Atomic clocks in the age of gravitational wave detectors - Day 3 - Andrei Derevianko - IPPP ...
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Day 3
Atomic clocks in the age of
gravitational wave detectors
Andrei Dereviank
University of Nevada, Reno, USA
o
What will we cover today?
• Dark matter and modi ed gravit
• Tests of general relativity (GR
• Detection of gravitational wave
• Exotic eld modality in multi-messenger
astronom
• Do not throw away outliers
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Atomic clocks as quantum sensors
Quantum oscillator (qubit) is well protected from the
traditional physics environmental perturbations
Residual traditional physics perturbations are
well characterized ⟹ low-level backgroun
Exotic physics can leave uncharacterized
perturbations in atomic and cavity frequencies
d
Portals to exotic physics
fclock f′clock
➡ Exotic elds can change atomic/cavity frequencies
[variation of fundamental constants by dark sector,…]
➡ Effects of special/general relativity on ticking rate
[modi ed gravity,…]
➡ Comparison link - effective index of refraction
[gravitational waves/dark sector,…]

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Dark matter/dark energy
DM: Handful of observational evidence from gravitational interactions on galactic scale
Conventional paradigm = DM is made out of particles/ eld
What is the microscopic composition
Are there non-gravitational interactions?
Andrei Derevianko - U. Nevada-Reno
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Dif culties with particle dark matter
paradigm
Galactic core cusps vs observed at density pro les
Predicts too many satellite galaxie
Does not explain alignment of satellite galaxies
At odds with bosonic Tully-Fisher relatio
At odds with Renzo’s rul
Collisions of galaxies are too fast (DM has friction)
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Alternative: modi ed gravity
Galactic core
On the largest and/or smallest scales,
gravity acts in novel ways compared Number of satellite galaxie
to the well-tested scales in the middle
Alignment of satellite galaxies
Bosonic Tully-Fisher relatio
Renzo’s rul
Collisions of galaxies
Tests of General Relativity
Dif culties: peaks in cosmic microwave background power spectrum,
early universe, galaxy clusters
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Duality?
Modi ed gravity
Dark matter
We need to search for both manifestations
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Tests of General Relativity
Testing GR with gravitational red shift
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U + ΔU
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Δfclock ΔU
= (1 + α) ×
fclock U
deviation from GR
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U
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Best terrestrial: | α | ≲ 9 × 10−5 Tokyo Skytree (optical clocks)
Best constraints: | α | ≲ 0.19 × 10−5 Galileo GNSS arXiv:1906.06161
Proposed: | α |min ∼ 10−9 FOCOS (Oats)Tokyo Skytree experiment Takamoto, Ushijima, N. Ohmae,Yahagi, Kokado, Shinkai, & Katori, Nat. Photonics 14, 411 (2020)
FOCOS (Fundamental physics with an
Optical Clock Orbiting in Space)
Highly elliptical orbit => variation in U
+ comparison with terrestrial clocks ( xed U)
Chris Oats ++
fiGravitational waves (GW)
Laser Interferometer Gravitational-Wave
Observatory (LIGO)
https://commons.wikimedia.org/w/index.php?curid=46922746Black-hole merger & LIGO detection
LIGO collaboration. Phys. Rev. Lett. 116, 61102 (2016)
Credit: NASA/C. Henze
So far ~20 GW events observed (as of 2021) SNR ~ 5-7Credit: NASA
Some GR/GW basics
( ds) x = ( ct,r )
Line element 2 µ ν µ
(Lorentz scalar) = g µν dx dx
metric
Flat space time
( ds) = ( cdt ) − ( dx ) − ( dy ) − ( dz )
2 2 2 2 2
(flat)
g µν = diag(1,−1,−1,−1)
+ gravitational wave
g µν = g µν
(flat)
+ hµν cos ( k ⋅r − ω t )
Strain ~10-21 (LIGO)Proper time
Dr Greg, commons.wikimedia.org/w/index.php?curid=3812171
τ = ∫ g00 dt
For stationary clock in GW metric
g00 = 1+ h00 cos ( k ⋅r − ω t )
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τ ≈ t + h00 ∫ cos ( k ⋅r − ω t ')dt '
The dark blue vertical line represents an inertial
observer measuring a coordinate time
interval t between events E1 and E2. The red 2
curve represents a clock measuring its proper
time interval τ between the same two events.Clock comparison template in GR
Koop & Finn, PRD 96, 042118 (2014)
emitter receiver
(clock #1) (clock #2)
Emit pulses at regular time intervals and measure intervals b/w arriving pulsesLoeb & Maoz proposal
Loeb & Maoz arxiv astro-ph:1501.00996
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τ ≈ t + h00 ∫ cos ( k ⋅r − ω t ')dt '
2Sr optical clock analysis
S. Kolkowitz et al., Phys. Rev. D 94, 124043 (2016)
Track GW in the intermediate frequency band between LISA and LIGOProposed clock space missions
SAGE: Space Atomic Gravity Explorer
Eur. Phys. J. D 73, 228 (2019)
AEDGE: Atomic Experiment for Dark Matter and Gravity Exploration
Eur. Phys. J. Quantum Technol. 7, 6 (2020)
SAGE and AEDGE: Primary goal is detection of gravitational waves
with secondary goals like dark matter detection and tests of quantum mechanics
ACES: Atomic Clock Ensemble in Space (2015-2016)
main objective is to demonstrate the performances of Cs fountain clock
in the microgravity environment of the International Space Station (ISS).
