ABRACADABRA: Detecting axion dark matter

0902.1089

Fermi (NASA) Ben Safdi 1406.0507 MIT / University of Michigan Y. Kahn, B.S., J. Thaler, PRL 2016 ABRA-10 cm collaboration

2017 I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

I Axion couples to QED

1 µν αEM = gaγγaFµνF˜ gaγγ L −4 ∝ fa

I Axion (field) can make up all of dark matter

Axions

-22 -12 -3 9 12 27

log10(ma/eV)

I Axion solves strong CP problem (neutron EDM) 2 a g ˜µν axion = 2 GµνG L −fa 32π

Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978 I Axion couples to QED

1 µν αEM = gaγγaFµνF˜ gaγγ L −4 ∝ fa

I Axion (field) can make up all of dark matter

Axions

-22 -12 -3 9 12 27

log10(ma/eV)

I Axion solves strong CP problem (neutron EDM) 2 a g ˜µν axion = 2 GµνG L −fa 32π

I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978 I Axion (field) can make up all of dark matter

Axions

-22 -12 -3 9 12 27

log10(ma/eV)

I Axion solves strong CP problem (neutron EDM) 2 a g ˜µν axion = 2 GµνG L −fa 32π

I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

I Axion couples to QED

1 µν αEM = gaγγaFµνF˜ gaγγ L −4 ∝ fa

Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978 Axions

-22 -12 -3 9 12 27

log10(ma/eV)

I Axion solves strong CP problem (neutron EDM) 2 a g ˜µν axion = 2 GµνG L −fa 32π

I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

I Axion couples to QED

1 µν αEM = gaγγaFµνF˜ gaγγ L −4 ∝ fa

I Axion (field) can make up all of dark matter Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978 Motivation

PDG • Search for 10-14-10-6 eV pseudoscalar (ALP) dark matter

• Motivated by Strong CP Problem and String Theory

• Created via realignment mechanism

• Couples weakly to E&M: 1 g aF F˜µ⌫ L 4 a µ⌫

Reyco Henning PATRAS 2017 — May 16,2017 ABRACADABRA !3 Motivation

PDG • Search for 10-14-10-6 eV pseudoscalar (ALP) dark matter

• Motivated by Strong CP Problem and String Theory

• Created via realignment mechanism

• Couples weakly to E&M: 1 g aF F˜µ⌫ L 4 a µ⌫

Reyco Henning PATRAS 2017 — May 16,2017 ABRACADABRA !3 Motivation

PDG • Search for 10-14-10-6 eV pseudoscalar (ALP) dark matter

• Motivated by Strong CP Problem and String Theory

• Created via realignment mechanism

• Couples weakly to E&M: 1 g aF F˜µ⌫ L 4 a µ⌫

Reyco Henning PATRAS 2017 — May 16,2017 ABRACADABRA !3 Motivation

PDG • Search for 10-14-10-6 eV pseudoscalar (ALP) dark matter

• Motivated by Strong CP Problem and String Theory

• Created via realignment mechanism

• Couples weakly to E&M: 1 g aF F˜µ⌫ L 4 a µ⌫

Reyco Henning PATRAS 2017 — May 16,2017 ABRACADABRA !3 I Magnetoquasistatic approximation: new electric current that follows B-field lines ∂a B = g B ∇ × aγγ ∂t

1 2 2 I Locally: a(t) a sin(m t) and m a = ρ ≈ 0 a 2 a 0 DM I Jeff = gaγγ 2 ρDMB sin(mat) p

Axion dark matter modifies Maxwell’s equations

I Recall axions also couple to QED:

1 µν αEM = gaγγaFµνF˜ gaγγ L −4 ∝ fa 1 2 2 I Locally: a(t) a sin(m t) and m a = ρ ≈ 0 a 2 a 0 DM I Jeff = gaγγ 2 ρDMB sin(mat) p

Axion dark matter modifies Maxwell’s equations

I Recall axions also couple to QED:

1 µν αEM = gaγγaFµνF˜ gaγγ L −4 ∝ fa

I Magnetoquasistatic approximation: new electric current that follows B-field lines ∂a B = g B ∇ × aγγ ∂t Axion dark matter modifies Maxwell’s equations

I Recall axions also couple to QED:

1 µν αEM = gaγγaFµνF˜ gaγγ L −4 ∝ fa

I Magnetoquasistatic approximation: new electric current that follows B-field lines ∂a B = g B ∇ × aγγ ∂t

