Precision spectroscopy of

atomic hydrogen and the proton

charge radius puzzle

N. Kolachevsky

MPQMPQ

Why proton charge radius is so

important?- needed for accurate Rydberg constant

determination

R

1 2S S

Hydrogen atomic levels

Schrödinger :Schrödinger (atomic units):

Dirac:QED:

recoil:

nuclear size correction:

Fundamental constants

2 , , n e pE R F m M r

Relative uncertainties:10: 3 10 10: 4 10em M

Do not contribute

(small corrections!)

2 : 1%pr Leading uncertainty!

L1Sself-energy vacuum pol. rp

total

e p 8 383 MHz -215 MHz 1.253(50) MHz 8 172 MHz

Method 1: Electron scattering

e p

d

d

Measured

value

Mott cross-section:

ep

Transferred momentum

Non point-like proton:

form-factor

For small q

(0) 1F impact parameter >>

proton size

Form-factor and charge radius

Form-factor is the Fourier transformation of the charge distribution

Mean proton charge radius

0

0 0

/( ) , 0.8 fm

r rr e r

Since proton possesses anomalous magnetic moment :

1F

2F

“Dirac” charge form-factor

“Anomalous” magnetic form-factor

(1 )

2

p

p

p

e

m

1.79p

Electric and magnetic form-factors

Electric Magnetic

2

2 22

2

( )6

0

p

E

r

dG q

dqQ

Derivative at q=0

e-p scattering results

Hydrogen spectroscopy

2 , , n e prE mR F MTwo unknowns

Two equations necessary!

Hydrogen spectroscopy: limitations

Precision spectroscopy in H:

- ALL levels except 2S promptly decay

3 3 (4 ) 10 MHzS P P

- Natural linewidth of Rydberg states reduces, but they become

sensitive to electric fields (Stark effect)

7

DCE n

Scattered electric field at the level of 1V/m is hard to control!

Hydrogen spectroscopy: results

Dominating uncertainty results from spectroscopy of higher excited

states (not 2S)

Muonic hydrogen p

p

Hydrogen Muonic

hydrogen

Bohr radius 50 pm 0.25 pm

Lyman- 121 nm

(10 eV)

2 keV

200

em m

mc

2 23 8mc

L2Sself-energy vacuum pol. rp

total

e p 1 085 MHz -27 MHz 0.14 MHz 1 057 MHz

p 0.1 THz -45 THz 0.93 THz -49 THz

Spectroscopy of 2S-2P transition in p

Transition line width 10 GHzGoal – uncertainty of 1 GHz

(1999)

Target (H2)

Resonance line 2S-2P in p

Where the problem resides ?!

-Errors in QED calculations are

excluded at such level of discrepancy

“New”

physics?

Are

- e-p scatteing experiments

- H spectroscopy results

flawless?

Hydrogen spectroscopy

Measurements of the 1S-2S transition

Hydrogen

Theory

Frequency comb

Mobile fountain clock

Optical fiber link

Christian Parthey

Arthur Matveev

Janis Alnis

Axel Beyer

Nikolai Kolachevsky

Randolf Pohl

Thomas Udem

Theodor Häncsh

Tobias Wilken

Birgitta Benhardt

Ulrich Jents

Brett Altschul

Michel Abgrall

Daniele Rovera

Christophe Salomon

Philippe Laurent

Katharina Predehl

Stefan Droste

Ronald Holzwarth

Harald Schnatz

Gesine Grosche

Thomas Legero

Stefan Weyers

The Team

Prof. T.W. Hänsch’s

group

The BossHydrogen 1S-2S

Frequency Comb & Menlo Systems

The team

2009-A. Beyer,

Ph.D.

J. Alnis

Post. Doc.

A. Matveev

Post. Doc.

K. Khabarova

Post. Doc.

C. Partey

Ph. D.

Th. Udem

T.W. Hänsch

me

N. Kolachevsky et al., Opt. Lett. 36, 4299 (2011)

1.5 cm÷ 3

Standard ECDL

25 cm

EOM

Long cavity ECDL

972 nm diode laser with a 20 cm long external resonator and intra-cavity EOM

Beat note diode - dye laser

Master oscillator

2exp rmsη φ

64

eff IRη η8-photon process =>

at 972 nm

-25 -20 -15 -10 -5 0 5 10 15 20 25

0

1000

2000

3000

Frequency detuning, kHz

Long cavity diode laser

Dye laser

Co

un

t ra

te,

co

un

ts/s

FP1-FP2 Allan deviation

0,01 0,1 1 10 100 1000 10000

1E-15

1E-14

1s Gate time, 5.5 Hours of measurement

10 ms Gate time, 350 s of measurement

gate time, s

Alla

n d

evia

tion

Thermal noise limit

Fiber

Laser

I()

Hydrogen maser

Stabilized

op

tical fiber

FP5

Distributionamplifier

Wenzel Chain 4 5 5

Wenzel Chain 4 5 5

PLL

PLL

I()

temperature stabilized

1GHz

1GHz

Comb-comb comparison setup

250 MHzsystem

100 MHzsystem

1542 nm

17107200/2 THzmHz

Comb-comb comparison: result

The Hydrogen spectrometer1S-2S spectrometer

C.G. Parthey et al., PRL 107, 203001 (2011)

C.G. Parthey et al., PRL 107, 203001 (2011)

C.G. Parthey et al., PRL 107, 203001 (2011)

Uncertainly in the 1S-2S transition

cannot solve the proton charge

radius puzzle

It is desirable to measure

independently other transitions in H

with higher accuracy

We already use a laser to excite 2S-4P

(486 nm) transition in a cold atomic

beam of H

2S-4P transition measurements (Yale’95)

2S-4P spectroscopy at MPQ

Cold beam of metastable atoms

(4 K)

Optically populated only one

hyperfine sublevel 2S (F=0)

Velocity selective detection,

typical velocities down to 100

m/s

Frequency measurement is

reliable

Natural line width of

the 4P level

13 MHz

2S-4P experimental setup

H(2S)

486 nm

Antiparallel BeamsActive fiber-based retroreflector:

Inside the chamber

Gaussian beam

Assembly of spherical lenses

Aspherical lens

4 mm

Data evaluation

Data scattering (polarization dependent?)

Cross damping: coherent and incoherent parts

incoherent

coherent

Cross damping problem in the 2S-4P experiment

P1/2

P3/2

Analysis of systematic

effects is

still in progress

Simple rule: if one wants to split the line by the factor

of N, the perturbing line should be further away as N

Thank you for attention!

MPQ