High precision spectroscopy of positronium
D. A. Cooke1, P. Crivelli1, J. Alnis2, A. Antognini1, K. Kirch1,
A. Rubbia1, B. Brown3, T. Haensch2
1ETH Zurich Institute for Particle Physics, Otto Stern Weg 5, 8093 Zurich,Switzerland
2Max-Planck-Institute of Quantum Optics, D-85741 Garching, Germany
3Physics Department, Marquette University, 1250 W. Wisconsin Avenue,Milwaukee, WI 53233, USA
October 23, 2015
Positronium
Positronium is the bound state of positron and electron:
• Para-positronium
• Decays into 2 511 keV
photons
• Lifetime 125 ps
• Ortho-positronium
• Decays into 3 photons.
1.022 MeV shared
between them
• Lifetime 142 ns
Positronium spectroscopy
• Purely leptonic system—good for testing bound state QED.
• Free from finite nuclear size effects.
Contribution H-like atom Ps
Schrodinger contributions
• with M = ∞ 1 1
• with mR corr. mM
1
Relativistic corrections
• Dirac equation Zα)2α
2
• two-body effects (Zα)2 mM
α2
Quantum electrodynamics
• self-energy α(Zα)2 ln(Zα) α3 lnα
• radiative width α(Zα)2α
3
• vacuum polarization α(Zα)2α
3
• annihilation (virtual) — α2
• annihilation (real) — α3
Nuclear effects
• magnetic moment (Zα)2 mM
α2
• charge distribution(
ZαmcRN~
)
—
Ps spectroscopy
• Two-photon excitation at 486
nm.
• Natural linewidth dominated by
lifetime of ground state
(compare with 1.3 Hz for 1S–2S
transition in H).
• Use two counter-propagating
beams to eliminate 1st-order
Doppler broadening.
Status of 1S-2S Ps determination
• Previously measured in the 1980s and 90s:a,b
Calculations of this now include terms up to α7c. For this experiment:
• Initial precision aim is 0.5 ppb
• Sufficient to test α7 level calculations.• Would provide highest precision determination of positron:electron mass
ratio to date.
aS. Chu, A. P. Mills and J. L. Hall, Phys. Rev. Lett., 52, 1689, (1984)bM. S. Fee, S. Chu, A. P. Mills, R. J. Chichester, D. M. Zuckerman, E. D.
Shaw and K. Danzmann, Phys. Rev. A, 48, 192, (1993)cK. Pachucki and S. G. Karshenboim, Phys. Rev. A, 60, 2792, (1999)
Ps spectroscopy
Sources of line broadening and shift:
• 2nd-order (relativistic) Doppler effect ∝ v2
• Transit time ∝ v
• DC Stark shift (2S–2P mixing) ∝ |E|2
• Zeeman shift ∝ |B|
• Motional Stark shift ∝ |(v × B)|2
• AC Stark shift ∝ laser intensity
• Photoionization ∝ laser intensity
• Laser linewidth: continuous wave (CW) preferred to pulse
lasers (no chirping effects)
Positronium spectroscopy
• Major uncertainties arise from velocity of Ps (Doppler shift,
transit-time broadening).
• We plan to use Stark deceleration of Rydberg Ps to
dramtically lower the velocity (105 m/s → 103 m/s).
• Ultimate precision could then be at the kHz level (∼ 1 ppt),
then it could be possible to determine the Rydberg
constant (with motivated theorists . . . ).
Experimental setup: e+ beam
Experimental setup: detection scheme
• Detection method using
differing lifetimes of 1S
(142 ns) and 2S (1.1 µs)
states
• Start time from detection
of secondary electrons
• Stop time from detection
of γ rays. Also allows
energy of γ rays to be
recorded.
Experimental setup: detection scheme
• Can also use
photoionization (PI) to
detect 2S Ps.
• Positrons extracted by same
field as secondary electrons
• Lower efficiency than
lifetime method, but
provides additional
information about Ps energy
if position is recorded.
Experimental setup: Ps formation
• Ideally, we need cold Ps (low v ).
• Ps formed in porous solidtargets—diverse targets studied:
silica, zeolites, metal-organic
frameworks (MOFs).
• Positrons thermalize in the material
and can form Ps.
