ABRACADABRA: A Broadband/Resonant Search for Axions Yonatan Kahn, - PowerPoint PPT Presentation

ABRACADABRA: 
 A Broadband/Resonant Search for Axions Yonatan Kahn, Princeton University for the ABRACADABRA collaboration 2nd Workshop on Microwave Cavities 
 and Detectors for Axion Research LLNL, Jan. 11 2017

Why low-frequency axions? If axion exists (PQ broken) before inflation… a θ i = a i /f a initial a ∝ T 3 / 2 cos( m a t ) misalignment a H t L 3 H = m a solve 
 strong CP, DM with ~1% 
 tuning t ◆ 7 / 6 ✓ ◆ 2 ✓ f a θ i Ω a h 2 ∼ 0 . 1 10 16 GeV 5 × 10 − 3 ✓ 10 16 GeV ◆ GUT-scale = m a ∼ 6 × 10 − 10 eV 100 kHz f a

ALP DM: field, not particle vs. Light bosonic DM behaves collectively: useful to think in terms of charges and currents, rather than Feynman diagrams

ALP DM: Properties today Focus on mass range m a ⌧ 1eV Bosonic DM + macroscopic occupation # = classical field: √ 2 ρ DM a ( t ) = a 0 sin( m a t ) = sin( m a t ) m a

ALP DM: Properties today Focus on mass range m a ⌧ 1eV Bosonic DM + macroscopic occupation # = classical field: √ 2 ρ DM a ( t ) = a 0 sin( m a t ) = sin( m a t ) m a Spatially and temporally coherent on macroscopic scales: ≈ 100 km 10 − 8 eV 2 π λ ∼ m a v DM m a ≈ 0 . 4 s 10 − 8 eV 2 π τ ∼ m a v 2 m a DM

ALP DM: Properties today Focus on mass range m a ⌧ 1eV √ 2 ρ DM a ( t ) = a 0 sin( m a t ) = sin( m a t ) m a L ⊃ − 1 4 g a γγ aF µ ν e F µ ν In presence of static background EM fields, 
 induces oscillating response fields:

ALP DM: Properties today Focus on mass range m a ⌧ 1eV √ 2 ρ DM a ( t ) = a 0 sin( m a t ) = sin( m a t ) m a L ⊃ − 1 4 g a γγ aF µ ν e F µ ν In presence of static background EM fields, 
 induces oscillating response fields: ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t r · E r = � g a γγ B 0 · r a

ALP DM: Properties today Focus on mass range m a ⌧ 1eV √ 2 ρ DM a ( t ) = a 0 sin( m a t ) = sin( m a t ) m a L ⊃ − 1 4 g a γγ aF µ ν e F µ ν In presence of static background EM fields, 
 induces oscillating response fields: ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t r · E r = � g a γγ B 0 · r a gradients suppressed by v DM ∼ 10 − 3

Axion-sourced current ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t

Axion-sourced current v DM ⌧ 1 ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t

Axion-sourced current v DM ⌧ 1 ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t (MQS approximation)

Axion-sourced current v DM ⌧ 1 ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t (MQS approximation) p = ⇒ J e ff = g a γγ 2 ρ DM cos( m a t ) B 0 Current follows lines of B, oscillates at axion mass How to detect an oscillating current?

Axion-sourced current v DM ⌧ 1 ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t (MQS approximation) p = ⇒ J e ff = g a γγ 2 ρ DM cos( m a t ) B 0 Current follows lines of B, oscillates at axion mass How to detect an oscillating current? • Radiated power (at infinity) 
 Time-varying flux (locally) •

Axion-sourced current v DM ⌧ 1 ✓ ◆ r ⇥ B r = ∂ E r ∂ a E 0 ⇥ r a � B 0 ∂ t � g a γγ ∂ t (MQS approximation) p = ⇒ J e ff = g a γγ 2 ρ DM cos( m a t ) B 0 Current follows lines of B, oscillates at axion mass How to detect an oscillating current? • Radiated power (at infinity) 
 Time-varying flux (locally) •

ABRACADABRA! [YK, Safdi, Thaler, Phys. Rev. Lett. 2016] Theory: Experiment: R r a h B 0 Toroidal geometry for 
 zero-field detection M M Δω L i L p L L p L C L i R Interchangeable readout: 
 ABRA-10cm @ MIT broadband (low freq.) or 
 resonant (high freq.)

THEORY

ABRACADABRA geometry B a detection in zero-field region! gap (or overlap) for return current R r in MQS regime a J eff geometric factor, 
 ~0.1 for r = R = a = h/3 h B 0 p Φ a ( t ) = g a γγ 2 ρ DM cos( m a t ) × ( B max V G toroid ) { V B

