Precision measurement withultracold atoms & molecules

Jun Ye

JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado at Boulder

$ Funding $

NIST, ONR, NSF, AFOSR, NASA, DOE

http://jilawww.colorado.edu/YeLabsUS – Japan Seminar, Breckenridge, August 23, 2006

Ultracold molecules: Test fundamental principles

QEDElectronic ~ α

e- e-

e- e-

• Ultrahigh resolution spectroscopy• Standards in wide spectral ranges• Molecular interferometry• Precision measurement

Excited electronic state

Ground electronic state

One system, two different fundamental forces!

Vibration ~ me/mp(mass on a spring) Strong interactions

First, let there be light

Continuous wave laser: < 1 Hz stability and accuracy

Ultrafast pulse: < 1 fs generation and control

Figure of merit: 10-15

Phase coherence after 1015 optical cycles

Precision spectroscopy and quantum control at highest resolution over widest optical bandwidth

Frequency comb: state-of-the-art

νn= n fr – fo

• Optical Synthesizer

I(ν)

ν

fr

f0

Visible

Frequency (Hz)1010 1011 1012 1013 1014 1015

Freq. comb106 :1 Reduction Gear

Molecular spectroscopyThorpe et al., Science 311, 1595 (2006). C. Gohle et al.,

Nature 436, 234 (2005).

Jones et al. PRL 94, 193201 (2005).

XUV combStowe et al., PRL 96, 153001(2006).

Quantum control

Optical coherence > 1 s, across entire visible

Laser 21064 nm

Cavity 2Laser 1700 nm

Cavity 1

ν

Laser 1Laser 2

Femto comb30 m

noise-cancelled fiber

35 m

noise

-canc

elled

fibe

r

Ludlow et al., PRL 96, 033003(2006).

-6 -4 -2 0 2 4 6 8 10

0

1

2

3

Lin

ear

Sign

al (a

. u.) Optical

linewidth:250 mHz

4/11/ 2006

Hz

Clean separation between internal & external degrees of freedom

Control of matter

Long - term quantum coherence:

Both in well defined quantum states

Magic wavelength dipole trapTrapping of Single Atoms in Cavity QED

Ye, Vernooy & Kimble, Phys. Rev. Lett. 83, 4987 (1999).

For clocks: Katori et al., Katori et al., J. Phys. Soc. Jpn 68, 2429 (1999)

6th Symp. Freq. Standards & Metrology (2002); Phys. Rev. Lett. 91, 173005 (2003).

T ~ 0.5 photon recoil~ 220 nK

Cool Alkaline Earth – Strontium

1S0

3P1

1P1

689 nm(7.4 kHz)

461nm (32 MHz) 3P0

698 nmΔν ∼1 mHz

~ 1 mHz ~10-1887Sr 1S0-3P0

δν/ν0 at 1sΔν

τνδν 111

0

⋅⋅≈NSQ

noise

νΔν0≈Q

JILA work: Phys.Rev.Lett. 90, 193002 (2003); Phys.Rev.Lett. 93, 073003 (2004); Phys.Rev.Lett. 94, 153001 (2005); Phys.Rev.Lett. 94, 173002 (2005); Phys.Rev.Lett. 96, 033003 (2006); Phys.Rev.Lett. 96, 203201 (2006).

Spectroscopy at the magic wavelength

trapωh

1S0

3P0

trapclock

traprecoil

ω

ωω

<<Γ

<<

1-D Lamb-Dicke Regimeη = kx0 = (ωrecoil / ωz )0.5 ~ 0.23

-60 -40 -20 0 20 40 60500

1000

1500

2000

2500

3000

3500

Pho

ton

coun

ts

Optical frequency (Hz)

Red sideband

ωtrapBlue SB

Carrier

Zoom into the carrier of 87Sr 1S0 – 3P0

-300 -200 -100 0 100 200 300

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05G

roun

d St

ate

Popu

latio

n (a

rb.)