1 2 2 I Locally: a(t) a sin(m t) and m a = ρ ≈ 0 a 2 a 0 DM I Jeff = gaγγ 2 ρDMB sin(mat) p Axion dark matter generates magnetic flux Y. Kahn, B.S., J. Thaler, PRL 2016

Superconducting pickup loop

R r a h B0 Two readout strategies

Broadband Resonant M Δω M

L L i Lp L p C L R Li

Better at low frequency Better at high frequency f [Hz] 102 103 104 105 106 107 108 109 8 10

10 CAST 10

IAXO

] 12 1 10 [GeV ADMX a g 14 10

16 10

KSVZ 12 11 10 9 8 7 6 5 10 10 10 10 10 10 10 10 ma [eV] ABRA-10 cm (happening now!) f [Hz] 102 103 104 105 106 107 108 109 8 10 ABRA-10cm (Broad.)

10 CAST 10

IAXO

] 12 1 10 Broadband Resonant [GeV M Δω ADMX M a g 14 10 L L i Lp L p C L R Li 16 10 1 month Better at low frequency Better at high frequency B = 1 T KSVZ 12 11 10 9 8 7 6 5 10 10 10 10 10 10 10 10 ma [eV] ABRA-10 cm (happening now!)

f [Hz] 102 103 104 105 106 107 108 109 8 10 ABRA-10cm (Broad.) ABRA-10cm (Res.)

10 CAST 10

IAXO

] 12 1 10

Broadband Resonant [GeV M M ADMX Δω a g 14 10 L L i Lp L p C L R Li

16 10 Better at low frequency Better at high frequency 1 month B = 1 T KSVZ 12 11 10 9 8 7 6 5 10 10 10 10 10 10 10 10 ma [eV] ABRA-Gen2 f [Hz] 102 103 104 105 106 107 108 109 8 10 ABRA-10cm (Broad.) ABRA-100cm (Broad.) ABRA-300cm (Broad.) CAST 10 10 ABRA-10cm (Res.) ABRA-100cm (Res.) ABRA-300cm (Res.) IAXO

] 12 1 10 [GeV ADMX a g 14 10

16 10 1 year B = 5 T KSVZ 12 11 10 9 8 7 6 5 10 10 10 10 10 10 10 10 ma [eV] The MIT prototype: ABRACADABRA-10 cm

I ABRACADABRA: A Broadband/Resonant Approach to Cosmic Axion Detection with an Amplifying B-field Ring Apparatus

I People (LNS+CTP, PSFC, Princeton, UNC, UMich): Janet Conrad, Joe Formaggio, Sarah Heine, Reyco Henning, Yoni Kahn, Joe Minervini, Jonathan Ouellet, Kerstin Perez, Alexey Radovinsky, B.S., Jesse Thaler, Daniel Winklehner, Lindley Winslow

I Funded by the NSF! ABRACADABRA-10Cosmic Axion cm Detection at MIT with an AmplifyingABRACADABRA-10cm B-field Ring Apparatus 12 cm

Super conducting pickup cylinder

12 cm

Bmax ≈ 1 T Counter-wound superconducting coils.

Reyco Henning PATRAS 2017 — May 16,2017 ABRACADABRA !16 Ben Safdi Massachusetts Institute of Technology

2015 ABRA-10 cm

Jonathan Ouellet (postdoc) Lindley Winslow (PI) ABRA-10 cm ABRA-10 cm Light bosonic dark matter future

I MIT: ABRA-10 cm followed by ABRA-1 m (B 5 T) ∼

I Axions and light bosonic dark matter well motivated by strong-CP problem and high-scale physics (e.g., compactified string theory)

I New ideas to search for ultra-light scalars, dark-photons, etc. (laboratory experiments + astrophysics) 17 19 I e.g., CASPEr experiment (fa 10 10 GeV) ∼ 17− 19 I Black Hole superradiance (fa 10 10 GeV) 15 ∼ − I Florida LC circuit (fa 10 GeV) 11 ∼ I ADMX-HF (f 10 GeV) a ∼ I CMB (isocurvature + ∆Neff) I DM-radio (dark photons) Questions? Axion backup 2 I Axion effective current: I R J eff ∼ eff Ieff I B R g 2 ρ B0 sin(m t) ∼ R ∼ aγγ DM a 16 −22 I f = 10 GeV, B0p 5 T, R 4 m: B 10 T (KSVZ) a ∼ ∼ ∼

Axion dark matter generates magnetic flux

Superconducting pickup loop

R r a h B0

I Estimate B-field induced through pickup loop (r = a = h = R) Axion dark matter generates magnetic flux

