atomic clocks for new physics searches - indico€¦ · how atomic clocks work applications of...

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!







( )0

1 12y NT

σ τπν τ

≈ ( ) 15 11 10/y s

σ ττ

−= ×



3 years!







( )0

1 12y NT

σ τπν τ

≈ ( ) 16 11 10/y s

σ ττ

−= ×



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


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

≈


Make N such measurements, preferably regularly spaced Single clock ratio measurement: averaging over time τ1


Τ

τ


No more than one dark matter oscillationduring this time or use extra pulse sequence

Al least one dark matter oscillationduring this time

ωφ


Make N such measurements, preferably regularly spaced Single clock ratio measurement: averaging over time τ1


Τ

τ


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

atomic clocks for new physics searches - indico€¦ · how atomic clocks work applications of...

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