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Atomic Clocks for New Physics Searches
Marianna Safronova
New Physics oN the Low-eNergy PrecisioN FroNtier, cerN
Department of Physics and Astronomy, University of Delaware, Delaware, USAJoint Quantum Institute, NIST and the University of Maryland, College Park, Maryland, USA
GPS satellites: microwave atomic clocksAccuracy: 0.1 ns
airandspace.si.edu
Optical atomic clocks will not lose one second in 30 billion years
0hν
0E
1E
0
1
What dark matter affects atomic energy levels?
What dark matter can you detect if you can measure changes in
atomic/nuclear frequencies to 20 digits?
0ν is a clock frequency0hν
0E
1E
0
1
Outline
How atomic clocks work Applications of atomic clocks How good is the clock: stability and uncertainty Dark matter searches with clocks - oscillatory and transient signals Future clock progress
• Improvement of current clocks • Highly charged ion clocks• Nuclear clock
Projected sensitivity of a nuclear clock to relaxion searches
Ingredients for a clock1. Need a system with periodic behavior:
it cycles occur at constant frequency
NOAA/Thomas G. Andrews
2. Count the cycles to produce time interval3. Agree on the origin of time to generate a time scale
Ludlow et al., RMP 87, 637 (2015)
Ingredients for an atomic clock
1. Atoms are all the same and will oscillate at exactly the same frequency (in the same environment): You now have a perfect oscillator!
2. Take a sample of atoms (or just one)
3. Build a laser in resonance with this atomic frequency
4. Count cycles of this signal
Ludlow et al., RMP 87, 637 (2015)
171Yb+
ION
0hν
0E
1E
0
1
How optical atomic clock works
The laser is resonant with the atomic transition. A correction signal is derived from atomic spectroscopy that is fed back to the laser.
From: Poli et al. “Optical atomic clocks”, La rivista del Nuovo Cimento 36, 555 (2018) arXiv:1401.2378v2
An optical frequency synthesizer (optical frequency comb) is used to divide the optical frequency down to countable microwave or radio frequency signals.
0hν
0E
1E
0
1
The laser is resonant with the atomic transition. A correction signal is derived from atomic spectroscopy that is fed back to the laser.
Extraordinary progress in the control of atomic systems300K
nKTrappedUltracold
3D
Image: Ye group and Steven Burrows, JILA
Precisely controlled
Strontium optical latticeneutral atom clock
http://www.nist.gov/pml/div689/20140122_strontium.cfm
4f146s 2S1/2
4f136s2 2F7/2
467 nm
E3
E2 435 nm
4f145d 2D3/2
Yb+ single trapped ion clock
Yb+
PTB
MgAl+CdSrYbHg
Neutral atoms in optical lattice vs. a single trapped ion
10 years
Applications of atomic clocks
Image Credits: NOAA, Science 281,1825; 346, 1467, University of Hannover, PTB, PRD 94, 124043, Eur. Phys. J. Web Conf. 95 04009
GPS, deep space probes
Very Long Baseline Interferometry Relativistic geodesy
Quantum simulationSearches for physics beyond the
Standard ModelDefinition of the second
10 -18
1 cm height
Gravity Sensor
Magma chamber
Atomic clocks can measure and compare frequencies to exceptional precisions!
If fundamental constants change (now)due to for various “new physics” effectsatomic clock may be able to detect it.
Search for physics beyond the standard model with atomic clocks
Frequencywill change BEYOND THE
STANDARD MODEL?0hν
0E
1E
0
1
Searches for physics beyond the Standard Model with atomic clocks
Dark matter searches
Search for the violation of Lorentz invariance
Tests of the equivalence principle
Are fundamental constants constant?
αGravitational wave detection with atomic clocks PRD 94, 124043 (2016)
Image credit: NASA
Image credit: Jun Ye’s group
RMP 90, 025008 (2018)
http://www.nist.gov/pml/div689/20140122_strontium.cfm
JILA Sr clock2×10-18
• Table-top devices• Quite a few already constructed,
based on different atoms• Several clocks are usually in one place• Will be made portable (prototypes exist)• Will continue to rapidly improve• Will be sent to space
Clocks: new dark matter detectors
How good is the clock?
