collaborators: prof. a. lezama (inst. of phys. montevideo, uruguay) students: george c. cardoso...
TRANSCRIPT
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Collaborators:Prof. A. Lezama (Inst. of Phys. Montevideo, Uruguay)
Students: George C. Cardoso (PhD, Post-doc/USA)
Sergio Barreiro (PhD)
Financial support: FINEP, CNPq: Pronex, Instituto do Milenio
J. W. Tabosa
Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil [email protected]
Coherent Spectroscopy of Cold Cesium Atoms Using Light Carrying Orbital Angular Momentum
Quantum Optics II – Cozumel, Dec. 6-9, 2004
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OUTLINE:
Second Part:• Population Grating Transfer in Cold Atoms: Applications for Cold Atoms
Velocimetry
• Coherence Grating Transfer in Cold Atoms.
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
Summary and Conclusions
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Phase Dislocation in an Optical Field
)],,(exp[),(),,( zrizrAzrE
Dislocations are located in positions where:
0)},,(Im{)},,(Re{ zrEzrE
Screw dislocation (Vortex):
0)}(Im{
0)}(Re{
0
0
rE
rE
IntensityPhase
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Orbital and Spin Angular Momentum of Light with Screw Phase Dislocation
Phase front:
Total Energy: }{2
30 EErdW
(L. Allen et al. PRA, (1992))
Total Angular Momentum: }{30 BErrdJ
SpinOrbital
SL
)],([exp),(),,( zrmizrAzrE
Topological charge
Laguerre-Gaussian Mode:
mPhotonLz OAM per Photon:
For Laguerre-Gauss Mode: )(1
mW
J zonpolarizaticircular
onpolarizatilinear
,1
,0
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Generation of Vortex Beams•Mode Converter:
•Computer-generated holograms:
m=1 m=2
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Collinear Noncollinear
Interferograms for a single charged beam
Measuring the topological charge:
Reference wave
CCD
Vortex beamMask
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Mach-Zehnder Interferometer: mode selector
mshiftPhase :
m=even
m=odd
m
Arbitrary mode selector:
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Nature (2002), Zeilinger et at.
OAM Conservation:
Spontaneous Parametric dow-conversion:
...111100 1,11,10,0 CCC
Emitted photon state:
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OUTLINE:
Second Part:• Population Grating Transfer in Cold Atoms: Applications for Cold Atoms
Velocimetry
• Coherence Grating Transfer in Cold Atoms.
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
Summary and Conclusions
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Coherent Effects in Three-Level Systems: Electromagnetically Induced Transparency (EIT)
Boller, Imamoglu, Harris, PRL (1991)b
c
Coupling field
C
Probe field
P
a
Transparency window ground states dephasing rate
Raman resonance)
ddn
n
c
dk
dVg
Group Velocity:
R
- Light storage: C. Liu et al, Nature (2001); M.D. Lukin, Rev. Mod. Phys. (2003)
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Electromagnetically Induced Grating (EIG)Ling, Li, and Xial, PRA (1998)
-2 -1 0 1 2Ab
sorp
tio
n S
pec
tru
m
EIT
-2 -1 0 1 2
EIG
sig
na
l
EIG
Spatially Modulated EIT
ca
)(rC
b
P
Spatially Modulated Coherence: FWM
EIT gratingC~
C~
P
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Coherent spectroscopy in Recife
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Cold Atoms:
KmKT
cmatoms
atomsN
310
7
/10
10
I
I
Repumping
The Magneto-Optical Trap (MOT)
E. Raab, et al (1987)
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Scanning frequency:P F
F PBS
BPF )||(Beams polarization:
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
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OUTLINE:
Second Part:• Population Grating Transfer in Cold Atoms: Applications for Cold Atoms
Velocimetry
• Coherence Grating Transfer in Cold Atoms.
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
Summary and Conclusions
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FWM in a closed degenerate two-level system
Fe=5
Fg=4
DTLS of Cesium: Fg=4 – Fe=5
F BP
S
Zeeman coherence grating
F BPS
PBF )||(
Two-level systems
BPF ||||F
P
B
S
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Theoretical Model
Master equation:
DTLS Fe=2
Fg=1
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Measured and Calculated FWM Spectra
Lezama, Cardoso, JWT, PRA (2001)
Parallel polarization
BPF ||||
•Narrow dip: quantum interference of Zeeman pairs with different values of mi
Orthogonal polarization
PBF )||(
•Zeeman coherence grating
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Generation of ligth with OAM via coherence induced grating
Experimental Scheme
FPS
B
(F||B) P
200 KHz
S. Brarreiro and JWT, PRL (2003)
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Coherently Generated Beam with OAMTopological charge: m=1
outin
Generated reference wave
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Topological charge: m=2
in out
OAM conservation:
PPBFS LLLLL
PSBFS KKKKK
Energy and linear momentum conservation:
PBFS
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Generation of coherent Superposition of OAM States
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m=1+m=2
m=0+m=1+m=2
Incident and generated superposition of OAM
IN OUT
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)2exp( iab
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OUTLINE:
Second Part:• Population Grating Transfer in Cold Atoms: Applications for Cold Atoms
Velocimetry
• Coherence Grating Transfer in Cold Atoms.
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
Summary and Conclusions
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Population Grating Transfer in Cold Cesium Atoms Bragg diffraction into a transferred population grating
F'=5 F'=4 F'=3
(d)
(c)
(b)
(a)
(F//B) P
B (F//P)
F//P//B
Observed spectra
2
)(
G
t
D etI Diffraction Decay:
Cesium D2 Line
R
T
F,
P,
B, D
Grating and repumping: Off
mGaussian fitting
Cold atoms velocimetry:
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Coherence transfer: •theoretical model (V-scheme)
Master Equation: (Barrat and C. Cohen-Tannoudji) g g, ;1 1
e e, ; 1 1
W W,
SE
R
g e, ; ,1 0
DDiffracted spectrum:
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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.
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Experimental observation of Zeeman grating transfer
Cesium level scheme:
Observed Bragg diffraction spectra:
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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.