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 Ωp2 + Ωc

2

ℏH|D =

0 0 Ωp0 0 ΩcΩp Ωc 0

Ωc−Ωp0

=

3-level Hamiltonian on resonance: H =ℏ

2

0 0 Ωp0 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 ΩpΩp 0

00

ΩcΩp − ΩpΩc= 0|D

Basics and first observation

A dark eigenvector

Eigenstates of the Hamiltonian:

|𝜑+ = 1

2sin 𝜃 1 + cos 𝜃 2 + |3

|𝜑− = 1

2sin 𝜃 1 + cos 𝜃 2 − |3

|D = Ωp2 + Ωc

2 −1

Ωc|1 − Ωp|2

|1

|2 ωp, Ωp

ωc, Ωc |3

2 Ωp2 + Ωc

2

ℏH|D =

0 0 Ωp0 0 ΩcΩp Ωc 0

Ωc−Ωp0

=

Apply Hamiltonian to |D :

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

00

ΩcΩp − ΩpΩc= 0|D

Basics and first observation

A dark eigenvector

Eigenstates of the Hamiltonian:

|𝜑+ = 1

2sin 𝜃 1 + cos 𝜃 2 + |3

|𝜑− = 1

2sin 𝜃 1 + cos 𝜃 2 − |3

|D = Ωp2 + 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

• Broadening by applied fields

p p‘

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

ν32 ∝ M322ρ E32 ∝ Ωc

2

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

Transition rate:

Broadening of EIT feature is proportional to Ωc2

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

ansm

issi

on

(%

) R

ef. i

nd

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

dω

−1

= c

n + ωdndω

=c

1 + ωpdndωp

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