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, USA Joint Quantum Institute, NIST and the University of Maryland, College Park, Maryland, USA Optical atomic clocks will not lose one second in 30 billion years

airandspace.si.edu

GPS satellites: microwave atomic clocks Accuracy: 0.1 ns

E1 1

hν 0

E0 0 What dark matter affects atomic energy levels?

E1 1 ν is a clock frequency hν 0 0

E0 0

What dark matter can you detect if you can measure changes in atomic/nuclear frequencies to 20 digits? 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 clock

1. Need a system with periodic behavior: it cycles occur at constant frequency

2. Count the cycles to produce time interval 3. Agree on the origin of time to generate a time scale

NOAA/Thomas G. Andrews 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): E1 1 You now have a perfect oscillator! hν 0

2. Take a sample of atoms (or just one) E0 0

171 + 3. Build a laser in resonance with this atomic Yb frequency ION

4. Count cycles of this signal

Ludlow et al., RMP 87, 637 (2015) How optical atomic clock works

E1 1

hν 0

E0 0

The laserThe laseris resonant is resonant with the with atomic the transition.atomic A correctiontransition. signalA correction is derived from atomicsignal isspectroscopy derived from that atomic is fed back to thespectroscopy laser. that is fed back to the laser.

An optical frequency synthesizer (optical frequency comb) is used to divide the optical frequency down to countable microwave or radio frequency signals. From: Poli et al. “Optical atomic clocks”, La rivista del Nuovo Cimento 36, 555 (2018) arXiv:1401.2378v2 Extraordinary progress in the control of atomic systems 300K

nK Image: Ye group and Steven Burrows, JILA Ultracold Trapped Precisely controlled Neutral atoms in optical lattice vs. a single trapped ion

+ 14 2 Yb 4f 5d D3/2 PTB E2 435 nm 10 years 13 2 2 Mg 4f 6s F7/2 Al+ Cd E3 Sr 467 nm Yb Hg 14 2 4f 6s S1/2 Strontium optical lattice neutral atom clock Yb+ single trapped ion clock http://www.nist.gov/pml/div689/20140122_strontium.cfm Applications of atomic clocks 10 -18 1 cm height

Magma chamber

GPS, deep Very Long Baseline Interferometry Relativistic geodesy Gravity Sensor space probes

Searches for physics beyond the Definition of the second Quantum simulation Standard Model Image Credits: NOAA, Science 281,1825; 346, 1467, University of Hannover, PTB, PRD 94, 124043, Eur. Phys. J. Web Conf. 95 04009 Search for physics beyond the standard model with atomic clocks

Atomic clocks can measure and compare frequencies to exceptional precisions!

If fundamental constants change (now) due to for various “new physics” effects atomic clock may be able to detect it.

Frequency E1 1 will change hν 0 BEYOND THE E 0 0 STANDARD MODEL? Searches for physics beyond the Standard Model with atomic clocks

Dark matter Image credit: Jun Ye’s group searches Search for the violation Tests of the of Lorentz invariance equivalence principle

Image credit: NASA Are fundamental α constants constant? Gravitational wave detection with atomic clocks PRD 94, 124043 (2016) RMP 90, 025008 (2018) http://www.nist.gov/pml/div689/20140122_strontium.cfm

JILA Sr clock Clocks: new dark matter detectors 2×10-18

• 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 How good is the clock? E 1 1 How optical atomic clock works hν 0 Ramsey scheme E0 0 Measure: 0 or 1 ?

01+ E2

π 2 π E1 detect 2 wait 2 fluorescence E0 0 Quantum projection noise: can only get 0 or 1

Initialize Initialize Repeat many times to get probability of Atom should be now excitation, scan different in 1 if on resonance frequencies to maximize How good is a clock: stability and uncertainty

Stability is a measure of the precision with which we can measure a quantity. Uncertainty: how well we understand It is usually stated as a function of averaging the physical processes that can shift the time since for many noise processes the measured frequency from its unperturbed precision increases (i.e., the noise is reduced (“bare"), natural atomic frequency. through averaging) with more measurements. From: Poli et al. “Optical atomic clocks”, arXiv:1401.2378v2 How good is a clock: stability and uncertainty

Sr lattice clock

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). Clock instability Quantum projection noise limit

