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### Transcript of Electromagnetically induced transparency (EIT) Electromagnetically induced transparency (EIT)...

• Electromagnetically induced transparency (EIT)

Norbert Kalb 19.6.2013

• Intro

Absorption

Suppress absorption by avoiding population in the excited state!

ℏω ℏω

nℏω (n-1)ℏω

a) Detune frequency c) EIT b) Saturate absorber

• 1. Basics and first observation

2. EIT with a single atom in a cavity

3. Slow light in ultracold atomic gases

4. Summary

Intro

Outline

J. Q. You et al., Nature 474, 589 (2011)

• 2 Ωp 2 + Ωc

2

ℏ H|D =

0 0 Ωp 0 0 Ωc Ωp Ωc 0

Ωc −Ωp 0

=

3-level Hamiltonian on resonance: H = ℏ

2

0 0 Ωp 0 0 Ωc Ωp Ωc 0

Apply Hamiltonian to |D :

|D is eigenvector of H and contains no contribution of the excited state

2-level Hamiltonian on resonance: ℏ

2

0 Ωp Ωp 0

0 0

ΩcΩp − ΩpΩc = 0|D

Basics and first observation

A dark eigenvector

Eigenstates of the Hamiltonian:

|𝜑+ = 1

2 sin 𝜃 1 + cos 𝜃 2 + |3

|𝜑− = 1

2 sin 𝜃 1 + cos 𝜃 2 − |3

|D = Ωp 2 + Ωc

2 −1

Ωc|1 − Ωp|2

|1

|2 ωp, Ωp

ωc, Ωc |3

• 2 Ωp 2 + Ωc

2

ℏ H|D =

0 0 Ωp 0 0 Ωc Ωp Ωc 0

Ωc −Ωp 0

=

Apply Hamiltonian to |D :

|D is eigenvector of H and contains no contribution of the excited state

0 0

ΩcΩp − ΩpΩc = 0|D

Basics and first observation

A dark eigenvector

Eigenstates of the Hamiltonian:

|𝜑+ = 1

2 sin 𝜃 1 + cos 𝜃 2 + |3

|𝜑− = 1

2 sin 𝜃 1 + cos 𝜃 2 − |3

|D = Ωp 2 + Ωc

2 −1

Ωc|1 − Ωp|2

|1

|2 Ωp

Ωc |3

• |3

|1 |2

Basics and first observation

Interference of excitation paths

Excitation path |2 → |3 Excitation path |1 → |3

|D ∝ Ωc|1 − Ωp|2

• K. J. Boller et al , PRL 66, 2593 (1991)

ωp

ωc

|3

|1 |2

|3

|1

Basics and first observation

First experimental observation

• K. J. Boller et al , PRL 66, 2593 (1991)

ωp

ωc

|3

|1 |2

Basics and first observation

First experimental observation

• Basics and first observation

Linewidth of the EIT feature

Probe the lifetime of the dark state

|1 |2

Both states in |D can not decay spontaneously.  Dephasing mechanisms result in decay time • Collisions

• Fluctuating magnetic fields

p p‘

M. Fleischhauer et al. , Rev. Mod. Phys. 66, 2593 (2005)

ν32 ∝ M32 2ρ E32 ∝ Ωc

2

Γ If Γ ≫ Ωc, treat population transfer by Ωc as perturbation

Transition rate:

 Broadening of EIT feature is proportional to Ωc 2

Heisenberg‘s uncertainty principle ∆E ⋅ ∆t ≥ ℏ

⇒ Γ|𝐷 = 1/τ|𝐷

• Combining both spectra hints at the response of the system

ωp

ωc

ωp

Cavity QED EIT medium

Cavity EIT

Principle

• Empty resonator Cavity QED Cavity EIT

Cavity EIT

Experimental procedure

M. Mücke et al., Nature 465, 755 (2010)

• M. Mücke et al., Nature 465, 755 (2010)

N ≈ 15 atoms

Cavity EIT

Multiple atoms Empty resonator Cavity QED Cavity EIT

Contrast

• Cavity EIT

Changing the number of atoms

M. Mücke et al., Nature 465, 755 (2010)

Empty resonator Cavity QED Cavity EIT

N = 4 atoms N = 7 atoms

• Cavity EIT

A single atom Empty resonator Cavity QED Cavity EIT

M. Mücke et al., Nature 465, 755 (2010)

• • Linewidth is proportional to |Ωc| 2

• Contrast is limited by the coupling constant g

• Effective light-light interaction mediated by a single atom

Cavity EIT

Coherent control of the system‘s parameters

M. Mücke et al., Nature 465, 755 (2010)

• 1. Basics and first observation

2. EIT with a single atom in a cavity

3. Slow light in ultracold atomic gases

4. Summary

J. Q. You et al., Nature 474, 589 (2011)

Slow light

Outline

• Absorption coefficient: Refractive index: n ≈ 1 + Re(χ)/2

A = Im(χ)

Re(χ(ω′)) = 1

π Im(χ(ω))

ω − ω′ dω

+∞

−∞

Kramers-Kronig relations

• Steep linear feature around dark state

• Width of the feature is determined by width of transparency window ∝|Ωc|

2

Slow light

Refractive index of EIT media Tr

an sm

is si

o n

( %

) R

ef . i

n d

ex

Probe detuning (MHz)

• Susceptibility : Response of several atoms adds up!

ωp

ωc

χ = χ N = 1,ωp

ωc

ωp

χ = N ⋅ χ N = 1,ωp

∝ |Ω𝑐| 2

Group velocity of a pulse in homogeneous media

k = n ω ω

c vg =

dk

−1

= c

n + ω dn dω

= c

1 + ωp dn dωp

Slope of the refractive index around the dark state?

vg ∝ |Ωc|

2

N

Slow light

Group velocity and slow pulses

L. V. Hau et al., Nature 397, 594 (1999)

• • BECs have a very high optical density! Absorption = 1 − e−110 ≈ 1 − 10−48

• Sodium atoms trapped at nK temperature

• Camera 1 helps adjusting the pinhole

• Camera 2 provides the length of the cloud

Slow light

Experimental setup

L. V. Hau et al., Nature 397, 594 (1999)

Control beam

• Slow light

Group velocity measurements

PM

Reference shot

PM

Slow pulse

L

L. V. Hau et al., Nature 397, 594 (1999)

• vg ∝ |Ωc|

2

N

Slow light

Changing parameters

L. V. Hau et al., Nature 397, 594 (1999)

• • Opaque media become transparent when a tailored control field is applied

• Cavity EIT gives rise to strong non-linearities from single atoms

• Usain Bolt could outrun light! (Under very restricted conditions)

Summary

• Thank you for your attention!

Dr. Stephan Ritter Manuel Brekenfeld