Ultracold 3He and 4He atoms near quantum degeneracy:

QED test and the size of the helion and -particle

Rob van Rooij, Joe Borbely, Juliette Simonet*, Maarten Hoogerland**, Kjeld Eikema, Roel Rozendaal and Wim Vassen

* École Normale Supérieure, Laboratoire Kastler-Brossel, Paris, France ** University of Auckland, Auckland, New Zealand

Outline

• What is quantum electrodynamics (QED)?

• Why use helium spectroscopy to test QED?

• How we tested QED (and also nuclear few-body physics)

What is quantum electrodynamics (QED)?

vacuum is never empty, but filled with virtual particles – appearing suddenly and then quickly disappearing

electron self energy

Dirac

relativity,electron spin

100 GHz

Lamb

10 GHz

QED2n

R

Modern era of QED began with the discovery of the Lamb shift in 1947 (Willis Lamb; hydrogen atom)

BohrEnergyn=1

(13.6 eV = 106 GHz)

1 GHz

proton spin

Hyper-finesplitting

0.01 GHz

proton size

Nuclear effects

2

tE Heisenberg uncertainty principle

vacuum polarization

Vacuum produces electron-positron pairs

A theory that describes how light and matter interactcontributions from empty space (the vacuum)

Shift:

Electrons interact with themselves

Why use helium spectroscopy to test QED?

• Next simplest atom (from a theoretical point of view) after atomic hydrogen• 2-electron atom (get electron-electron interactions)• 3-body system (electron, electron, nucleus)

First excited state: 1s2s 23S1

( n 2S+1LJ )

Ground state: 1s2 11S0

n=1,2,3,…S = s1+s2 , s=±½L = 0,1,2,… (S,P,D…)J = |L-S|,…,|L+S|

E = h x 5 130 494.9(9) GHzPrecision: 175 parts per billion (10-9)

3 years later…E = h x 5 130 495.04(17) GHzPrecision: 34 parts per billion (10-9)

Why use helium spectroscopy to test QED?

• Next simplest atom (from a theoretical point of view) after atomic hydrogen• 2-electron atom (get electron-electron interactions)• 3-body system (electron, electron, nucleus)

E = h x 5 945 204 212(6) MHzPrecision: 1 part per billion (10-9)

Why use helium spectroscopy to test QED?

• Next simplest atom (from a theoretical point of view) after atomic hydrogen• 2-electron atom (get electron-electron interactions)• 3-body system (electron, electron, nucleus)

E = h x 192 510 702 145.6(1.8) kHzPrecision: 8 parts per trillion (10-12)

Lifetimes (He*)

2 1S0: 20 ms , FWHM = 8 Hz

2 3S1: 8000 s

QED effects strongest for low-lying S states

Why use helium spectroscopy to test QED?

• Next simplest atom (from a theoretical point of view) after atomic hydrogen• 2-electron atom (get electron-electron interactions)• 3-body system (electron, electron, nucleus)

E = h x 192 510 702 145.6(1.8) kHzPrecision: 8 parts per trillion (10-12)

Extremely weak transition long interaction time

Modified from E. Eyler Science 333,164 (2011)

Particle accelerators

Sun (surface)

Supernova

Sun (centre)

Room temperature

Interstellar space

1557 nm laser light

1083 nm laser light

MCP

Same laser but different frequency detunings for:• collimation• slowing• cooling• trapping• detection

How we tested QED: Experimental setupEnergy

1s2s 1S0

1557 nm

1s2s 3P2

1s1s 1S0

1s2s 3S1

electron bombardment(20 eV)

1083 nm

1s2s 1S0

1s2s 3S1

1557 nm

1s2s 3P2

1s2s 1P1

1s1s 1S0

2 3S1 can be trapped at 1557 nm(red detuned from 23S1→23P2: 1083 nm)

2 1S0 anti-trapped(blue detuned from 21S0→21P1: 2060 nm)

