Quantum Optics II – Cozumel, Dec. 6-9, 2004 J. W. Tabosa Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil tabosa@df.ufpe.br Coherent Spectroscopy of Cold Cesium Atoms Using Light Carrying Orbital Angular Momentum Quantum Optics II – Cozumel, Dec. 6-9, 2004 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) PASI_2003

OUTLINE: First Part: Second Part: Summary and Conclusions 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 Second Part: Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry Coherence Grating Transfer in Cold Atoms. Summary and Conclusions PASI_2003

Phase Dislocation in an Optical Field Dislocations are located in positions where: Screw dislocation (Vortex): Intensity Phase PASI_2003

Laguerre-Gaussian Mode: Orbital and Spin Angular Momentum of Light with Screw Phase Dislocation Topological charge Laguerre-Gaussian Mode: Phase front: (L. Allen et al. PRA, (1992)) Total Angular Momentum: Spin Orbital Total Energy: For Laguerre-Gauss Mode: OAM per Photon: PASI_2003

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

Interferograms for a single charged beam Measuring the topological charge: Reference wave CCD Vortex beam Mask Collinear Noncollinear Interferograms for a single charged beam PASI_2003

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

Nature (2002), Zeilinger et at. Spontaneous Parametric dow-conversion: w w/2 OAM Conservation: Emitted photon state: PASI_2003

OUTLINE: First Part: Second Part: Summary and Conclusions 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 Second Part: Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry Coherence Grating Transfer in Cold Atoms. Summary and Conclusions PASI_2003

Transparency window Dn: ground states dephasing rate g Coherent Effects in Three-Level Systems: Electromagnetically Induced Transparency (EIT) Boller, Imamoglu, Harris, PRL (1991) Coupling field WC Probe field WP a d D Transparency window Dn: ground states dephasing rate g d=0 (Raman resonance) Dw Group Velocity: - Light storage: C. Liu et al, Nature (2001); M.D. Lukin, Rev. Mod. Phys. (2003) PASI_2003

Spatially Modulated EIT Spatially Modulated Coherence: FWM Electromagnetically Induced Grating (EIG) Ling, Li, and Xial, PRA (1998) Spatially Modulated EIT D d Spatially Modulated Coherence: FWM EIT grating -2 -1 1 2 Absorption Spectrum d/G EIT -2 -1 1 2 EIG signal d/G EIG PASI_2003

Coherent spectroscopy in Recife

The Magneto-Optical Trap (MOT) E. Raab, et al (1987) Cold Atoms: I s+ s- Repumping The Magneto-Optical Trap (MOT) E. Raab, et al (1987) Essa é uma representaáo simplificada da armadilha. O vapor de cesio está ampola de quartzo, com ultra alto vacuo, cerca de 10^-9 torr. O resfriamento é porporcionado por tres pares de feixes contrapropagantes, com polarizacoes circulares e opostas, e quase ressonantes com uma transição ciclica do sistema atomico. Para criar um minimo de potencial, que aprisione s a´tmos, utiliza-se um campo magnetico gradiente, que é zero no centro da armadilha e crece em todas as direcoes. Se o atomo tenta escapar, o efeito Zeeman colocao-o em ressonancia com um dos feixes de armadilhaemto que traz de volta o atomo pro centro da armadilha. Essas bobinas bobinas com correntes eletricas em direcoes opostas geram esse campo magnético O que se tem n apratica é um aglomerado de átomos em torno do centro da armadilha, formando uma bola de atomos frios, em nosso caso com cerca de 10 milhoes de atomos num raio de cerca de 1 milimetro. O vacuo evita colisoes com atomos não aprisionados, o que destroi a armadilha. PASI_2003

Transition: 6S1/2 , Fg=4-6P3/2 , Fe=4 Electromagnetically Induced gratings in degenerate two-level system G.C.Cardoso and JWT, PRA (2002) DTLS of Cesium: Transition: 6S1/2 , Fg=4-6P3/2 , Fe=4 F P B S Beams polarization: Scanning frequency: wP wF PASI_2003

OUTLINE: First Part: Second Part: Summary and Conclusions 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 Second Part: Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry Coherence Grating Transfer in Cold Atoms. Summary and Conclusions PASI_2003

FWM in a closed degenerate two-level system Fe=5 Fg=4 d w w-d w+d DTLS of Cesium: Fg=4 – Fe=5 F B P S Two-level systems F P B S Zeeman coherence grating F B P S PASI_2003

Theoretical Model DTLS Fe=2 Fg=1 Master equation: PASI_2003

Measured and Calculated FWM Spectra Lezama, Cardoso, JWT, PRA (2001) Parallel polarization Orthogonal polarization Zeeman coherence grating Narrow dip: quantum interference of Zeeman pairs with different values of mi PASI_2003

Generation of ligth with OAM via coherence induced grating S. Brarreiro and JWT, PRL (2003) Experimental Scheme F P S B (F||B) P 200 KHz PASI_2003

Coherently Generated Beam with OAM Topological charge: m=1 out in Generated reference wave PASI_2003

Topological charge: m=2 in out Energy and linear momentum conservation: OAM conservation: PASI_2003

Generation of coherent Superposition of OAM States

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

OUTLINE: First Part: Second Part: Summary and Conclusions 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 Second Part: Population Grating Transfer in Cold Atoms: Applications for Cold Atoms Velocimetry Coherence Grating Transfer in Cold Atoms. Summary and Conclusions PASI_2003

Population Grating Transfer in Cold Cesium Atoms Bragg diffraction into a transferred population grating w 1 F'=5 F'=4 F'=3 (d) (c) (b) (a) (F//B) ^__ P B ^_ (F//P) F//P//B Observed spectra Cesium D2 Line gT F,w1 P,w1 gR B, w2 D Grating and repumping: Off L=27mm Gaussian fitting Cold atoms velocimetry: Diffraction Decay: PASI_2003

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

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

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

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. Current research: Storage of light carrying OAM in an atomic coherence. Squeezing via four-wave mixing in an EIT medium. PASI_2003