in

  22. Generation of coherent Superposition of OAM States

  23. Incident and generated superposition of OAM IN OUT m=1+m=2 m=0+m=1+m=2

  24. First Part: • Introduction: The Orbital Angular Momentum (OAM) of Light (Entanglement of OAM states in Parametric Down Conversion) • Electromagnetically Induced Transparency (EIT) and Electromagnetically Induced Grating (EIG) • Coherent Four-Wave Mixing Using Light with OAM: Generation of Superposition of OAM states OUTLINE: • Second Part: • Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry • Coherence Grating Transfer in Cold Atoms. • Summary and Conclusions

  25. Observed spectra (a) F'=3 F'=4 F'=5 F,w1 F//P//B (b) P,w1 gR (c) ^_ (F//P) B D (d) P (F//B) ^__ B, w2 Grating and repumping: Off w 1 Cold atoms velocimetry: L=27mm Gaussian fitting gT Diffraction Decay: Population Grating Transfer in Cold Cesium Atoms Bragg diffraction into a transferred population grating Cesium D2 Line

  26. SE Diffracted spectrum: Coherence transfer: • theoretical model (V-L scheme) Master Equation: (Barrat and C. Cohen-Tannoudji)

  27. Experimental setup: - MOT beams and magnetic field are switched off. Observation of grating coherence transfer:S. Barreiro and JWT, to appear in PRA (2005) Cesium level scheme:

  28. Experimental observation of Zeeman grating transfer Cesium level scheme: Observed Bragg diffraction spectra:

  29. Current research: • Storage of light carrying OAM in an atomic coherence. • Squeezing via four-wave mixing in an EIT medium. Summary and Conclusions • Generation of superposition states of OAM via coherence grating:possibility to store a multidimensional quantum state of light in a long-lived atomic coherence. Theoretical and experimental demonstration of coherence grating transfer between different pairs of Zeeman sublevels.

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