Clock Laser Detuning (Hz)

Radial Sidebands

νr ~ 125 Hz

E

g

-20 -10 0 10 20 301200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

Phot

on C

ount

s

Clock Laser Detuning (Hz)

FWHM:4.6 Hz

April, 2006

Q ~ 1 x 1014 Single trace without averaging

Zoom into the carrier of 87Sr 1S0 – 3P0

E

g

Reproducibility ~ 1 x 10-15

(March – June, 2006)

Projected stability< 1 x 10-15 at 1 s

• 3P0 g-factor different than 1S0 due to HFI• Shift of ~110 x mF Hz/Gauss for ΔmF=0• State preparation, field control• HF structure introduces slight lattice polarization sensitivity

Differential g-factor – Tensor polarizability

1S0

3P0

HFI

1P1

3P1

I = 9/2

mf

-9/2

+9/2

1S0

3P0

mf

-9/2

+9/2

1S0

3P0

Santra et al., Phys. Rev. Lett. 94, 173002 (2005).Hong et al., Phys. Rev. Lett. 94, 050801 (2005).Barber et al., Phys. Rev. Lett. 96, 083002 (2006).

-400 -200 0 200 4000.00

0.02

0.04

0.06

0.08

0.10

-9/2-7/2

-5/2

-3/2

-1/2+1/2

+3/2

+9/2+7/2

3 P 0 Sig

nal (

Nor

m.)

Laser Detuning (Hz)

+5/2

Optical Measurement of Nuclear g-factor (NMR-like experiment in the optical domain)

π

21+

29+

23+

25+

27+

21+

29+

23+

25+

27+

21−

27−2

9−

25−

23−

21−

27−2

9−

25−

23−

01S

03P

No net electronic angular momentumΔg = -108.5(4) Hz/(G mF)3P0 lifetime 140(40) s

1S0

3P0

0 1 2 3 4 5 60

2

4

6

8

Occ

urre

nces

Transition Linewidth (Hz)

Fourier Limit ~1.8 Hz

-6 -4 -2 0 2 4 6

0.00

0.02

0.04

0.06

0.08

0.10

3 P 0(mF=5

/2) P

opul

atio

n

Laser Detuning (Hz)

1.5 Hz

-6 -4 -2 0 2 4 6

0.00

0.02

0.04

0.06

0.08

0.10

3 P 0(mF=5

/2) P

opul

atio

n

Laser Detuning (Hz)

2.1 Hz

Coherent spectroscopy Q ~ 3 x 1014

-60 -30 0 30 60 90 1200.00

0.04

0.08

0.12

0.16

0.20

3 P 0(mF=5

/2) P

opul

atio

n

Laser Detuning (Hz)

-10 -5 0 5 100.00

0.04

0.08

10 Hz

1.7 Hz

Ramsey

Ultracold Sr2 molecules via narrow-linePhotoassociation

3P1 + 1S0

1S0 + 1S0

Laser detuning

Trap Loss

< 100 kHz

Zelevinsky et al., Phys. Rev. Lett. 96, 203201 (2006).

Narrow-line Photo-association Spectroscopy

• New Territory for PAS

• Interesting regime, C3 C6 crossover

• Ground/Excited state similar for large detunings

• Hyperfine-free for bosonic isotopes• Useful for precision tests• Optical control of cold collisions with

low loss

66

33

RC

RC

≈ at Δ~500 MHz

(5s2) 1S0

689 n

m, γ

= 7.

6 kH

z

3P1 (5s5p)All bound states are resolved by the narrow line

Theory: Paul Julienne

σ-polarizedprobe

magicStarkshift

1S0

3P1

mJ0 +1-1

0.5 Wstanding wave

Ωlattice>>εrecoil

PAlaser

Doppler- and recoil-free

Photoassociation inside a Magic wavelength lattice

3P0

1S0

700 750 800 850 900Laserwavelength nm

-450-400-350-300-250-200

Star

k sh

ift (k

Hz)

1S0

3P0

3P1

Photoassociation: Experiment vs. theory

Nine least bound states measured

10-5 agreement for near detuning, 0.1-1% agreement deeper in the potential curve

Ground State Molecules

Vg

0uSimilar excited and ground state wavefunctions~90% of molecules in 8.4 GHz state decay to single g.s.

Should be possible to drive Molecules to deepest g.s.

Sr2

Magic wavelength trap for molecules?Theory: P. Julienne and A. Derevianko

νpump νprobe

δ(νpump – νprobe) < 0.5 Hz

ν

Time-variation of electron-proton mass ratio?D. DeMille, private communications (2005). Chin and Flambaum, Phys. Rev. Lett. 96, 230801 (2006).

Test of fundamental constants

• Early universe• Not so clear…Webb et al., PRL 87, 091301 (2001).Astron. Astrophys. 415, L7 (2004).– Conflicting results

Impact

α: fine structure constant•Modern epoch

• Atomic clock measurementsare consistent with zero

Δα/α < 10-15/yr

ν

Cold OH molecules to constrain α

Hyperfineinteractions ~ α 4

Lambda doubling ~ α 0.42Π3/2

F’= 2

F’= 1

F= 2

F= 1Multiple transitions from the same gas cloud (different dependences on α)(Self check on systematics)Current uncertainly in laboratory based experiments is 100 Hz,leading to Δα/α ~ 10-5

ter Meulen & Dymanus, Astrophys. J. 172, L21(1972).

