1. Quantum Optics II – Cozumel, Dec. 6-9, 2004
J. W. Tabosa
Departamento de Física, Universidade Federal de Pernambuco, Recife, PE, Brazil
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)
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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
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3. Phase Dislocation in an Optical Field
Dislocations are located in positions where:
Screw dislocation (Vortex):
Intensity
Phase
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4. 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:
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5. Generation of Vortex Beams
Mode Converter:
Computer-generated holograms:
m=1
m=2

6. Interferograms for a single charged beam
Measuring the topological charge:
Reference wave
CCD
Vortex beam
Mask
Collinear
Noncollinear
Interferograms for a single charged beam
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8. Arbitrary mode selector:
Mach-Zehnder Interferometer: mode selector m
m=even
m=odd
Arbitrary mode selector:

9. Nature (2002), Zeilinger et at.
Spontaneous Parametric dow-conversion: w
w/2
OAM Conservation:
Emitted photon state:
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10. 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
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11. 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)
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12. 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
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13. Coherent spectroscopy in Recife

14. 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.
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15. 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
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16. 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
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17. 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
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18. Theoretical Model
DTLS
Fe=2
Fg=1
Master equation:
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19. 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
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20. 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
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21. Coherently Generated Beam with OAM
Topological charge: m=1
out in
Generated reference wave
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22. Topological charge: m=2in
out
Energy and linear momentum conservation:
OAM conservation:
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23. Generation of coherent Superposition of OAM States

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

26. 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
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27. 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:
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28. theoretical model (V-L scheme)
Coherence transfer:
theoretical model (V-L scheme) SE
Master Equation: (Barrat and C. Cohen-Tannoudji)
Diffracted spectrum:

29. 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.

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

31. 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.
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