Optimization of dc SQUID Voltmeter and Magnetometer Circuits 411 3. VOLTMETERS It is convenient to write Eq. (10) in terms of a noise temperature TN defined by setting.(V~ )/SN(f)B = 1 with (E~ 2) = 4kB TNR~B. The value of B must be small enough to ensure uniformity of the signal-to-noise ratio within the chosen bandwidth. We find [(yvT+ T )Iz=i ~2RL, 2o~2ywV,~LT(I + Xi ] +ot4y,L2V~T] GL- R L--E,J J (11) Low-frequency readout: 3.1. Resistive Source with Tuned Input As an example, we assume that the source is resistive, and that the input is tuned with a capacitor Ci, so that Z~ = Ri -j/toC~ (see Fig. 3a). We further assume that the losses in Li and Ci are negligible compared with the dissipation in Ri and that TA << yvT, as is the case for a SQUID operated in broadband or resonant? the 4He temperature range, since TA~-IK and yv~8. Equation (11) becomes w2RLiT Ri o~ 2toL\ 2 / 1 2 TN :2 2LRiV~ {YV[L\(--+wLi -4--R-DD) + ~1 2~_,,C; ) ] 4 r2T12~ 2aEyvjLV,~(1 SQUID magnetometry: 1 ) a "/IL v~[ Low-field MRI: (12) + R \ m 2L---~- - + R 2 J Optimization of dc SQUID Voltmeter and Magnetometer Circuits 419 characteristic of ideal dc SQUIDS. Since the performance of real devices is SQUID tuned magnetometer quite close to ideal, we expect that the results will be broadly applicable in practice with small corrections to the values of 7v, 3'J, and 3~vj. At frequencies below a few kHz we find that voltmeters may be SQUID untuned (a) (b) gradiometer characterized by a noise temperature TN which is so much smaller than the SQUID tuned ambient temperature that the voltage measurement is always limited by gradiometer Johnson noise in the input circuit. In this frequency range, there seems little Conventional Faraday need to use the tuned voltmeter, especially as the large values of capacitance I_p f and inductance involved would make these elements rather cumbersome. However, at higher frequencies, TN oc ~, and the noise temperature of the 100 mT prepolarized Static field Cc) (d) untuned voltmeter may become comparable with the ambient temperature. (a) Tuned voltmeter, (b) untuned voltmeter, (c) Fig. 3. In this limit the lower noise temperature offered by the tuned voltmeter may untuned magnetometer, (d) tuned magnetometer. be significant. In the same way, the untuned magnetometer is preferable to the tuned magnetometer at low frequencies. However, at frequencies above a few been added in quadrature to the detector noise. As dis- hundred Hz the tuned magnetometer offers a clear improvement in sensi- cussed above, prepolarized SQUID untuned detection is tivity, provided that feedback is used properly to improve the frequency the optimal detection modality at frequencies below response. It seems likely that the tuned magnetometer will become widely 50 kHz. Between 50 kHz and 4 MHz, prepolarized used in future applications where high sensitivity in a relatively restricted bandwidth is required. [Myers et al., 2007] [Clarke, Tesche, and Giffard, 1979] ACKNOWLEDGMENT One of us (JC) gratefully acknowledges the hospitality of the Institute We will see crossover frequency is temperature-dependent, 
 fur Theorie der Kondensierten Materie, University of Karlsruhe, West Germany, during the preparation of this manuscript. but broadband is advantageous for lightest axions REFERENCES 1. V. R. Radhakrishnan and V. L. Newhouse, J. Appl. Phys. 42, 129 (1971). 2. J. C]arke, Proc. IEEE 61, 8 (1973). 3. A. Davidson, R. S. Newbower, and M. R. Beasley, Rev. Sci. lnstr. 45, 838 (1974). 4. J. H. Claasen, J. Appl. Phys. 46, 2268 (1975). 5. J. Clarke, in Superconductor Applications: SQUIDS and Machines, B. B. Schwartz and S. Foner, eds. (Plenum, 1977), p. 67. 6. V. V. Danilov, K. K. Likharev, O. V. Sniguiriev, and E. S. Soldatov, IEEE Trans. Magn. MAG-13, 240 (1977). 7. A. V. Gusev and V. N. Rudenko, Zh. Eksp. Teor. Fiz. 74, 819 (1978) [Soy. Phys.--JETP 47, 428 (1978)]. 8. F. Bordoni, P. Carelli, I. Modena, and G. L. Romani, Y. Phys. (Paris) 39, C6-1213 (1978). 9. M. B. Simmonds, W. A. Fertig, and R. P. Giffard, IEEE Trans. Mag. MAG-15, 478 (1979). 10. W. S. Goree and V. W. Hesterman, in Applied Superconductivity, Vol. 1, V. L. Newhouse, ed. (Academic Press, New York, 1975). 11. G. Ehnholm, J. Low Temp. Phys. 29, 1 (19"77). 12. R. P. Giffard and J. N. Hollenhorst, Appl. Phys. Lett. 32, 767 (1978).

Broadband: readout circuit M L p L pickup loop SQUID L i input coil superconducting = SQUID noise dominates thermal noise s L ⇒ Φ SQUID ≈ α Inductance matching: L i ≈ L p = Φ pickup L p 2 { huge area = B 2 dV = Φ 2 1 Z Optimal coupling*: amplification ≈ 0 . 01 2 L p 2 *thanks to K. Irwin for pointing this out

Broadband: S/N and sensitivity Take data for time : t √ If , S/N improves like t (random walk) t < τ S/N ∼ | Φ SQUID | ( t τ ) 1 / 4 /S 1 / 2 Our regime is : t � τ Φ , 0 S/N = 1 ⇒ sensitivity to = ◆ 1 / 4 5 T ◆ 5 / 2 s S 1 / 2 ✓ ✓ 0 . 85 m 0 . 3 GeV / cm 3 m a 1 year g a γγ > 6 . 3 × 10 − 18 GeV − 1 Φ , 0 × √ 10 − 12 eV t B max R 10 − 6 Φ 0 / Hz ρ DM improves at low masses R = r = a = h/3: 
 from coherence time tall toroid increases B-field energy