Electromagnetically induced transparency (EIT) Electromagnetically induced transparency (EIT)...

Click here to load reader

  • date post

    19-Jun-2020
  • Category

    Documents

  • view

    6
  • download

    0

Embed Size (px)

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

    • Broadening by applied 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