Superconducting pickup loop

R r a h B0

I Estimate B-field induced through pickup loop (r = a = h = R) 2 I Axion effective current: I R J eff ∼ eff Ieff I B R g 2 ρ B0 sin(m t) ∼ R ∼ aγγ DM a 16 −22 I f = 10 GeV, B0p 5 T, R 4 m: B 10 T (KSVZ) a ∼ ∼ ∼ I Scale to R 4 m 1/2 ≈ 20 I S 5 10− T/√Hz B ≈ × I t = 1 year interrogation time for GUT scale axion 2 3 I Coherence time: τ 2π/(mav ) 10 s (v 10− ) 1∼/2 1/4 ∼ 22 ∼ I S/N = 1 for B = S (tτ)− 10− T B ∼

Broadband estimate M

R Lp L

Li

I Example from MRI application: (Myers et. al. 2007) 1/2 17 I B-field sensitivity: S 6.4 10− T/√Hz B ≈ × I R 3.3 cm ≈ I t = 1 year interrogation time for GUT scale axion 2 3 I Coherence time: τ 2π/(mav ) 10 s (v 10− ) 1∼/2 1/4 ∼ 22 ∼ I S/N = 1 for B = S (tτ)− 10− T B ∼

Broadband estimate M

R Lp L

Li

I Example from MRI application: (Myers et. al. 2007) 1/2 17 I B-field sensitivity: S 6.4 10− T/√Hz B ≈ × I R 3.3 cm ≈ I Scale to R 4 m 1/2 ≈ 20 I S 5 10− T/√Hz B ≈ × 1/2 1/4 22 I S/N = 1 for B = S (tτ)− 10− T B ∼

Broadband estimate M

R Lp L

Li

I Example from MRI application: (Myers et. al. 2007) 1/2 17 I B-field sensitivity: S 6.4 10− T/√Hz B ≈ × I R 3.3 cm ≈ I Scale to R 4 m 1/2 ≈ 20 I S 5 10− T/√Hz B ≈ × I t = 1 year interrogation time for GUT scale axion 2 3 I Coherence time: τ 2π/(m v ) 10 s (v 10− ) ∼ a ∼ ∼ Broadband estimate M

R Lp L

Li

I Example from MRI application: (Myers et. al. 2007) 1/2 17 I B-field sensitivity: S 6.4 10− T/√Hz B ≈ × I R 3.3 cm ≈ I Scale to R 4 m 1/2 ≈ 20 I S 5 10− T/√Hz B ≈ × I t = 1 year interrogation time for GUT scale axion 2 3 I Coherence time: τ 2π/(mav ) 10 s (v 10− ) 1∼/2 1/4 ∼ 22 ∼ I S/N = 1 for B = S (tτ)− 10− T B ∼ ABRA-10 cm: vertical cut

test wire ABRA-10 cm: pickup cylinder

Superconducting pickup cylinder

Pickup loop leads

Cut cylinder so current returns through leads 1 T P (ω) dtB(t) sin(ωt) = P0(ω) + Pn(ω) ≡ √T Z0

2 1/2 I Spectral density: lim Pn(ω) S (ω) [T /√Hz] T →∞ | | → B I T < τ: 2 2 2 1/2 I P (ω ) B T B = S (ω )/T | 0 0 | ∝ → B 0 I T > τ 2 2 B 2 I P (ω ) T τ = B τ | 0 0 | ∝ T × I But, line-width is broad and can resolve N = T/τ different frequencies 2 1/2 √ 1/2 √ I B = SB (ω0)/τ/ N = SB (ω0)/ T τ

Magnetic field sensitivity calculation

I B(t) = B0 sin[ω0t + φ(t)] + Bn(t) I φ(t): evolves over coherence time τ 2 1/2 I Spectral density: lim Pn(ω) S (ω) [T /√Hz] T →∞ | | → B I T < τ: 2 2 2 1/2 I P (ω ) B T B = S (ω )/T | 0 0 | ∝ → B 0 I T > τ 2 2 B 2 I P (ω ) T τ = B τ | 0 0 | ∝ T × I But, line-width is broad and can resolve N = T/τ different frequencies 2 1/2 √ 1/2 √ I B = SB (ω0)/τ/ N = SB (ω0)/ T τ