How we tested QED: Optical trapping

Energy

How we tested QED: Experimental tools

Nobel prize in physics milestones:

• 2001: Eric A. Cornell, Wolfgang Ketterle, Carl E. Wieman achievement of Bose-Einstein condensation

• 2005: Roy J. Glauber, John L. Hall, Theodor W. Hänsch optical coherence / optical frequency comb

How we tested QED: Experimental toolsBose-Einstein condensate

Long-interaction times

W Ketterle2001 Nobel lecture

Frequency comb locked to an atomic clock

How we tested QED: Experimental toolsKjeld Eikema

XUV: < 100 nm IR: > 800 nm

Optical ruler

1014 Hz 107 HzOptical frequencies Microwave frequencies

beat note

Frequency Comb

Accurate timebase

Load atoms into the optical dipole trap

Determine remaining atom number

Apply spectroscopy beam

Turn off the trap and record MCP signal

2 3S1 2 1S0(trapped) (anti-trapped)

How we tested QED: Experiment procedure

Recoil shift: ~20 kHzhv

p

AC Stark shift: ~ 1 kHz / 1 mW

Mean field shift: < 1 kHz (collisional shift)

How we tested QED: Systematics

(Energy shift due to external laser light)

Frequency comb: ~ 0.4 kHz (uncertainty in the time base)

(Momentum transfer)

MJ=+1

MJ=0

MJ=-1

fR FEnerg

y

0

B-field

How we tested QED: Results

4He:

3He:

Agreement with QED theory BUT

QED 1000 times less precise(challenge for theorists)

Relative Precision

192 510 702 145.6 (1.8) kHz

192 504 914 426.4 (1.5) kHz

9 x 10-12

8 x 10-12

Our Result

GWF Drake: Can J Phys 86 45-54 (2008)

Measure “identical” transitions in different isotopes: 3He, 4He

QED terms independent of /M cancel

Radiative recoil ~ 10 kHzcontribute to the uncertainty

How we tested nuclear few-body theory

Nuclear charge radius

)()()()43()43(

4232 QEDExperimentcc

HeHeHeHe

ffkHerHer

Only relative charge radii can be deduced.

To determine absolute charge radii the radius of the reference nucleus, 4He, must be known with the best possible precision

rc (4He) = 1.681(4) fm elastic electron scattering from 4He nucleus

GWF Drake: Can. J. Phys. 83: 311–325 (2005)

Measure “identical” transitions in different isotopes: 3He, 4He

How we tested nuclear few-body theory

Helium spectroscopy + QED:

Nuclear theory + scattering:

1.961(4) fm

1.965(13) fm

calculate the radius of the proton and the neutron the distribution in the nucleus

Summary

First time:

spectroscopy on ultracold trapped 4He and 3He

observation of the 1557 nm 2 3S1 → 2 1S0 transition

Challenge for absolute QED energy calculations to 8 x 10-12

Determined the size of the 3He nucleus to 4 x 10-18 m

LaserLaB Amsterdam:Rob van Rooij, Joe Borbely, Juliette Simonet ‡, Maarten Hoogerland ¶, Kjeld Eikema, Roel Rozendaal‡ ENS, Paris ¶ University of Auckland, New Zealand

MaartenJoe Juliette WV

Science 333, 196 (July 2011)

The metrology team

Rob

1. The classical Hanbury Brown -Twiss effect:

light as an electromagnetic

wave

2. Quantum Optics interpretation of the HBT

effect: light as a beam of photons

3. The HBT effect for atoms: 4He bosons

4. What about fermions? The 3He case.

Hanbury Brown Twiss effect for ultracold bosons and fermions

Quantum Optics (Wikipedia):

the study of the nature and effects of light as quantized photons

Before 1960: light interference understoodin electromagnetic wave picture, i.e. phase differences in amplitude of electric field

1956: Robert Hanbury Brown and Richard Twiss extended intensity interferometry tothe optical domain

