Second of two lectures on using atomic physics techniques to look for exotic physics, given at the Nordita Workshop for Science Writers on Quantum Theory. This one focusses on the measuring of tiny frequency shifts using techniques developed for atomic clocks.

1. High Precision, Not High Energy
Using Atomic Physics to Look Beyond the Standard Model
Part 2: Never Measure Anything But Frequency

2. Beyond the Standard Model
Ways to look for new physics:
1) Direct creation
2) Passive detection
Image: Mike Tarbutt/ Physics World
3) Precision measurement
Look for exotic physics in
relatively mundane systems
using precision spectroscopy to
measure extremely tiny effects

3. New Physics from Forbidden Events
Parity-Violating Transitions
 Observed, levels consistent with Standard Model
Photon Statistics, other departures from normal
 No sign, consistent with Standard Model
Lorentz/ CPT symmetry violation
 No sign, consistent with Standard Model
 Standard Model holding strong…
… but more stringent tests possible
 frequency shift measurements

4. Frequency
“Never measure anything but frequency!”
-- Arthur Schawlow
(1981 Nobel in Physics)
Art Schawlow, ca. 1960
http://www.aip.org/history/exhibits/
laser/sections/whoinvented.html
Extremely well-developed techniques for
frequency measurements
 Atomic clocks
Same techniques enable
ultra-precise measurements of
all sorts of frequencies

5. Clocks
Harrison’s marine chronometer
Image: Royal Museums Greenwich
Newgrange passage tomb
Built ~3000 BCE
Timekeeping: counting “ticks”
Clock: Model compared to
standard

6. Comparing Clocks
Step 1: Synchronize unknown clock with standard
http://time.gov/

7. Comparing Clocks
Step 1: Synchronize unknown clock with standard
Step 2: Wait a while

8. Comparing Clocks
Step 1: Synchronize unknown clock with standard
Step 2: Wait a while
Step 3: Check standard again
Adjust as needed…

9. Atomic Clocks
Δ퐸 = ℎ푓
Atoms are ideal time standards:
Frequency of light fixed by Quantum Mechanics
No moving parts (not accessible by users…)
All atoms of given isotope are identical
SI Unit of Time (definition 1967):
The second is the duration of 9,192,631,770 periods of the
radiation corresponding to the transition between the two
hyperfine levels of the ground state of the cesium 133 atom.

10. Ramsey Interferometry
Norman Ramsey ca. 1952
Image: AIP, Emilio Segre archive
Atomic clock:
Microwave source compared
to atomic transition
Complicated by motion of atoms
 Doppler shifts
 Inhomogeneities
 Limited interaction time
Best frequency measurements use Ramsey Interferometry
(1989 Nobel Prize in Physics)

11. Ramsey Interferometry
Step 1: Prepare superposition state
Light from lab oscillator used to make “p/2-pulse”
p/2
“Bloch Sphere” picture

12. Ramsey Interferometry
Step 1: Prepare superposition state
“Bloch Sphere” picture
Step 2: Free evolution for time T
Upper and lower states evolve at different rates “phase”
(wave frequency depends on energy of state)

13. Ramsey Interferometry
Step 1: Prepare superposition state
“Bloch Sphere” picture
Step 2: Free evolution for time T
Step 3: Second p/2-pulse, interference
Final population determined by phase between states
p/2

14. Ramsey Interferometry
Step 1: Prepare superposition state
“Bloch Sphere” picture
Step 2: Free evolution for time T
Step 3: Second p/2-pulse, interference
Final population determined by phase between states
p/2

15. Ramsey Interferometry
Clock signal:
interference fringes
Maximum probability exactly
on resonance frequency
Uncertainty in frequency
depends on 1/T
For best performance, need to maximize free evolution time T
 Cold atoms, fountain clocks
Image: NIST

16. Fountain Clock
Dawn Meekhof and Steve Jefferts
with NIST-F1 (Images: NIST)
T~1s
Part in 1016 accuracy
1.0000000000000000 ±0.0000000000000001 s

17. Clocks for New Physics
Clock technology enables
15-digit precision
Experimental clocks at
17-18 digits
Change in clock frequency due to
33-cm change in elevation
(Data from Chou et al.,
Science 329, 1630-1633 (2010))
Sensitive to tiny shifts
Lorentz violation
Changing “constants”
Forbidden moments
General Relativity

18. Fine Structure Constant
훼 =
1
4휋휖0
푒2
ℏ푐
~
1
137
Enrico Fermi Image: Chicago/AIP
Determines strength of EM force
Energies of atomic states
“Fine structure”: DEfs ~ Z2a2
“Hyperfine”: DEhfs ~ Za2 푚푒푙푒푐푡푟표푛
푚푝푟표푡표푛
 Exotic physics changes a
(not this much
change…)

19. Electron g-Factor
(from Hanneke et al., PRA 83 052122 (2011))
Best measurement of a uses
single trapped electron
Rotation:
Δ퐸 = ℎ휈푐
Spin flip:
Δ퐸 =
푔
2
ℎ휈푐
Dirac Equation predicts g=2
Difference tests QED
g = 2.00231930436146 ± 0.00000000000056