How optical atomic clock worksRamsey scheme
2π
Measure:In
itial
ize
wait
0 12
+
0hν
0E
1E
0
1
0
2π
0 or 1 ?
Atom should be nowin if on resonance1
0E
1E2E
Quantum projection noise: can only get
Repeat many timesto get probability of excitation, scan different frequencies to maximize
0 or 1
detectfluorescence
How good is a clock: stability and uncertainty
From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2
Stability is a measure of the precision with which we can measure a quantity.It is usually stated as a function of averaging time since for many noise processes the precision increases (i.e., the noise is reduced through averaging) with more measurements.
Uncertainty: how well we understand the physical processes that can shift the measured frequency from its unperturbed (“bare"), natural atomic frequency.
How good is a clock: stability and uncertainty
Stability as a function of averaging time
Systematic evaluation of an atomic clock at 2×10-18 total uncertainty, T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, Nature Commun. 6, 6896 (2015).
Sr lattice clock
Clock instabilityQuantum projection noise limit
The number of atoms orions used in a single measurement
N=1 for ionsN>1000 for neutral atoms
Duration of single measurement cycle
The averaging period
Clock transitionfrequency
( )0
1 12y NT
σ τπν τ
≈ ( ) 15 15 10/y s
σ ττ
−= ×
How long will it take to get to 10-19 uncertainty?
Limited by clock state lifetime and laser stability
79 years!
Clock instabilityQuantum projection noise limit
The number of atoms orions used in a single measurement
N=1 for ionsN>1000 for neutral atoms
Duration of single measurement cycle
The averaging period
Clock transitionfrequency
( )0
1 12y NT
σ τπν τ
≈ ( ) 15 11 10/y s
σ ττ
−= ×
How long will it take to get to 10-19 uncertainty?
Limited by clock state lifetime and laser stability
3 years!
Clock instabilityQuantum projection noise limit
The number of atoms orions used in a single measurement
N=1 for ionsN>1000 for neutral atoms
Duration of single measurement cycle
The averaging period
Clock transitionfrequency
( )0
1 12y NT
σ τπν τ
≈ ( ) 16 11 10/y s
σ ττ
−= ×
How long will it take to get to 10-19 uncertainty?
Limited by clock state lifetime and laser stability
11.6 days
N=1 need T=10 seconds
2π
2π
wait mea
sure
initi
alize
Theories with varying dimensionless fundamental constantsString theoriesOther theories with extra dimensionsLoop quantum gravity Dark energy theories: chameleon and quintessence models…many others
Variation of fundamental constants
J.-P. Uzan, Living Rev. Relativity 14, 2 (2011)
Frequency of optical transitionsdepends on the fine-structure constant α.
Measure the ratio of two optical clock frequencies to search for the variation of α.
Dark matter can also cause variation of fundamental constants!
A. Derevianko and M. Pospelov, Nature Phys. 10, 933 (2014), A. Arvanitaki et al., PRD 91, 015015 (2015)
Theories with varying dimensionless fundamental constantsString theoriesOther theories with extra dimensionsLoop quantum gravity Dark energy theories: chameleon and quintessence models…many others
Variation of fundamental constants
J.-P. Uzan, Living Rev. Relativity 14, 2 (2011)
Frequency of optical transitionsdepends on the fine-structure constant α.
Measure the ratio of two optical clock frequencies to search for the variation of α. Keep doing this for a while.
Some clocks are more sensitive to this effect than others
Sensitivity of optical clocks to α-variation/dark matter
0
2K qE
=
22
11
1ln ( )Kvt v t
K αα
∂ ∂=
∂ ∂−
2
0 20
1E E αα
= + −
q
Enhancement factor
Need: large K for at least one for the clocksBest case: large K2 and K1 of opposite sign for clocks 1 and 2
10010-18Frequency ratioaccuracy
Test of α-variation
10-20
Easier to measure large effects!