• Ps lifetime reduced by local
electron density; Tao–Eldrup model
used to predict pore size fromlifetime.
• Treats Ps in pore as ‘particle in abox’ =⇒ lowest energy = ground
state energy
Experimental setup: laser
• Frequency-doubled 972
nm diode laser
• Stabilized using reference
cavity or wavemeter
• Build up 0.5–1 kW
circulating laser power in
high finesse resonator
• Frequency reference
possible using Te2
saturation spectroscopy.
Experimental setup: laser stabilisation
Laser
I Piezo
slow
Photodiode (transmission)
Camera
slow
fast
486 nm
EOM
Photodiode(reflection)
Enhancement Cavity
Wavemeter
Experimental setup:
enhancement cavity
• Cavity suspension
designed to minimize
gravitational structural
distortion.
• Properties:
• F ∼ 80000• FSR = 0.55 GHz• linewidth = 7 kHz• Enhancement factor
∼ 6000
Experimental setup:
enhancement cavity
• Up to 700 W of circulating laser power has been achieved,
but this is the damage threshold of the mirrors.
Experimental setup: Ps formation
• Ps target placed inside a containment tube with a carbon
foil window
• Signal enhanced by Ps reflection from the walls
• Spectroscopy region is E-field free.
-5 kV
Laser Target
Carbonfoile+
-e
Ps Mirror
Mirror
Preliminary results
-40 -20 0 20 40 60Frequency (arb, MHz)
5
10
15
20
25
30
35
Cou
nts
• 107 triggers per point.
• No absolute frequency
reference, but check
against Te2 reference
shows minimal drift
during measurement
period (four hours).
• Laser–cavity lock
unstable over longer
periods.
• Time-of-flight broadening
of ∼ 30 MHZ.
• Consistent with expected
signal rate for 500 W and
e+/Ps conversion
efficiency of 10%.
Next steps
Aim to repeat measurement at higher precision
• Move to buffer gas trap-based beam (much high signal tonoise ratio)
• Time-bunching of positron pulses• Extraction to electromagnetic field free region• Focussing of positron pulses
• (Much) colder Ps
• Laser cooling?• Stark deceleration of Rydberg Ps
Present status: positron beam
Buffer gas trap up and running.
• Trap moderated positrons
from source using
collisions with nitrogen
gas in a
Penning–Malmberg trap
• Release them as a pulse
by lowering the final
electrode
Present status: positron beam
• Output of trap is time bunched to ∼ 1 ns (FWHM) using an
electrode with potential varying as V ∝ t−2
• Pulse is then accelerated out of magnetic field
• Focussed to 1 mm spot size and centered with lens system
B−
field
(G
)
Distance (mm)
Pot
entia
l (kV
)
Mu−metal
Buncher Elevator
Lens
Grid
MCP
0 250 500 750
060
120
−2
03.
25
Present status: positron beam
• Positron pulse is then
accelerated using an
‘elevator’ system: high
voltage pulse applied to
an electrode while the
positrons are inside it.
• Positrons are then
extracted from magnetic
field through a hole in a
three-layer mumetal
shield.
Present status: positron beam
Pulses can then be electrostatically focussed to ∼ 1 mm radius.
Whole system from trap exit to target has maximum efficiency
around 90%.
0 1000 2000 3000 4000 5000Elevator voltage (V)
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Effi
cien
cy
Present status: Rydberg Ps
• Plan to excite Ps to n = 22 state using two-photon
excitation
• Some Stark states of this can then be decelerated using
time-varying electric field gradients
• Simulation shows efficiency could be ∼ 10% for
decelerating room-temperature Ps to less than 5000 m s−1
Present status
• Overall efficiency for excitation–deceleration–de-excitation
process around 10−4
• Subsequent excitation to 2S state can be achieved withlower power laser than in preliminary measurement(greatly increased interaction time)
• Reduced 2nd order Doppler shift, time-of-flight broadening
and AC Stark shift• Use photoionization method for detection of 2S state
With source/moderator upgrade, we could expect ∼ 1 2S
positronium atom per second.
Acknowledgements
Thanks to:
• Lars Gerchow, Giandrin Barundun, Samuel Haas,
Susanne Friedreich, Christian Seiler, F. Merkt.
• The organizers.
• Thanks for listening!