https://earth.esa.int/web/eoportal/satellite-missions/i/iss-acesExotic eld modality in multi-messenger astronomy fi
ELF module overview
• Exotic low-mass elds (ELFs
• ELF production mechanism
• Expected signal and characteristic anti-chir
• Discovery reach of existing network
• Preliminary results from the GPS data
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pSourced exotic elds
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fiMulti-messenger astronomy
GW170817
Merger of two neutron stars (Aug 17, 2017)
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Host galaxy 40 megaparsecs away
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Trigger: gravitational waves detected by LIGO–Virgo
The source was observed in a comprehensive campaign across the electromagnetic spectrum
- in the X-ray, ultraviolet, optical, infrared, and radio bands
- over hours, days, and weeks.
Can we see the merger in the atomic clock data?Exotic Low-mass Fields (ELFs)
• Modern clocks are not sensitive to gravitational waves
(requires clock comparison over huge baselines
• Exquisite sensitivity to “new” physics beyond the Standard mode
• Focus on exotic, BSM, scalar (S = 0) elds
• abundant in BSM theories [axions, dilatons, relaxions, etc
• can solve the hierarchy & strong-CP problem
• dark-matter candidate
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lELFs as a signature of quantum gravity?
• Coalescing singularities in black hole mergers?
yet unknown theory of quantum gravity
• Scalar-tensor gravity.
BH and NS immersed in the scalar eld. Modes can be excited during the merger.
Dynamic scalarization + monopole scalar emission
• Scalar elds can be trapped in neutron stars - released during the merger
• Clouds of scalars (superatoms) around black holes
up to 10% of BH mass is in the cloud
• Direct production
(e.g., γ + γ → ϕ + ϕ or N + N → N + N + ϕ + ϕ
A pragmatic observational approach based on energy arguments:
ELF channel energy ΔE = fraction of M⊙c 2
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)⇒ Signal at the sensor? Generic wave-form independent of the production mechanism
Scalar bootcamp
Massive (mass m) and spin-less (S = 0) eld
Relativistic Schrödinger eqn [ Klein-Gorgon eqn]
( ℏ )
2
1 ∂2 2 mc
φ−∇ φ+ φ=0
c ∂t
2 2
Solutions: the usual spherical and plane waves
φ ∼ e i(ωt−k⋅r)
Relativistic energy-momentum relation => dispersion relation
ε = ℏω = [(cℏk) + (mc ) ]
2 2 1/2
2
fiScalar waves are like E&M waves
“Internal” refractive index (ultrarelativistic scalars)
1 mc 2
n(ω) ≈ 1 −
2 ℏω
Most of Jackson E&M problems/intuition can be directly transferred
• Group velocity vg ≲ c
• Dispersive propagationWhat kind of ELFs can we detect?
Gravitational wave travels @ c over 108 light-years
vg v c
g
GW
Reasonable time delay < a week ⇒ vg ≈ c
1. ELFs must be ultrarelativistic: mc 2 ≪ ε = ℏω
2. For a clock, max(ω) = 2π Hz ⇒ m ≪ 10−14 eV
ELFs must be ultralightEnergetics
Copious emission
ΔE = fraction of M⊙c 2
∼ 1070 ELFs
ε = 10−10 eV
Large mode occupation numbers => classical eld all the way to the sensor
R ( R )
1 1
φ∼ ∼ 3/2 with dispersion
fiAnti-chirp signature
• Start with a Gaussian pulse (ω0, τ0)
• higher frequency ω have larger momenta ℏk ⇒
Higher frequencies arrive earlier!