11 −15 1 στy ( ) ≈ στy ( ) =5 × 10 2πν 0 NTτ τ / s How long will it take to get to 10-19 uncertainty? Clock transition The frequency averaging period The number of atoms or ions used in a single 79 years! measurement Duration of single measurement cycle N=1 for ions N>1000 for neutral atoms Limited by clock state lifetime and laser stability Clock instability Quantum projection noise limit

11 −15 1 στy ( ) ≈ στy ( ) =1 × 10 2πν 0 NTτ τ / s How long will it take to get to 10-19 uncertainty? Clock transition The frequency averaging period The number of atoms or ions used in a single 3 years! measurement Duration of single measurement cycle N=1 for ions N>1000 for neutral atoms Limited by clock state lifetime and laser stability Clock instability Quantum projection noise limit

11 −16 1 στy ( ) ≈ στy ( ) =1 × 10 2πν 0 NTτ τ / s How long will it take to get to 10-19 uncertainty? Clock transition The frequency averaging period The number of atoms or 11.6 days ions used in a single measurement Duration of single N=1 need T=10 seconds measurement cycle N=1 for ions π π N>1000 for neutral atoms Limited by clock state

2 wait measure

initialize 2 lifetime and laser stability Variation of fundamental constants Theories with varying dimensionless fundamental constants J.-P. Uzan, Living Rev. Relativity 14, 2 (2011) String theories Other theories with extra dimensions Loop quantum gravity Dark energy theories: chameleon and quintessence models …many others

Frequency of optical transitions depends 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) Variation of fundamental constants Theories with varying dimensionless fundamental constants J.-P. Uzan, Living Rev. Relativity 14, 2 (2011) String theories Other theories with extra dimensions Loop quantum gravity Dark energy theories: chameleon and quintessence models …many others Frequency of optical transitions depends on the fine-structure constant α.

Some clocks are more sensitive to this effect than others

Measure the ratio of two optical clock frequencies to search for the variation of α. Keep doing this for a while. Sensitivity of optical clocks to α-variation/dark matter

α 2 Enhancement factor EE=+−0 q1 2q 2 = α0 K E0 Can calculate with high accuracy Need: large K for at least one for the clocks Best case: large K2 and K1 of opposite sign for clocks 1 and 2

∂∂v2 1 α ln = ()K2 − K1 ∂∂tv1 α t Frequency ratio Test of α-variation accuracy -18 -20 10 100 10 Easier to measure large effects! Enhancement factors for current clocks 2q K = K E0 Cavity: part of the + clock laser systems + 1 K( Hg) = 0.8, K( Yb E2) = 1 K() Sr = 0.4 Effective K=1 K() Yb = 0.3 0 K( Al++) = 0.01, K() Sr= 0.06, K( Ca ) = 0.1 Excellent stability N ~ 1000

-3 K() Hg + = −2.9 Single ion clocks, N = 1 ∂∂α + v2 1 -6 K() Yb E36= − ln = ()K2 − K1 ∂∂tv1 α t Observable: ratio of two clock frequencies

+ Measure a ratio of Al+ clock ν (Hg + ) K() Hg = −2.9 Sensitivity factors frequency to Hg+ clock Not sensitive to α-variation, ν + K Al + = 0.01 frequency (Al ) ( ) used as reference 1126 nm 1070 nm

laser fiber laser

×2 ×2

fiber

×2 ×2 9Be+ 199Hg++ fb,Al Hg fb,Hg 27Al+

n frep+ fceo m frep+ fceo Picture credit: Jim Bergquist Science 319, 1808 (2008) Why search for dark matter?

Slide from Andrew Long’s 2018 LDW talk 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 Simon Knapen, 2018 KITP Dilatons −3 Dark matter density in our Galaxy > λdB

λdB is the de Broglie wavelength of the particle. Then, the scalar dark matter exhibits coherence and behaves like a wave A. Arvanitaki et al., PRD 91, 015015 (2015) How to detect ultralight dark matter with clocks?

