Predictions of Multilevel Coherent Population Trapping in Lithium7

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Predictions of Multi-level Coherent Population
Trapping in Lithium-7
J.N. Philippson, R.C. Shiell
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Features of the L-System

• Closely spaced ground states and
• Large separation between ground states and
  excited state
• The transition is dipole
  forbidden
• Monochromatic light fields, with frequencies
  , near-resonant with and
  transitions respectively
• D1, D2 are detunings for each transition,
  
• W31 and W32 are the Rabi frequencies, giving the
  coupling of the laser beams to the respective
  transitions
• Separation of ground states sufficient to
  prevent crosstalk, i.e. W3x depends only on
  intensity of light with frequency
• Decay from with rate G, to states outside
  the L-system. No relaxation within system.

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The L-System
rxx gives the population of state
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Amplitude Equations
Interaction picture
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L-System, Evidence of CPT
Decay from reduces the total system
population.
Note the finite steady state population.
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The Dark/ Absorbing Basis
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Coherent Population Trapping
The remaining population oscillates between
and , decaying with rate G.
The dark state is a coherent superposition of
states and , which does not absorb
energy from either light field.
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Departure from Raman Detuning
Raman detuning
Departure from Raman detuning leads to decay of
the dark state.
Once D1 is large enough, the slower transfer to
causes the time-constant to increase.
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Adiabatic Population Transfer (APT)

• Light field on dark state composed
  entirely of .
• Adiabatic transfer slowly turn off ,
  while turning on .
• Light field off population entirely
  in .

Population may be transferred across forbidden
transitions
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APT Linear Change in Electric Field
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Quantifying Non-Adiabaticity
At low slew-rates, we observe a roughly linear
relationship
At high slew-rates population loss is constant.
A truly adiabatic process occurs at an
infinitesimal rate
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Stimulated Raman Adiabatic Passage (STIRAP)
Partially overlapping laser beams provide the two
light fields.
Coherent population transfer among quantum states
of atoms and molecules, K. Bergmann, H. Theuer,
and B. W. Shore, Reviews of Modern Physics, Vol.
70, No. 3, July 1998
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APT Gaussian Change in Intensity
STIRAP provides a practical way to effect
adiabatic population transfer in an atomic or
molecular beam.
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STIRAP Non-Adiabaticity
Normalised Gaussian beam
At larger beam-widths population loss is constant.
Population loss is small even for low beam-widths
efficient population transfer technique.
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Features of the Double L-System

• Second excited level with separation from
  given by D4, small enough that laser with
  frequency couples to both and
  transitions
• Dx D4 gives the detuning of laser frequency
  from the transition
• Existence of dark state depends on relative
  phases of light fields and atomic wavefunction
• Relaxation rates from excited state to
  state(s) outside the system, given by Gy
• Both and transitions
  dipole forbidden
• Again no relaxation within the system.

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The Double L-System
rxx gives the population of state
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Level Schemes of Atomic Lithium
Double L-system in hyperfine structure of both
stable isotopes.
4-level results presented, based on 7Li level
scheme D1 line.
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Double L-System Phase Dependence
The double L-system is a closed level scheme in
which the relative phases of the light and the
atomic wavefunction become important in
determining behaviour.
symmetric
anti-symmetric
Coherent Population Trapping in Multi-Level
Atomic Systems, L. Windholz Physica Scripta. T95,
81-91 (2001)
Maintaining a dark state requires a symmetric
phase condition.
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Phase Dependent Coherent Population Trapping
symmetric
anti-symmetric
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APT Linear Change in Intensity
APT based on a linear change in intensity,
produces dramatic oscillations. As yet these
have no physical explanation and may be an
artefact of the simulation.
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Quantifying Non-Adiabaticity
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Double L-System No Relaxation
A double L-system illuminated with light
frequencies and , exhibits a long
period oscillation in the maxima and minima.
D1 D2 0,
D4 94 MHz
Light fields only weakly coupled to
transitions very little population
driven into state .
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Decoupling the 4th Level
Sensitivity of system to phase condition depends
on frequency splitting of
transition.
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Double L-System 4 Light Frequencies
We still observe coherent population trapping.
Transitions are now driven as
strongly as .
The added frequencies are evident in the system
behaviour.
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Collisional Dephasing
Phase changing collisions redistribute population
within the system.
Although dark state population is lost, some
remains.