Magnetic field sensitivity calculation

I B(t) = B0 sin[ω0t + φ(t)] + Bn(t) I φ(t): evolves over coherence time τ 1 T P (ω) dtB(t) sin(ωt) = P0(ω) + Pn(ω) ≡ √T Z0 I T < τ: 2 2 2 1/2 I P (ω ) B T B = S (ω )/T | 0 0 | ∝ → B 0 I T > τ 2 2 B 2 I P (ω ) T τ = B τ | 0 0 | ∝ T × I But, line-width is broad and can resolve N = T/τ different frequencies 2 1/2 √ 1/2 √ I B = SB (ω0)/τ/ N = SB (ω0)/ T τ

Magnetic field sensitivity calculation

I B(t) = B0 sin[ω0t + φ(t)] + Bn(t) I φ(t): evolves over coherence time τ 1 T P (ω) dtB(t) sin(ωt) = P0(ω) + Pn(ω) ≡ √T Z0

2 1/2 I Spectral density: lim Pn(ω) S (ω) [T /√Hz] T →∞ | | → B I T > τ 2 2 B 2 I P (ω ) T τ = B τ | 0 0 | ∝ T × I But, line-width is broad and can resolve N = T/τ different frequencies 2 1/2 √ 1/2 √ I B = SB (ω0)/τ/ N = SB (ω0)/ T τ

Magnetic field sensitivity calculation

I B(t) = B0 sin[ω0t + φ(t)] + Bn(t) I φ(t): evolves over coherence time τ 1 T P (ω) dtB(t) sin(ωt) = P0(ω) + Pn(ω) ≡ √T Z0

2 1/2 I Spectral density: lim Pn(ω) S (ω) [T /√Hz] T →∞ | | → B I T < τ: 2 2 2 1/2 I P (ω ) B T B = S (ω )/T | 0 0 | ∝ → B 0 I But, line-width is broad and can resolve N = T/τ different frequencies 2 1/2 √ 1/2 √ I B = SB (ω0)/τ/ N = SB (ω0)/ T τ

Magnetic field sensitivity calculation

I B(t) = B0 sin[ω0t + φ(t)] + Bn(t) I φ(t): evolves over coherence time τ 1 T P (ω) dtB(t) sin(ωt) = P0(ω) + Pn(ω) ≡ √T Z0

2 1/2 I Spectral density: lim Pn(ω) S (ω) [T /√Hz] T →∞ | | → B I T < τ: 2 2 2 1/2 I P (ω ) B T B = S (ω )/T | 0 0 | ∝ → B 0 I T > τ 2 2 B 2 I P (ω ) T τ = B τ | 0 0 | ∝ T × 2 1/2 √ 1/2 √ I B = SB (ω0)/τ/ N = SB (ω0)/ T τ

Magnetic field sensitivity calculation

I B(t) = B0 sin[ω0t + φ(t)] + Bn(t) I φ(t): evolves over coherence time τ 1 T P (ω) dtB(t) sin(ωt) = P0(ω) + Pn(ω) ≡ √T Z0

2 1/2 I Spectral density: lim Pn(ω) S (ω) [T /√Hz] T →∞ | | → B I T < τ: 2 2 2 1/2 I P (ω ) B T B = S (ω )/T | 0 0 | ∝ → B 0 I T > τ 2 2 B 2 I P (ω ) T τ = B τ | 0 0 | ∝ T × I But, line-width is broad and can resolve N = T/τ different frequencies Magnetic field sensitivity calculation

I B(t) = B0 sin[ω0t + φ(t)] + Bn(t) I φ(t): evolves over coherence time τ 1 T P (ω) dtB(t) sin(ωt) = P0(ω) + Pn(ω) ≡ √T Z0

2 1/2 I Spectral density: lim Pn(ω) S (ω) [T /√Hz] T →∞ | | → B I T < τ: 2 2 2 1/2 I P (ω ) B T B = S (ω )/T | 0 0 | ∝ → B 0 I T > τ 2 2 B 2 I P (ω ) T τ = B τ | 0 0 | ∝ T × I But, line-width is broad and can resolve N = T/τ different frequencies 2 1/2 √ 1/2 √ I B = SB (ω0)/τ/ N = SB (ω0)/ T τ Complementary proposals for axion dark matter experiments CASPEr:CASPEr: oscillating NMR neutron EDM detection [Budker et al., 1306.6089] a g2 i ¯ ˜µνp2⇢DM axion = θµ⌫+ 2 GµνG gdaNLµ⌫ 5NF− fa 32dπn = gd cos(mat) L 2   ma 2.4 10−16 e cm dn(t)frequency = gHzd a(t) , gd × · 102 104 106 108 1010 1012 1014 ≈ 4 fa resonance !4 New Force ! " 10 frequency Hz

2 4 6 8 10 12 14 10!6 10 10 10 10 10 10 10 Static EDM ! " sin [(2µBext ma)t] 10!8 SN 1987A M(t) npµE⇤✏ d sin(2µB t) 10!5 S n ext ⇡ 2µBext ma !10 " 10 1 SN 1987A !

