Detection Sensitive Systematic Effects in 1S-3S spectroscopy of Atomic Hydrogen

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Detection Sensitive Systematic Effects in
1S-3S spectroscopy of Atomic Hydrogen

• Arthur Matveev, Elisabeth Peters, Dylan C. Yost,
  
• Theodor W. Hänsch, Thomas Udem
• Max-Planck-Institute für Quantenoptik

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Hydrogen spectroscopy and fundamental constants
Frequency of transition in Hydrogen can be
calculated from fundamental constants Fine
structure constant and electron to proton mass
ratio are measured with high precision. From two
transitions one can calculate Rydberg constant
and proton charge radius.
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Proton size puzzle Hydrogen measurements
Plot is taken from R. Pohl et. al.,
arXiv1301.0905v2
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Proton size puzzle electron scattering data
Plot is taken from R. Pohl et. al.,
arXiv1301.0905v2
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1S-3S Transition
Our goal is to measure a proton charge radius via
the measurement of 1S-3S transition in atomic
hydrogen.
Excitation laser wavelength 205 nm Detection of
the excited atoms can be done via detection of
3S-2P decays or 2P-1S decays Acuraccy needed 1
kHz to contribute into the Proton Size Puzzle
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Two-photon excitation with a frequency comb
With CW laser
With Mode-locked laser
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Setup
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Detector
Balmer alpha photons from 3s/3d decays are
coupled into the multimode fibers leading out of
the vacuum chamber. They are passing interference
filter and then counted with a PMT head
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Experimental lineshape 328 MHz
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Line pulling

• Simple example Toy hydrogen
• There are two models
• Perturbation model
• Optical Bloch equations

Incoherent line pulling
Coherent line pulling
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Playing with Repetition rate 329 MHz
Repetition rate 329 MHz
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Playing with Repetition rate 315 MHz
Repetition rate 315 MHz
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Playing with Repetition rate 348 MHz
Repetition rate 348 MHz
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Experimental line 328.16 MHz
Statistical uncertainty 25 kHz in one day
measurement
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Coherent line pulling modeling

• Master Equation model implements
• a density matrix formalism
• Total number of states for hydrogen 32
• Total number of differential equations 1024
• To speed up the calculation we have implemented
• two-steps
• First program (Mathematica 8) derive the
• Equations and generate C code for second step
• -Second step (C) fast code calculates the
• behavior of the atom

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Coherent line pulling
300 K beam
5 K beam
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Coherent line pulling delayed detection
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Coherent line pulling Line centers
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Delayed detection with rectangular window
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Delayed detection with rectangular window
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Second Order Doppler Shift
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AC Stark shift
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DC Stark shift patch charges
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DC Stark shift line shift in strong field
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DC Stark shift linewidth in strong field
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Pressure shift

• Modeling of the pressure shift
• in Impact approximation
• - Calculate interaction potential between
• 1s and 3s atoms.
• Calculate a phase shift in elementary
• collision of two atoms
• Integrate over velocity distribution and
• Impact parameter

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Summary
Effect Correction Uncertainty
Incoherent line pulling lt0.1 kHz lt0.1 kHz
Coherent line pulling 2 kHz 1 kHz
Second order Doppler 1.1 kHz 0.2 kHz
AC Stark shift -0.2 kHz 0.02 kHz
DC Stark shift -0.2 kHz 0.2 kHz
Pressure shift 1-10 kHz 1 kHz
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Thank you for attention
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Photoionization detector of Ly-alpha photons
Ly-alpha photons (121 nm) ionize benzene
molecules, starting avalanche-like discharge
Scattered 205 nm photons doesnt ionize gas since
the energy of the photon is not enough
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New detector Ba-alpha photons
Balmer-alpha photons (656 nm) are collected into
a fiber mode (7 multimode fibers with NA1.2)
without additional optics. The tip of the fiber
is 0.5 mm away from the pulse collision
point. Interference filter after the fiber is
used to separate Balmer-alpha photons. The
photons are counted using the PMT.