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!