Helium SpectroscopySpectroscopy of a forbidden transition in a 4He BEC and a 3He degenerate Fermi gasRob van Rooij, Juliette Simonet*, Maarten Hoogerland**, Roel Rozendaal,

Joe Borbely, Kjeld Eikema, and Wim Vassen

Institute for Lasers, Life and Biophotonics, VU University, Amsterdam

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

He Energy Levels

First excited state: 19.82 eV

All bound states are (1s)(nl)

2 3S1 ( n 2S+1LJ )

He Energy Levels

First excited state: 19.82 eV

All bound states are (1s)(nl)

2 3S1 ( n 2S+1LJ )

What can we learn from helium spectroscopy?

2. determine the fine-structure constant,

1. test 2-electron QED theory

Derived from measurements of the isotope shift.Important for nucelar structure

1970s: ML Lewis and PH Serafino ; M Douglas and NM Kroll O(6mc2)

Modern era of QED began with the discovery of the Lamb shift in 1947(electron self energy and vacuum polarization)

1990s - present: GWF Drake ; K Pachucki O(7mc2) , O(8mc2)

1964: C Schwartz developed a scheme for an O(6mc2) calculation

Coupling strength of electromagnetic interactions between charged elementary particles

proportional to the strengthof the electromagnetic force

3. nuclear charge radius

Argonne National Laboratory, Argonne, Illinois, USA

What can we learn from helium spectroscopy?

1 1S0 –to – 2 1P1 Test 2-electron QED

theory• 58 nm transition in helium

• Lamb shift measurements in helium provide a stringent test of QED effects

• Isotope shift measurement: 3He and 4He

2 3S1 –to – 2 3P0,1,2

Hydrogen n=2

2P3/2

2S1/2

2P1/21.0 GHz

0

0.2

0.4

0.6

0.81

1.2

-6-4

-20

24

6

Natural width 100 MHz=1.6 ns(to 1S)

Helium 23PJ

23P0

2. 3 GHz

00.20.40.60.8

11.2

-6-4

-20

24

6

Natural width 1.6 MHz

23P1

23P2

(60X narrower than H)

(3X larger than H)

(to 23S)

180X better candidate than H!

=98 ns

I. large energy intervals (2.3 GHz and 29.6 GHz)II. long lifetime (= 98 ns)

Why use the 2 3PJ states of helium to determine ?

29. 6 GHz9.9 GHz

2 3S1 –to – 2 3P0,1,2 How does one determine from helium fine structure?

Comparison between theory and experiment for the 29.6 GHz interval is used to determine

The smaller 2.3 GHz interval tests 2-electron QED.

Nonrelativistic Schrödinger equation,

Kinetic energyof the 2 electrons

Potential energyfrom the nucleus and

between the 2 electrons

transformation intocenter-of-mass

frame of the nucleus.(Mass polarization term)

2 3S1 –to – 2 3P0,1,2

The fine-structure energies are expressed as a power series expansion of since 2 ~ 10-4 one can use perturbation theory

How does one determine from helium fine structure?Comparison between theory and experiment

for the 29.6 GHz interval is used to determine The smaller 2.3 GHz interval tests 2-electron QED.

”

Each coefficient, C, is itself a power series expansion of the form (/M ~ 10-4)

30 GHz 50 MHz 1 MHz 50 kHz <15 kHz

2 3S1 –to – 2 3P0,1,2

Relating experiment and theory (K. Pachucki: Phys Rev A 79 062516)

experiment theory

How does one determine from helium fine structure?Comparison between theory and experiment

for the 29.6 GHz interval is used to determine The smaller 2.3 GHz interval tests 2-electron QED.

It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.

i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same

systematic errors

Determinations of

AC Josephson

137.036000 137.036005137.035990-1

137.035995

dc vaoltage, V, applied across a superconducting junction leads toan alternating current of frequency f

It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.

i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same

systematic errors

Determinations of

AC Josephson

137.036000 137.036005137.035990-1

137.035995

muonium hfs

+ (antiparticle to -)

Ground state HFS

It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.

i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same

systematic errors

Determinations of

quantum Hall effect

AC Josephson

137.036000 137.036005137.035990-1

137.035995

muonium hfs

A strong, perpendicular magnetic field is applied to a two-dimensionalelectron gas at a low temperature, the resistance of the gas is quantized with n

It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.

i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same

systematic errors

Determinations of

Cs recoil Rb recoil

quantum Hall effect

AC Josephson

137.036000 137.036005137.035990-1

137.035995

muonium hfs

hv

p

It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.

i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same

systematic errors

Determinations of

Cs recoil Rb recoil

quantum Hall effect

AC Josephson

137.036000 137.036005137.035990-1

137.035995

muonium hfs

ge(electron magnetic moment)(0.37ppb)

one-electron orbit in a Penning trap (amp. & freq. not to scale)

measure trap frequencies yields gs

It is vital to measure using a variety of approaches. Such as: single particle physics, atomic physics, and solid state physics.