Asimina Arvanitaki, Junwu Huang, and Ken Van Tilburg, PRD 91, 015015 (2015)

10-22 eV 10-12 eV µeV eV GeV

Dark matter field couples to electromagnetic interaction and “normal matter”

It will make fundamental coupling constants and mass ratios oscillate

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

… photons Dark matter Then, clock frequencies will oscillate! DM virial velocities ~ 300 km/s

One oscillation per second

One oscillation per 11 days Ultralight dark matter

… photons Dark matter Then, clock frequencies will oscillate! DM virial velocities ~ 300 km/s

Measure clock frequency ratios:

Result: plot couplings de vs. DM mass mf Sensitivity factors to α-variation Clock measurement protocols for the dark matter detection Make a clock ratio measurement over time ∆τ

Make N such measurements, preferably regularly spaced

π π Need excellent SHORT term stability

2 wait 2 measure τ

Τ For example 1 second 11 ω στ( ) ≈ φ y 2πν τ Detection signal: 0 NT A peak with monochromatic frequency in the discrete Fourier transform of this time series. A. Arvanitaki et al., PRD 91, 015015 (2015) Clock measurement protocols for the dark matter detection

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

Al least one dark matter oscillation during this time τ

Τ No more than one dark matter oscillation during this time or use extra pulse sequence

Detection signal: A peak with monochromatic frequency in the discrete Fourier transform of this time series. ωφ A. Arvanitaki et al., PRD 91, 015015 (2015) Clock measurement protocols for the dark matter detection

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

Al least one dark matter oscillation during this time τ

Τ No more than one dark matter oscillation during this time – actually need 4-5 measurement points per DM oscillation to get correct frequency

Detection signal: A peak with monochromatic frequency in the discrete Fourier transform of this time series. ωφ A. Arvanitaki et al., PRD 91, 015015 (2015) Present scalar DM limits

? Dynamic decoupling?

From PRL 120, 141101 (2018) Transient variations

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.

GPM.DM collaboration: Roberts at el., Nature Communications 8, 1195 (2017) 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 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 Improve atomic clocks: better stability and uncertainty

Ion chains Large ion crystals 3D optical lattice clocks

Measurements beyond the quantum limit Entangled clocks Image credits: NIST, Innsbruck group, MIT Vuletic group, Ye JILA group 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. Enhancement factors for current clocks 2q K = K E0 Cavity: part of the + clock laser systems + 1 K( Hg) = 0.8, K( Yb E2) = 1 K() Sr = 0.4 Effective K=1 K() Yb = 0.3 0 K( Al++) = 0.01, K() Sr= 0.06, K( Ca ) = 0.1 Excellent stability N ~ 1000

-3 K() Hg + = −2.9 Single ion clocks, N = 1 ∂∂α + v2 1 -6 K() Yb E36= − ln = ()K2 − K1 ∂∂tv1 α t Need very precise frequency standards using NEW systems with very large K

∂∂ν 2 1 α ln = ()K2 − K1 ∂∂ttνα1 The Future: New Atomic Clocks

Science 347, 1233 (2015)

Clocks with ultracold highly charged ions Nuclear clock ∆K ~ 110 possible K ~ 104-105 First demonstration of quantum logic spectroscopy at PTB, Germany, 10-15! From atomic to nuclear clocks!

Clock based on transitions in atoms

What about transitions in nuclei? M. S. Safronova, Annalen der Physik 531, 1800364 (2019) Obvious problem: typical nuclear energy levels are in MeV Six orders of magnitude from ~few eV we can access by lasers!

Nature 533, 47 (2016) A very special nucleus: thorium 229

MeV Excited Atomic nuclear 1.0 states Nucleus

0 Ground state Only ONE exception! 229mTh Laser spectroscopic characterization of the nuclear clock isomer 229mTh, Thielking et al., Nuclear transition Nature 556, 321 (2018) 150(3) nm [8.3(2)eV] Lifetime ~ 5000s Energy of the 229Th nuclear clock transition Seiferle et al., Nature 573, 243 (2019) 229Th Th nuclear clock: Exceptional sensitivity to new physics

ground state isomer 8.3 eV Coulomb Coulomb contribution contribution MeV scale Total binding energy Total m α q Possible 4-5 orders of magnitude enhancement to the variation of and Λ but orders of magnitude uncertainty in the enhancement factors. QCD

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! Picture credit: Thorsten Schumm Broadband relaxion detection with a nuclear clock Ignoring dark matter coherence time

Prelim: Banerjee, Kim, Matsedonski, Perez, Safronova Relaxion detection with a nuclear clock Accounting dark matter coherence time, normal halo

Further work on dynamic decoupling is in progress Leibrandt, Hume, Safronova

Prelim: Banerjee, Kim, Matsedonski, Perez, Safronova Atomic clocks: Great potential for discovery of new physics

Many new developments coming in the next 10 years!

Need NEW IDEAS how to use clocks for new physics searches