• Instantaneous frequency chirp
dωDetailed analysis
1/2
( 0 s )
(t − ts)2
R ( 2π 3/2ω02τ ) ( 2τ 2 )
1 cΔE ω0 2
ϕ(t) ≈ exp − × cos ω (t − ts) − (t − t )
4δt
2
( ε0 ) 2c
2
mc R
Time lag between GW and ELF bursts δt =
Δε
Duration at the sensor τ ≈ 2 δt
ε0
dω(t) ω0
Frequency slope =−
dt 2δtLIGO style time frequency map
1. Chop data stream into equal chunk
2. Discrete Fourier Transform in each windo
3. Each tile = (window time stamp, frequency
4. Compute power spectral density in each tile
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)Power of the network
The same but time-shifted signal
+ locating progenitor in the skyELF power spectrum template
ELF burst duration τ
GW trigger
frequency
ω0
Δω
delay δt time
tGW ts
Anti-chirp is independent of the production mechanismNetwork desiderata
c 10
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L
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τ
Time resolution Δt
1. Resolve leading edge: Δt ≪ L/c
2. Resolve envelope: Δt ≪ τ
GNOME: L ∼ 10,000 km; L/c ∼ 40 ms ; Δt = 1 ms
GPS: L ∼ 50,000 km; L/c ∼ 0.2 s ; Δt = 30 s → 1 s
GPS can not track the leading edge = compound multi-node sensor
all clocks must have the same signalCoupling ELFs to sensors
Linear
Quadratic
Induced variation in fundamental constants
Δα Δme
= Γα φ(r, t) = Γme φ(r, t)
α me
⇒ affects clock frequencies and the measured timeProjected sensitivity GW170817 (NS+NS)
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�� �� ��� R = 40 Mpc
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mec 2ψ̄eψe
( 4Λα )
1 2 2
ℒ⊃ − + Fμν ϕ
Λme2 2Variations of fundamental constants (2021)
Oscillating
Slow drifts Transients Oscillations Stochastic
transients
“Clumpy” D Dilaton D Virialized D Black hole merger
Dark energy?
(2014) (2015) (2016) (2020)
Andrei Derevianko - U. Nevada-Reno
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sPreliminary results from GPS clocks
GPS.DM observatory
Credit: Conner Dailey
Mining ~20 years of archival data for atomic clocks onboard GPS satellite
30 second sampling time - need faster sampling rate for the ELF search
sExcess power in GPS atomic clocks
Gravitational wave trigger
1/2
3.0
3/8 2.5
Frequency (Hz)
Normalized Power
2.0
1 second GPS data by G. Blewitt
1/4
1.5
1/8 1.0
0.5
0
-1000 -800 -600 -400 -200 0 200 400 0
t-tc (s)
1/2
3.0
3/8 2.5
Frequency (Hz)
Normalized Power
2.0
1/4
1.5
1/8 1.0
0.5
0
1000 2000 3000 4000 5000 0
t-tc (s)Better 1 s data (Paul Reis, JPL)
• The “ELF signal” went away
• Work in progress - still artifacts in 1s data.
• We can set limits on quadratic couplings.
Conner Dailey, MSc thesis, U. Nevada, Reno (2019
Current efforts: Arko Pratim Sen
.
)Cavities vs clocks
At c, ELF burst propagates across Earth in 40 ms.
Clock sampling rate is slow ~ Hz. Terrestrial networks can not track ELFs
Cavities ~ 100 kHz. ELFs can be tracked
Campus-sized network ~ 3 km
A. Geraci, C. Bradley, D. Gao, J.Weinstein, and A. Derevianko, PRL 123, 31304 (2019)
!
.ELF summary
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ELF burst duration τ
GW trigger
frequency
ω0
Δω
delay δt time
tGW tsOutliers: Black swan physics
Black swan physics
Rare but dramatic events
[both in time and frequency domains
Pragmatic empirical approach to dat
Data is the king. Make it public.
Do not throw away outliers
[unless you know technical reasons]
Budker & Derevianko, Physics Today 68, 10 (2015)
a
]“Fundamental” physics sensors summary
"
α! & ∇α
• Variation of fundamental constant
• Dark matter searche
• Gravitational wave
• Tests of general relativit
• Multi-messenger astronom
•…
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