20. Fine Structure Constant
g = 2.00231930436146
± 0.00000000000056
Extract value of a from QED
1
훼
= 137.035999166(34)
Value from atom interferometry
1
훼
= 137.035999037(91)
8th-order Feynman
diagram
Comparison tests high-order QED, including muons and hadrons
Extend to positrons, protons, antiprotons…

21. Changing Constants
훼 =
1
4휋휖0
푒2
ℏ푐
=
1
137.035999166(34)
(Right now…)
Limits on past change:
Oklo “natural reactor”
Image: R. Loss/Curtin Univ. of Tech.
Fission products from
1.7 billion years ago
Constrains possible
change in a over
time

22. Astronomical Constraints
Image: NASA
Look at absorption/emission
lines from distant galaxies
Wavelength depends on
value of a in the past
Compare many transitions,
sort out redshift vs. Da

23. “Australian Dipole”
From King et al., arXiv:1202.4758 [astro-ph.CO]

24. Modern AMO Physics
Limits on change in a around
Δ훼
훼
≤ 10−5
Average rate of change:
훼
훼
≤ 10−16 푦푟−1
One year of atomic clock operation
Spatial variation should lead to
훼
훼
≈ 10−19 푦푟−1
Image: NASA
(Sun orbiting Milky Way moves through dipole)

25. Clock Comparisons
! " # " $ % &
14 years
6 years
~1 year
~1 year
훼
훼
= −0.16 ± 0.23 × 10−16 푦푟−1

26. Clocks for New Physics
Clock technology enables
15-digit precision
Experimental clocks at
17-18 digits
Change in clock frequency due to
33-cm change in elevation
(Data from Chou et al.,
Science 329, 1630-1633 (2010))
Sensitive to tiny shifts
Lorentz violation
Changing “constants”
Forbidden moments

27. Electric Dipole Moment
Fundamental particles have “spin”
 Magnetic dipole moment, energy shift in magnetic field
Electric dipole moment would violate T symmetry
 Only tiny EDM (~10-40 e-cm) allowed in Standard Model
 Larger in all Standard Model extensions

28. Electron EDM
Great Big Gap
Source: B. Spaun thesis, Harvard 2014

29. Measuring EDM
Basic procedure: Apply large electric field, look for change in energy
Problem 1: Electrons are charged, move in response to field
Solution 1: Look at electrons bound to atoms or molecules
Problem 2: Electrons redistribute to cancel internal field
Solution 2: Relativity limits cancelation, look at heavy atoms
Problem 3: Extremely large fields are difficult to produce in lab
Solution 3: Polar molecules provide extremely large (GV/cm)
internal fields for small applied lab fields
 Look for EDM in polar molecules involving heavy atoms

30. EDM Measurement
Atomic
Beam
Source
State
Preparation
State
Detection
Magnetic field
Electric field

31. Ramsey Interference
B E B E

32. EDM Limits
Source: B. Spaun thesis, Harvard 2014
YbF molecule
(Imperial College)
Thallium atom
(Berkeley)
ThO molecule
(Harvard/Yale)
de < 8.7 ×10-29 e-cm (90% c.l.)

33. Other Opportunities
1) Systematic improvement
Steady improvement of uncertainties in clocks, etc.
Longer run times
 ACME projects another factor of 10 in EDM limit

34. Other Opportunities
1) Systematic improvement
2) Similar processes, new systems
New molecules, ions for EDM searches
“Nuclear clock” in thorium
Dysprosium spectroscopy
Lorentz symmetry tests, coupling to dark matter

35. Other Opportunities
1) Systematic improvement
2) Similar processes, new systems
3) Exotic systems
Measure g-factor for positron, proton, antiproton
 Test CPT symmetry
Exotic “atoms” positronium, muonic hydrogen
 “Proton charge radius problem”

36. Other Opportunities
1) Systematic improvement
2) Similar processes, new systems
3) Exotic systems
4) ????
Never underestimate the ingenuity of physicists…
No new physics yet, but it has to be out there…
Just a matter of looking carefully in the right places

38. Names to Conjure With
Experiment Theory
Toichiro Kinoshita
Cornell University
Gerald Gabrielse
http://gabrielse.physics.harvard.edu/
Dave DeMille
http://www.yale.edu/demillegroup/
Ed Hinds
http://www3.imperial.ac.uk/ccm/
NIST Time and Frequency
http://www.nist.gov/pml/div688/
ACME Collaboration
http://laserstorm.harvard.edu/edm/
LNE-SYRTE
http://syrte.obspm.fr/tfc/frequences_optiques/accueil_en.php

39. Clock Comparisons
Single clock can’t detect change in a, but comparison of two atoms can
1) Cs-Rb ground-state hyperfine, monitored over 14 years
훼
훼
= −0.25 ± 0.26 × 10−16 푦푟−1
2) Sr optical lattice clocks, over 6 years (compare to Cs standard)
훼
훼
= −3.3 ± 3.0 × 10−16 푦푟−1
3) Al+ and Hg+ trapped ions, over 1 year
훼
훼
= −0.16 ± 0.23 × 10−16 푦푟−1

40. Frequency Comb
Ultra-fast pulsed laser: lots of little lasers with different frequencies
Spaced by repetition rate  determined by size of cavity
Allows comparison of laser frequencies over huge range
Frequency
Intensity
nn=n nrep+fcav ×2
nbeat = fcav
n2n=2n nrep+fcav