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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).
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