!12 ADMX

GeV 10 ALP DM ! 10!10

aNN !14 " g 10 2 B ! SQUID ext !16

10 GeV ADMX ! QCD Axion pickup d M g !15 QCD Axion 10!18 10 loop 10!20 E ,v !14 !12 !10 !8 !6 !4 !2 0 10 10!20 10 10 10 10 10 10 10 mass eV Figure 6

CASPEr setup. The applied magnetic field B~ ext is colinear with the sample magnetization, M~ .In Figure 7 10!14 10!12 10!10 10!8 10!6 10!4 10CASPEr-Wind!2µ⌫ 100 the nuclear spins precess around the local velocity of the dark matter, ~v,whilein Sensitivity• of the CASPEr-Wind proposal. ALP parameter! " space in pseudoscalar coupling ofCASPEr-Electric axion the nuclear EDM causes the spins to precess around an e↵ective electric field in Measures couplingmass eV to G µ ⌫ G through nucleon spin to nucleons Eqn. 20 vs mass of ALP. The purple line is the region in which the QCD axionthe may crystal E~ ⇤,perpendiculartoB~ ext.TheSQUIDpickuploopisarrangedtomeasurethe lie. The width of the purple band gives an approximation to the axion model-dependence in this FIG. 2: Estimated constraints in the ALP parameter space in the EDM coupling g (where the nucleontransverse EDM is magnetizationd = g a and of the sample. coupling.• The darker purple portion of the line shows the region in which thed QCD axion could be n d a is theMeasurement local value of the ALP field) vs. the ALP mass [17].taken The green region isin excluded external by the constraints on excess E cooling and B fields allof of supernova the dark 1987A matter [17]. and The have bluefa region

70), and is also well-motivated theoretically (24). 3Note that the Wind coupling leads to a spin-dependent force which could be probed using NMR techniques as well e.g. (80, 81, 82, 83, 84, 85, 86).

www.annualreviews.org Experimental Axion Searches 15 • How can we probe axion dark matter?

ADMX Limit (axion-DM resonant cavity) IAXO Projected (Axions from the Sun) ADMX Projected BH Superradiance?

e.g., Arvanitaki, Baryakhtar, Huang 2014 I Axion a removes dn: 2 a g ˜µν axion = 2 GµνG L −fa 32π

I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

I a as DM: a(t) √ρ cos(m t) ∼ DM a

The strong CP problem (neutron EDM)

-1/3 e -1/3 e I Calculation: d d d 10−15 e cm n ∼ · 15 10 m I Data: +2/3 e ⇠ d < 3 10−26 e cm u | n| × ·

Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978 I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

I a as DM: a(t) √ρ cos(m t) ∼ DM a

The strong CP problem (neutron EDM)

-1/3 e -1/3 e I Calculation: d d d 10−15 e cm n ∼ · 15 10 m I Data: +2/3 e ⇠ d < 3 10−26 e cm u | n| × ·

I Axion a removes dn: 2 a g ˜µν axion = 2 GµνG L −fa 32π

Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978 I a as DM: a(t) √ρ cos(m t) ∼ DM a

The strong CP problem (neutron EDM)

-1/3 e -1/3 e I Calculation: d d d 10−15 e cm n ∼ · 15 10 m I Data: +2/3 e ⇠ d < 3 10−26 e cm u | n| × ·

I Axion a removes dn: 2 a g ˜µν axion = 2 GµνG L −fa 32π

I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978 The strong CP problem (neutron EDM)

-1/3 e -1/3 e I Calculation: d d d 10−15 e cm n ∼ · 15 10 m I Data: +2/3 e ⇠ d < 3 10−26 e cm u | n| × ·

I Axion a removes dn: 2 a g ˜µν axion = 2 GµνG L −fa 32π

I QCD gives a mass: f 1016 GeV m π m 10−9 eV a ≈ f π ≈ f a  a 

I a as DM: a(t) √ρ cos(m t) ∼ DM a Peccei, Quinn 1977; Weinberg 1978; Wilczek 1978