Can calculatewith high accuracy
0
2qKE
=Enhancement factors for current clocks
01
K
-3
-6
( ) 0.8, 2 ( 1)K Hg K Yb E+= =
( ) ( )( )0.01, 0.06, 0.1K Al K Sr K Ca+ += = =( ) 0.3K Yb =( ) 0.4K Sr+ =
( ) 2.9K Hg + = −
( )3 6K Yb E+ = −
Cavity: part of the clock laser systems Effective K=1
Excellent stability N ~ 1000
Single ion clocks, N = 1
22
11
1ln ( )Kvt v t
K αα
∂ ∂=
∂ ∂−
Observable: ratio of two clock frequencies
fiber
fiber
fb,Al
m frep+ fceo
1070 nmlaser
×2
×2
×2
×2
fb,HgHg+
n frep+ fceo
199Hg+27Al+
9Be+
1126 nmlaser
Science 319, 1808 (2008)
Measure a ratio of Al+ clock frequency to Hg+ clock frequency
( )( )
+
+Al
Hgν
ν ( ) 0.01K Al+ =
( ) 2.9K Hg + = −Not sensitive to α-variation, used as reference
Picture credit: Jim Bergquist
Sensitivity factors
why search For dark matter?
Slide from Andrew Long’s 2018 LDW talk
Simon Knapen, 2018 KITP
Dark matter density in our Galaxy >is the de Broglie wavelength of the particle.
Then, the scalar dark matter exhibits coherence and behaveslike a wave
3dBλ −
dBλ
Dilatons
A. Arvanitaki et al., PRD 91, 015015 (2015)
10-22 eV 10-12 eV µeV eV GeV
Ultralight dark matter has to be bosonic – Fermi velocity for DM with mass >10 eV is higher than our Galaxy escape velocity.
10-22 eV 10-12 eV µeV eV GeV
How to detect ultralight dark matter with clocks?
It will make fundamental coupling constants and mass ratios oscillate
Dark matter field
couples to electromagnetic interaction and “normal matter”
Asimina Arvanitaki, Junwu Huang, and Ken Van Tilburg, PRD 91, 015015 (2015)
Atomic energy levels will oscillate so clock frequencies will oscillate
Can be detected with monitoring ratios of clock frequencies over time(or clock/cavity).
Ultralight dark matter
DM virial velocities ~ 300 km/s
photons
Dark matter
…
Then, clock frequencies will oscillate!
One oscillation per second
One oscillation per 11 days
Ultralight dark matter
DM virial velocities ~ 300 km/s
photons
Dark matter
Result: plot couplings de vs. DM mass mf
…
Then, clock frequencies will oscillate!
Measure clock frequency ratios:
Sensitivity factors to α-variation
Clock measurement protocols for the dark matter detection
Make N such measurements, preferably regularly spaced
Make a clock ratio measurement over time ∆τ
A. Arvanitaki et al., PRD 91, 015015 (2015)
Detection signal: A peak with monochromatic frequencyin the discrete Fourier transform of this time series.
Τ
τ
2π
2π
wait mea
sure
ωφ
Need excellent SHORT term stability
For example 1 second( )
0
1 12y TN
σ τπν τ
≈
Clock measurement protocols for the dark matter detection
Make N such measurements, preferably regularly spaced Single clock ratio measurement: averaging over time τ1
A. Arvanitaki et al., PRD 91, 015015 (2015)
Τ
τ
Detection signal: A peak with monochromatic frequencyin the discrete Fourier transform of this time series.
No more than one dark matter oscillationduring this time or use extra pulse sequence
Al least one dark matter oscillationduring this time
ωφ
Clock measurement protocols for the dark matter detection
Make N such measurements, preferably regularly spaced Single clock ratio measurement: averaging over time τ1
A. Arvanitaki et al., PRD 91, 015015 (2015)
Τ
τ
Detection signal: A peak with monochromatic frequencyin the discrete Fourier transform of this time series.
Al least one dark matter oscillationduring this time
No more than one dark matter oscillation during this time – actually need 4-5 measurement points per DM oscillation to get correct frequency
ωφ
?
From PRL 120, 141101 (2018)
Present scalar DM limits
Dynamic decoupling?
Dark matter clumps: point-like monopoles, one-dimensional strings or two-dimensional sheets (domain walls).
If they are large (size of the Earth) and frequent enough they may be detected by measuring changes in the synchronicity of a global network of atomic clocks, such as the Global Positioning System.
Transient variations
GPM.DM collaboration: Roberts at el., Nature Communications 8, 1195 (2017)
Topological dark matter may be detected by measuring changes in the synchronicity of a global network of atomic clocks, such as the Global Positioning System, as the Earth passes through the domain wall.