i) different degrees of reliance on QED expansions of the measured quantitiesii) experiments performed using dissimilar techniques are not affected by the same

systematic errors

Determinations of

Cs recoil Rb recoil

quantum Hall effect

AC Josephson

137.036000 137.036005137.035990-1

137.035995

muonium hfs

20 ppb – dominated by theoryge(electron magnetic moment)

(0.37ppb)

helium spectroscopy

X5 ppb

Nuclear Charge Radius

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

Measure “identical” transitions in different isotopes: 3He, 4He, 6He, 8He

”QED terms independent of /M cancel

Radiative recoil ~ 10 kHzcontribute to the uncertainty

2 3S1 –to– 2 3PJ

2 3S1 –to– 3 3PJ

2 3S1 –to– 2 1S0

1 1S0 –to– 2 1P1

Nuclear Charge RadiusMeasure “identical” transitions in different isotopes: 3He, 4He, 6He, 8He

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 ± 0.004 fm elastic electron scattering from 4He nucleus

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

2 3S1 –to– 2 1S0

2 3S1 –to– 2 1S0

0

20

22

eV 1s2s 1S0

1s2s 3S1

1557nm

1s2s 3P2

1s2s 1P1

1s1s 1S0

Lifetimes (He*)

2 1S0: 20 ms , 2 = 8 Hz

2 3S1: 8000 s

2 3S1 → 2 3P2 laser cooling / trapping

2 3S1 → 2 1S0 (M1): 1557 nm

QED effects strongestfor low-lying S states

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

2 1S0 anti-trapped(blue detuned from 21S→21P: 2060 nm)Isotope shift

Experimental setup

Crossed optical dipole trap at 1557 nm

Bose-Einstein condensate of 4He*

Degenerate Fermi gas of 3He* 210

160

170

180

190

200Time of Flight

(ms)

MC

P S

ignal (a

.u.)

TOF on Micro-channel Plate (MCP)

Absorption imaging

Dipole trap laser: 40 MHz detuned from

atomic transition

Mode-locked erbium doped fiber laser (Menlo Systems)Referenced to a GPS-controlled Rubidium clock

Frequency comb

770813 770814 770815770812

f beat

Mode-locked erbium doped fiber laser (Menlo Systems)Referenced to a GPS-controlled Rubidium clock

flaser = nfrep + fceo + fbeat

frep ~ 250 MHz

fceo ~ 20 MHz

fbeat ~ 60 MHz

Load a 4He BEC or 3He DFG from magnetic trap into optical dipole trap

Measurement sequence

160 170 180 190 200 210Time of Flight (ms)

MC

P S

ignal (a

.u.)

Determine remaining atom number

Apply spectroscopy beam

Turn off the trap and record MCP signal

FWHM: 90 kHz

60 60.1 60.2 60.3 60.4Beat frequency (MHz)

12010080

60

40

20

0Rem

ain

ing a

tom

s (%

)

Systematics

Recoil shift: ~20 kHz

2 3S1

MJ=+1MJ= 0

MJ=-1

MJ=+1

MJ=0

MJ=-1

fR FEnerg

y

0

B-field

hv

p

AC Stark shift:

Measure for various powers

Extrapolate to zero power

Mean field: < exp. uncertainty

Zeeman shift

AC Stark shift 4He

Accounted for:

– Recoil shift (20.6 kHz)

– Mean field shift

– Zeeman shift

192 510 702.150 4 (41) MHz

Relative uncertainty: 3 x 10-11

Preliminary result

Quantum statistical effect

4He* BEC

occupy ground state

fluctuating atom number

100

200

300

400

500

600Power

(mW)

0.2F

it T

em

pera

ture

(u

K)

0.6

0.4

3He* DFG, low power

atoms fill up the trap

constant atom number

3He* DFG, P > 300 mW

Trap depth large enough to accommodate full thermal distribution

Measured AC-Stark shift curve non-linear

AC Stark shift 3He

Accounted for:

– Recoil shift (27.3 kHz)

– Mean field shift

– Zeeman shift

192 504 914.431 7 (14) MHz

Relative uncertainty: 8 x 10-12

Preliminary result

Results

Drake

Pachucki

Indirect expt.

Our result

f – 192510700 (MHz)

Helium 4 transition frequency

f – 192502660 (MHz)

Drake

Pachucki

Our result

Indirect expt.

Helium 3 transition frequency

f – 8034 (MHz)

Drake

Pachucki

Our result

Isotope shift

Theoretical uncertainty dominated by nuclear charge radii determined from electron-nucleus scattering experiments

Summary

First time:

spectroscopy on ultracold trapped 4He* and 3He*

direct measurement between triplet and singlet states in He

observation of the 1557 nm 2 3S → 2 1S transition

Observed quantum statistical effects in the dipole trap