OH megamasers

High redshift z > 1Darling, Phys. Rev. Lett 91, 011301 (2003).Chengalur et al., Phys. Rev. Lett. 91, 241302 (2003).Kanekar et al., Phys. Rev. Lett. 93, 051302 (2004).

Stark Decelerator

Slower electrodes

Star

k en

ergy

Position

G. Meijer

OH after the Stark-decelerator

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.80.00

0.25

0.50

0.75

1.00

OH

den

sity

(arb

.)

Time (ms)

370 m/s

336 m/s

300 m/s

259 m/s211 m/s

148 m/s 33 m/s

Bochinski et al., Phys. Rev. Lett. 91, 243001 (2003); PRA 70, 043410 (2004).

Beam: 550 m/s to restTemp: 1 K to 10 mK104 – 106 molecules105 – 107 /cm3 density

Cold molecule based precision spectroscopy

PMT

Excitation laserMicrowave Interrogation cavity

HexapoleDecelerator

• Rabi or Ramsey interrogation on slowed OH beam• High resolution and precision• Systematic checks on beam (velocity) effects

Detection can

Weightedstandard meanerror range

Hudson et al., Phys. Rev. Lett. 96, 143004 (2006).

Precision measurement of OH structure

Δα/α measurement status

Δα / α = 1 ppm (and better) is now possible to measure over ~10 Gyr.Linear drift model → 10-16/yr.

Astrophysical measurements later this year plan better than 100 Hz accuracy.

Deep surveys of OH megamasers are active from the local Universe to red shift z ~ 4.

Optical clock comparisons ongoing, but test only modern epoch.

Tests on Δ(me/mp) / (me/mp) is possible (W. Ubach, PRL 92, 101302 (2004); PRL 96, 151101 (2006).)

e- e-

e- e-

Special thanks

Femtosecond comb& cold atoms

S. ForemanM. ThorpeD. HudsonM. StoweDr. A. Pe’erDr. R. J. Jones (Arizona)Dr. K. Moll (Precision Ph)

Ultracold Sr & Sr2

M. BoydA. LudlowS. BlattDr. T. ZelevinskyDr. T. ZanonDr. T. Ido (NICT,Tokyo)

Cold Polar Molecules

B. SawyerB. StuhlDr. B. LevE. Hudson (Yale)

http://jilawww.colorado.edu/YeLabs

Collaborators

J. Bohn, S. Cundiff, C. Greene, J. Hall (JILA) P. Julienne, S. Diddams, J. Bergquist, L. Hollberg, T. Parker (NIST)

E. Eyler (UConn), F. Krausz (MPQ)

|e,n>

|g,n+1>

|e,n-1>

|g,n>

Dipole force fluctuations: Heating and position-dependent decoherence

FORT beam

CQED probe

Caltech cavity QED lessonKimble group, 1999

The Solution:Match the AC Stark shift

between |e> and |g>

|e,n>

|g,n+1>

|e,n-1>

|g,n>

Kimble et al. ICOLS 99

Problems in the neutral atom land

Reproducibility

-20 0 20 40 60 80 1001201401600

20

40

60

80

100

120

Sam

ples

Optical frequency deviations (Hz)

40 60 80 100 1200

10

20

30

40

50

60

Sam

ples

Optical frequency deviations (Hz)

0 200 400 600 800 100066

68

70

72

74

76

Opt

ical

line

cent

er fr

eque

ncy

(Hz)

Error tolerance (Hz)

ν0 = 429,228,004,229,800 Hz

Center: 71.4 Hz ± 0.4 Hz

March – June 2006: 1020 measurements3 different NIST Cs-calibrated masers

1020 samples

1000 samples

2 Hz optical

Statistical error < 1 x 10-15

Global Sr Clock Comparison

800

820

840

860

880

900

920

940

960

JILA 2006(Preliminary)

Measurements Freq

uenc

y- 4

29,2

28,0

04,2

29,0

00 H

z

Tokyo 2005

JILA 2005

Paris 2006

Tokyo 2006? PTB?

Takamoto et al., Nature 435, 321 (2005). Ludlow et al., Phys. Rev. Lett. 96, 033003

~10 months

?