Physics Nobel Prize 2005:Roy Glauber, Jan Hall, Ted Hänsch

~1963: birth of Quantum Optics

First-order coherence

g(1) gives the contrast in amplitude interference experiments (Young’s double slit, Michelson interferometer, interfering Bose condensates)

22

*

)1(

)()(

)()(),(

rErE

rErErrg

First order (phase) coherence: correlations in the amplitude of the field

= statistical average

(= time average for stationary process)

Hanbury Brown and Twiss:

Intensity correlations:

HBT effect: (second-order) correlations between two photocurrents at two different points and times.

22*

**

)2(

)(

)()(

)()(

)()()()(),(

rI

rIrI

rErE

rErErErErrg

2

21)1(

21)2( );,(1);,( rrgrrg

Measuring intensity correlations gives information on phase coherence: g(2) deviates from 1 for r < lc (correlation length)

g(2)(0,0,0) = 2 Do photons bunch?How can they? Independentparticles, no interactions !

g(2)

r

Nature, January 7, 1956

2

21122211 DSDSDSDSP

Hanbury Brown and Twiss

Quantum Optics interpretation Quantum Optics interpretation (Glauber):(Glauber):

interference of probability amplitudes interference of probability amplitudes of of indistinguishableindistinguishable processes: processes:

(bosons)light for 2 classicalPP

Correlation length = detector separation for which interference survives

Sum over all pairs S1 and S2 in the sourcewashes the interference out unless d is small enoughd

1)()2( rg

For a laser:

(Glauber’s coherent states)

2)2(

)(

)()(),(

rI

rIrIrrg

Intensity correlations:joint probability of detecting two photons at locations r and r’

For all chaotic sources (so no laser):

Should also work for atoms !(BEC is like a laser)

2)1()2( )(1)( rgrg

Shot noise (independent particles)

Correlations due tobeat notes of random waves

1965, 1966: Armstrong, Arecchi1965, 1966: Armstrong, Arecchi

First experiment: Yasuda and Shimizu, Ne* MOT (1996), heroic experiment, T=100 K

Amsterdam

OrsayOrsay

MCP (He* detector)63 cm below trap

Measurement of correlation of two particles emitted at S1 and S2 to be detected at D1 and D2

Position-sensitive MCP from Orsay to Amsterdam

Science Science 310310, 648 , 648 (2005)(2005)

VU experiment:

Thermal 4He atoms show bunching

Fit: l=0.56 +/- 0.08 mm

; i

i ms

tl

t: drop time

Agrees very well with theory!

; 2i

Bi m

Tks

T=0.5 K

(above BEC, si >> T)

2

21122211 DSDSDSDSP

What about fermionic atoms ?

For fermions we need an antisymmetric wavefunction:

fermions )(identicalfor 0P

d

Does not really surprise us:

Pauli principle!

Interference takes place when particles arrive within the same phase space cell: Δx Δy Δz Δpx Δpy Δpz < h3

Pure effect of quantum statistics:no classical interpretation possible !

Expected correlation function g(2)

(0,0,z)for bosons and fermionsfor bosons and fermions

Bosons

Fermions

4He

3He

T=0.5 K

Fit:• l=0.75 +/- 0.07 mm• l=0.56 +/- 0.08 mm

(difference due to masses 3 and 4)

2i

Bi

ii

m

Tks

ms

tl

t: drop time

Jeltes et al., Nature 445, 402 (2007)

Comparison of the Hanbury Brown Twiss effect for bosons and fermions

The HBT team

John Martijn

ValentinaTom

WV

Laser Centre Amsterdam: Tom Jeltes, John McNamara, Wim Hogervorst

Orsay: Valentina Krachmalnicoff, Martijn Schellekens, Aurelien Perrin, Hong Chang, Denis Boiron, Alain Aspect, Chris Westbrook

Nature 445, 402 (2007)

KenBaldwin