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 tabosa@df.ufpe.br

Coherent Spectroscopy of Cold Cesium Atoms Using Light Carrying Orbital Angular Momentum

Quantum Optics II – Cozumel, Dec. 6-9, 2004

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

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

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

Generation of Vortex Beams•Mode Converter:

•Computer-generated holograms:

m=1 m=2

Collinear Noncollinear

Interferograms for a single charged beam

Measuring the topological charge:

Reference wave

CCD

Vortex beamMask

Mach-Zehnder Interferometer: mode selector

mshiftPhase :

m=even

m=odd

m

Arbitrary mode selector:

Nature (2002), Zeilinger et at.

OAM Conservation:

Spontaneous Parametric dow-conversion:

...111100 1,11,10,0 CCC

Emitted photon state:

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

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)

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

Coherent spectroscopy in Recife

Cold Atoms:

KmKT

cmatoms

atomsN

310

7

/10

10

I

I

Repumping

The Magneto-Optical Trap (MOT)

E. Raab, et al (1987)

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

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

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

Theoretical Model

Master equation:

DTLS Fe=2

Fg=1

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

Generation of ligth with OAM via coherence induced grating

Experimental Scheme

FPS

B

(F||B) P

200 KHz

S. Brarreiro and JWT, PRL (2003)

Coherently Generated Beam with OAMTopological charge: m=1

outin

Generated reference wave

Topological charge: m=2

in out

OAM conservation:

PPBFS LLLLL

PSBFS KKKKK

Energy and linear momentum conservation:

PBFS

Generation of coherent Superposition of OAM States

m=1+m=2

m=0+m=1+m=2

Incident and generated superposition of OAM

IN OUT

)2exp( iab

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

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:

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:

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.