1 MHz error in lattice wavelength → 5 x 10-18 clock inaccuracy

How Magic is the wavelength?

813.2 813.4 813.6 813.8

-400

-300

-200

-100

0

100

200

300 R

elat

ive

Clo

ck F

requ

ency

(Hz)

Lattice Wavelength (nm)

Sensitivity 884(15) Hz/nmI0= 10 kW/cm2

Ludlow et al., Phys. Rev. Lett. 96, 033003 Brusch et al., Phys. Rev. Lett. 96, 103003 (2006).

-40 -30 -20 -10 0 10 20 30 40

10

20

30

40

50

60

70

80

1 S 0-3 P 0 Lin

ewid

th (H

z)Magnetic Field (mG)

Total uncertainty ~0.5 Hz 1 x 10-15

-0.2 -0.1 0.0 0.1 0.2-120-100

-80-60-40-20

020406080

100120

Freq

uenc

y (H

z)

Magnetic Field (G)

-47.5 (32) Hz/ GField Uncertainty 13mGSystematic uncertainty = 0.42 Hz

Magnetic Shift: -47 (32 Hz)/G

Understanding systematics:Magnetic sensitivities

Magnetic Broadening

Trapped ion optical frequency standards

Ultra-stable probe laser

(local oscillator)

Single coldtrapped ion

(atomic reference)

Femtosecond comb (counter)

Optical clocks – future redefinition of the second?Fundamental constants and tests of physics

Future satellite navigation and ranging?

199Hg+, 88Sr+, 171Yb+,40Ca+, 115In+, 27Al+

NIST Hg+ systematic uncertainty< atomic fountain clock(Bergquist et al., 2006)

Helen MargolisPatrick Gill, et al., NPL

The point:Long coherence time in quantum measurement

Quantum Information science:NIST, Innsbruck, Michigan, Oxford, MIT, Ulm, …

Precision Measurement/Standards: NIST, NPL, PTB, NRC, JPL, … Innsbruck, Harvard, MPQ, Dusseldorf, …

Ion traps: Clean separation between the internal and external degrees of freedom

Wim Ubachs

Precision spectroscopy of H2and a possible variation of mp/me

over cosmological time

Dimensionless constants of nature:

1/α = 137.035 999 11 (46)

μ= Mp/me = 1836.152 672 61 (85)

various g - factors

Fundamental constants ?

Just empirical or deeper theory ?

Molecular structure and possibility of lif

Constant or slightly varying ?

PRL 96, 151101 (2006).

Matching the polarizabilities

3P0

1S0

700 750 800 850 900Laser wavelength nm

- 450

- 400

- 350

- 300

- 250

- 200St

ark

shift

(kH

z)

1S0

3P0

1S0

3P0 Sr, Yb, Ca, Hg, …

-800 -600 -400 -200 0 200 400 600 8000.00

0.02

0.04

0.06

3 P 0 Sig

nal (

Nor

m.)

Laser Detuning (Hz)

-7/2+9/2+7/2 -9/2

Optical Measurement of Nuclear g-factor

σ+σ-

21+

29+

23+

25+

27+

21+

29+

23+

25+

27+

21−

27−2

9−

25−

23−

21−

27−2

9−

25−

23−

01S

03P

No net electronic angular momentumΔg = -108.5(4) Hz/(G mF)3P0 lifetime 140(40) s

1S0

3P0

Ultracold Sr2 molecules to test time-variation of electron-proton mass ratio

PumpProbe

Sr2

νpump νprobe

δ(νpump – νprobe) < 0.5 Hz

ν

Chin and Flambaum, Phys. Rev. Lett. 96, 230801 (2006).D. DeMille, private communications (2005).

Magic wavelength trap for molecules?Theory: P. Julienne and A. Derevianko

Oscillator

Counter

Δν

νa

Atoms

New era for optical atomic clocks

NIST, JILA, PTB, NPL, SYRTE, …

Feedback(accuracy)

Ultrastable laser

optical comb

optical frequencysynthesizer & counter

RF or opticalreadout

Possible systematics in space

Electro-Magnetic field in space

Different velocities for different lines

Solutions:

OH sum rule

Main lines versus satellite lines

Emission and conjugate absorption

The OH ground state in a B-Field

-2 -1 0 1 2

SUM (2 satellites) = SUM (2 main lines)

Satellites calibrate B

Observed satellites conjugate

Kanekar et al., Phys. Rev. Lett. 93, 051302 (2004).