Axion Detection With NMR

Transcription

1 PRD 84 (2011) arxiv: to appear Axion Detection With NMR Peter Graham Stanford with Dmitry Budker Micah Ledbetter Surjeet Rajendran Alex Sushkov

2 Dark Matter Motivation two of the best candidates: WIMPs and Axions many experiments search for WIMPs, only one (ADMX) can search for axion DM currently challenging to discover axions in most of parameter space Important to find new ways to detect axions the QCD axion solves the Strong CP problem Easy to generate axions from high energy theories have a global PQ symmetry broken at a high scale fa string theory or extra dimensions naturally have axions from non-trivial topology Svrcek & Witten (2006) naturally expect large fa ~ GUT (10 16 GeV), string, or Planck (10 19 GeV) scales

3 f a (GeV) Constraints and Searches

4 f a (GeV) Constraints and Searches Axion dark matter

5 f a (GeV) Constraints and Searches Axion dark matter in most models: L a F F f = a E B a f a laser experiments: γ B 1 f 4 a 10 8 axion emission affects SN1987A, White Dwarfs, other astrophysical objects collider & laser experiments, ALPS, CAST

6 f a (GeV) Constraints and Searches Axion dark matter in most models: L a F F f = a E B a f a a axion-photon conversion suppressed 1 f 2 a γ size of cavity increases with fa signal 1 f 3 a B microwave cavity (ADMX) γ laser experiments: B 1 f 4 a 10 8 axion emission affects SN1987A, White Dwarfs, other astrophysical objects collider & laser experiments, ALPS, CAST

7 f a (GeV) Constraints and Searches Axion dark matter in most models: L a F F f = a E B a f a a axion-photon conversion suppressed 1 f 2 a γ size of cavity increases with fa signal 1 f 3 a B S. Thomas microwave cavity (ADMX) γ laser experiments: B 1 f 4 a 10 8 axion emission affects SN1987A, White Dwarfs, other astrophysical objects collider & laser experiments, ALPS, CAST Other ways to search for high fa axions?

8 Light Scalar Dark Matter A WIMP is a heavy particle very low phase space density other possibility is a light particle high phase space density if m 0.01 ev since ρ DM 0.3 GeV cm 3 (0.04 ev)4 the axion provides a well-motivated example of such a DM candidate general class is Axion-Like Particles (ALPs)

9 Light Scalar Dark Matter A WIMP is a heavy particle very low phase space density other possibility is a light particle high phase space density if m 0.01 ev since ρdm GeV (0.04 ev) cm3 the axion provides a well-motivated example of such a DM candidate general class is Axion-Like Particles (ALPs) such light scalar DM can often be described as a field: a (t, x) search for coherent effects of the entire field, not single hard particle scatterings

10 misalignment production: Cosmic Axions after inflation axion is a constant field, mass turns on at T ~ ΛQCD then axion oscillates V a(t) a 0 cos (m a t) a Preskill, Wise & Wilczek, Abott & Sikivie, Dine & Fischler (1983) axion easily produces correct abundance ρ = ρ DM requires ai f a fa M Pl late time entropy production eases this e.g. f a M Pl 10 7 a i f a 1 or f a M Pl 10 3 a i f a 10 2 inflationary cosmology does not prefer flat prior in ϴi over flat in fa all fa in DM range (all axion masses mev) equally reasonable

11 A Different Operator For Axion Detection So how can we detect high fa axions? Strong CP problem: L θ GG creates a nucleon EDM d θ e cm the axion: L a f a G G + m 2 aa 2 creates a nucleon EDM d a f a e cm

12 A Different Operator For Axion Detection So how can we detect high fa axions? Strong CP problem: L θ GG creates a nucleon EDM d θ e cm the axion: L a f a G G + m 2 aa 2 creates a nucleon EDM d a f a e cm a(t) a 0 cos (m a t) with m a (200 MeV)2 f a GeV MHz f a axion dark matter ρ DM m 2 aa 2 (200MeV) 4 a f a GeV cm 3 so today: a f a independent of fa the axion gives all nucleons a rapidly oscillating EDM independent of fa

13 A Different Operator For Axion Detection the axion gives all nucleons a rapidly oscillating EDM thus all (free) nucleons radiate standard EDM searches are not sensitive to oscillating EDM We ve considered two methods for axion detection: 1. EDM affects atomic energy levels (cold molecules) PRD 84 (2011) arxiv: collective effects of the EDM in condensed matter systems (to appear)

14 NMR Technique SQUID pickup loop µ B ext E high nuclear spin alignment achieved in several systems, persists for T1 ~ hours

15 NMR Technique SQUID pickup loop µ d B ext high nuclear spin alignment achieved in several systems, persists for T1 ~ hours applied E field causes precession of nucleus SQUID measures resulting transverse magnetization builds on e - EDM experiments Lamoreaux (2002) if Larmor frequency matches axion mass get resonant enhancement E

16 Transverse Magnetization Signal M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t)

17 Transverse Magnetization Signal M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) signal scales with large density of nuclei: n = cm 3

18 Transverse Magnetization Signal M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) signal scales with large density of nuclei: n = cm 3 example material: 207 Pb = µ =0.6µ N s 10 2

19 Transverse Magnetization Signal M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) signal scales with large density of nuclei: n = cm 3 example material: 207 Pb = µ =0.6µ N s 10 2 ~ few enhancement possible?