Rana Adhikari, Paul Hamiton & Holger Müller, Nature Physics 10, 906 (2014)N
Nature Communications 8, 1195 (2017)
Global sensor network. The participating Sr and Yb optical lattice atomic clocks reside at NIST, Boulder, CO, USA, at LNE-SYRTE, Paris, France, at KL FAMO, Torun, Poland, and at NICT, Tokyo, Japan
Wcisło et al., Sci. Adv. 4: eaau4869 (2018)
How to improve laboratory searches for the variation of fundamental constants & dark matter?
Improve atomic clocks: better stability and uncertainty
Large ion crystalsIon chains 3D optical lattice clocks
Measurements beyond the quantum limit Entangled clocksImage credits: NIST, Innsbruck group, MIT Vuletic group, Ye JILA group
Improve atomic clocks: better stability and uncertainty
?M. S. Safronova, D. Budker, D. DeMille, Derek F. Jackson-Kimball, A. Derevianko, and Charles W. Clark, Rev. Mod. Phys. 90, 025008 (2018).
How to improve laboratory searches for the variation of fundamental constants & dark matter?
Clock sensitivity to all types of the searches for the variation of fundamental constants, including dark matter searches require as large enhancement factors K to maximize the signal.
0
2qKE
=Enhancement factors for current clocks
01
K
-3
-6
( ) 0.8, 2 ( 1)K Hg K Yb E+= =
( ) ( )( )0.01, 0.06, 0.1K Al K Sr K Ca+ += = =( ) 0.3K Yb =( ) 0.4K Sr+ =
( ) 2.9K Hg + = −
( )3 6K Yb E+ = −
Cavity: part of the clock laser systems Effective K=1
Excellent stability N ~ 1000
Single ion clocks, N = 1
22
11
1ln ( )Kvt v t
K αα
∂ ∂=
∂ ∂−
Need very precise frequency standards using NEW systems with
very large K
22
11
1ln ( )Kt t
Kν αν α
∂ ∂=
∂ ∂−
The Future: New Atomic Clocks
Nuclear clockK ~ 104-105
Clocks with ultracoldhighly charged ions
∆K ~ 110 possibleFirst demonstration of quantum logic spectroscopy at PTB, Germany, 10-15!
Science 347, 1233 (2015)
From atomic to nuclear clocks!
M. S. Safronova, Annalen der Physik 531, 1800364 (2019)
Clock based on transitions in atoms
What about transitions in nuclei?
Nature 533, 47 (2016)
Obvious problem: typical nuclear energy levels are in MeV Six orders of magnitude from ~few eV we can access by lasers!
MeV
0
1.0
Groundstate
Excitednuclearstates
A very special nucleus: thorium 229
229mTh
229Th
Nuclear transition150(3) nm [8.3(2)eV]Lifetime ~ 5000s
Laser spectroscopic characterization of the nuclear clock isomer 229mTh, Thielking et al., Nature 556, 321 (2018)
Energy of the 229Th nuclear clock transitionSeiferle et al., Nature 573, 243 (2019)
Only ONE exception!
Atomic Nucleus
Possible 4-5 orders of magnitude enhancement to the variation of α and but orders of magnitude uncertainty in the enhancement factors.
Th nuclear clock: Exceptional sensitivity to new physics
q
QCD
mΛ
Provides access to couplings of Standard Model particles to dark matter via other terms besides the de (E&M), dg (particularly great for detection of relaxions) and dmq
It is crucial to establish actual enhancement!
Tota
l bin
ding
ene
rgy
Coulomb contribution Coulomb
contribution
ground state isomer
MeV scale
8.3 eV
Picture credit: Thorsten Schumm
Broadband relaxion detection with a nuclear clock Ignoring dark matter coherence time
Prelim: Banerjee, Kim, Matsedonski, Perez, Safronova
Prelim: Banerjee, Kim, Matsedonski, Perez, Safronova
Relaxion detection with a nuclear clockAccounting dark matter coherence time, normal halo
Further work on dynamic decoupling is in progressLeibrandt, Hume, Safronova
Many new developments coming in the next 10 years!
Atomic clocks: Great potential for discovery of new physics
Need NEW IDEAS how to use clocks for new physics searches