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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)
• 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