20 Transverse Magnetization Signal signal scales with large density of nuclei: n = cm 3 example material: M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) 207 Pb = resonant enhancement µ =0.6µ N s 10 2 ~ few enhancement possible? resonance scan over axion masses by changing Bext

21 Transverse Magnetization Signal signal scales with large density of nuclei: n = cm 3 example material: M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) 207 Pb = resonant enhancement µ =0.6µ N s 10 2 ~ few enhancement possible? resonance scan over axion masses by changing Bext take sample size: L 10 cm we take SQUID magnetometer: T Hz but SERF magnetometers are T Hz

22 Transverse Magnetization Signal M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) signal scales with large density of nuclei: n = cm 3 example material: 207 Pb = µ =0.6µ N s 10 2 ~ few enhancement possible? resonance scan over axion masses by changing Bext take sample size: L 10 cm we take SQUID magnetometer: T Hz but SERF magnetometers are T Hz measures an amplitude ( phase ) and not a rate

23 Ferroelectric below critical temperature some materials have ferroelectric phase transition ferroelectrics (e.g. PbTiO3) have large effective internal electric fields: E = V cm We don t need to flip directions dynamically, so any polar crystal should work may allow enhancement in E* by few

24 Resonant Enhancement M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) resonant enhancement limited by axion coherence time τ a and nuclear spin transverse relaxation time T 2 2π m a v 2

25 Resonant Enhancement M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) resonant enhancement limited by axion coherence time τ a and nuclear spin transverse relaxation time T 2 2π m a v 2 local B-field inhomogeneities: B(r1 ) = B(r2 ) B ext and spin-spin interactions source transverse spin dephasing naturally: T 2 µ N µn Å3 1 1 ms designed NMR pulse sequences can improve (dynamic decoupling) demonstrated T2 = 1300 s in Xe

26 Cosmic Axion Spin Precession Experiment (CASPEr) M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) resonance limited by nuclear spin transverse relaxation time T 2 dynamic decoupling can improve (demonstrated T2 = 1300 s in Xe)

27 Cosmic Axion Spin Precession Experiment (CASPEr) M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) resonance limited by nuclear spin transverse relaxation time T 2 dynamic decoupling can improve (demonstrated T2 = 1300 s in Xe) with B ext = 10 T at 4K polarization fraction p 10 3 in T 1 3 hr but optical pumping allows p O (1) for T 1 3 hrs demonstrated p ~ 0.5 in Xe

28 Cosmic Axion Spin Precession Experiment (CASPEr) M(t) nµ S d n E p sin ((2µB ext m a ) t) 2µB ext m a sin (2µB ext t) resonance limited by nuclear spin transverse relaxation time T 2 dynamic decoupling can improve (demonstrated T2 = 1300 s in Xe) with B ext = 10 T at 4K polarization fraction p 10 3 in T 1 3 hr but optical pumping allows p O (1) for T 1 3 hrs demonstrated p ~ 0.5 in Xe with designed NMR pulse sequences: Phase 1 Phase 2 polarization fraction p = 10 3 p 1 optical pumping T s 1s dynamic decoupling many options for increasing sensitivity

29 Magnetization Noise µ B ext a material sample has magnetization noise irreducible noise arises from quantum spin projection every spin necessarily has random quantum projection onto transverse direction Magnetization (quantum spin projection) noise: S (ω) = 1 8 T 2 1+T 2 2 (ω 2µ NB) 2 an approximate estimate, in a particular sample magnetization noise must be measured

30 Axion Limits on a f a F F A. Ringwald (2012)

31 Axion Limits on a f a G G frequency Hz Static EDM SN 1987A g d GeV ALP DM ADMX QCD Axion d N = i 2 g d a Nσ µν γ 5 NF µν mass ev

32 Axion Limits on a f a G G frequency Hz Static EDM SN 1987A g d GeV ALP DM phase 1 phase 2 ADMX QCD Axion magnetization noise d N = i 2 g d a Nσ µν γ 5 NF µν mass ev

33 Limits on Axion-Nucleon Coupling SN 1987A frequency Hz (Preliminary) ALP DM g ann GeV QCD Axion g ann ( µ a) Nγ µ γ 5 N mass ev

34 Limits on Axion-Electron Coupling frequency Hz White Dwarf gaee QCD Axion Frequency Hz ig aee a (ēγ 5 e)

35 Summary EDM is non-derivative coupling for axion (avoids axion wavelength suppressions) + amplitude measurement can reach high fa Many options for future improvements (magnetometers, T2, sample volume, material, polar crystal) AC signal gives resonant enhancement, helps reject noise Verify signal with spatial coherence of axion field Signal ρ so can search for subdominant component of dark matter

36 Axion Searches with Gluon Coupling f a (GeV) Planck GUT Axion dark matter microwave cavity (ADMX) astrophysical constraints

37 Axion Searches with Gluon Coupling f a (GeV) Planck NMR searches can most easily search in khz - GHz frequencies high fa GUT Axion dark matter microwave cavity (ADMX) astrophysical constraints

38 Axion Searches with Gluon Coupling f a (GeV) Planck NMR searches can most easily search in khz - GHz frequencies high fa GUT Axion dark matter technological challenges, similar to early stages of WIMP detection, axions deserve similar effort microwave cavity (ADMX) axion dark matter is very well-motivated, no other way to search for at high fa would be both the discovery of dark matter and a glimpse into physics at very high energies 10 8 astrophysical constraints

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40 Axion Coherence How large can T be? a v x Spatial homogeneity of the field? Classical field a(x) with velocity v 10 3 = a a 1 m a v spread in frequency (energy) of axion = T 1 m a v 2 = 1 s f a GeV