Electromagnetically Induced

Transparency (EIT)

b⟩c⟩

a⟩ γ γ

EC EP

D⟩B⟩

a⟩ γ γ

Bright and dark states:

Atomsdo not “see” light!2

P2C EE +

2C

2P

CP

EE

cEbEB

+

+=

2C

2P

PC

EE

cEbED

+

−=

Electromagnetically Induced

Transparency (EIT)

b⟩c⟩

a⟩ γ γ

EC EP

δ

Tran

smis

sion

δProbe frequency

Width of EIT peak is determined by control field intensity , but limited by spin coherence lifetime

Slow light via Electromagnetically

Induced Transparency (EIT)R

efra

ctiv

e in

dex

Probe frequency

Tran

smis

sion

1ddn >>

ωω

Steep dispersion

Narrow transmission resonance

LN

1E2

2C

EITλγ

∝γ

Group velocity manipulation

Ele

ctric

fiel

d

Light propagation direction

Group velocity

ωω+

=ω=

ddn

n

cdk

)k(dvg

Group velocity manipulation

Group velocity

ωω+

=ω=

ddn

n

cdk

)k(dvg

“Slow” light

1ddn >>

ωω vg<<c

reference

delayedpulse

Ele

ctric

fiel

d

Light propagation direction

vg=50m/s

Group velocity manipulation

Group velocity

ωω+

=ω=

ddn

n

cdk

)k(dvg

“Fast” light

0ddn <

ωω vg>c or vg<0

Ele

ctric

fiel

d

Light propagation direction

reference

advanced pulse

Time (ms)

vg=-180m/s

Group velocity manipulation

Eugeniy E. Mikhailov, Vladimir A. Sautenkov, Irina Novikova, and George R. WelchPhys. Rev. A 69, 063808 (2004)

Slow light in EITR

efra

ctiv

e in

dex Steep dispersion in EIT

means controllableslow group velocity

Probe frequency

Tran

smis

sion

γλπ∝

2C

2g

EN38

v

Group velocity

0ddn >>

ωω

What happens when control field goes to zero?

Coupling of a probe pulse and a spin

wave

b⟩c⟩

a⟩ γ γ

EC

Dark state:

2C

2P

PC

EE

cEbED

+

−=

b⟩c⟩

a⟩ γ γ

EC EP

Light-atoms interaction:

dark-state polariton

bcP ˆNsinEcosˆ σθ−θ=Ψ

Cg E

c

vcos ∝=θ

Photons of the probe field

Excitations of the spin wave

M. Fleischhauer and M.D. LukinPRL 84, 5094 (2000)

θ−θ=Ψ sincosˆ

Quantum memory for photons

γαΩ

=2

2v g

Ideal memory operation

How long does the dark state live?

Cold atoms

No Doppler broadening, butthere may be difficulties due to - uncompensated magnetic

fields- gravity- insufficient number of atoms- collisions between atoms

These are technical problems – if all are fixed, the ground state coherence was shown to live up to several seconds!

How long does the dark state live?

atoms fly away !

With buffer gas

No buffer gas Tva

t =a

with anti-relaxation coating

vT ≈ 400m/sRb cell

How long does the dark state live?

With buffer gaswith anti-relaxation coating

0 2.5 5−2.5−50.1

0.2

0.3

0.4

0.5

0.6

Two−photon detuning Ω (MHz)

Nor

mal

ized

tran

smis

sion