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?
for the ABRACADABRA collaboration
2nd Workshop on Microwave Cavities and Detectors for Axion Research
LLNL, Jan. 11 2017
a
t aHtL
initial misalignment 3H = ma a ∝ T 3/2 cos(mat)
θi = ai/fa
If axion exists (PQ broken) before inflation…
Ωah2 ∼ 0.1 ✓ fa 1016 GeV ◆7/6 ✓ θi 5 × 10−3 ◆2
ma ∼ 6 × 10−10 eV ✓1016 GeV fa ◆
solve strong CP, DM with ~1% tuning GUT-scale = 100 kHz
vs. Light bosonic DM behaves collectively: useful to think in terms of charges and currents, rather than Feynman diagrams
Focus on mass range ma ⌧ 1eV
Bosonic DM + macroscopic occupation # = classical field:
Focus on mass range ma ⌧ 1eV
Bosonic DM + macroscopic occupation # = classical field: Spatially and temporally coherent on macroscopic scales: λ ∼ 2π mavDM ≈ 100 km 10−8 eV ma τ ∼ 2π mav2
DM
≈ 0.4 s 10−8 eV ma
In presence of static background EM fields, induces oscillating response fields:
Focus on mass range ma ⌧ 1eV
In presence of static background EM fields, induces oscillating response fields: r · Er = gaγγB0 · ra r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆
Focus on mass range ma ⌧ 1eV
In presence of static background EM fields, induces oscillating response fields:
gradients suppressed by vDM ∼ 10−3
r · Er = gaγγB0 · ra r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆
Focus on mass range ma ⌧ 1eV
r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆
r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆ vDM ⌧ 1
r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆
(MQS approximation)
vDM ⌧ 1
= ⇒ Jeff = gaγγ p 2ρDM cos(mat)B0 Current follows lines of B, oscillates at axion mass How to detect an oscillating current? r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆
(MQS approximation)
vDM ⌧ 1
= ⇒ Jeff = gaγγ p 2ρDM cos(mat)B0 Current follows lines of B, oscillates at axion mass How to detect an oscillating current?
r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆
(MQS approximation)
vDM ⌧ 1
= ⇒ Jeff = gaγγ p 2ρDM cos(mat)B0 Current follows lines of B, oscillates at axion mass How to detect an oscillating current?
r ⇥ Br = ∂Er ∂t gaγγ ✓ E0 ⇥ ra B0 ∂a ∂t ◆
(MQS approximation)
vDM ⌧ 1
a h R B r
Toroidal geometry for zero-field detection
[YK, Safdi, Thaler, Phys. Rev. Lett. 2016]
Lp Li L M
L Lp
Li
M
C R Δω
Interchangeable readout: broadband (low freq.) or resonant (high freq.)
ABRA-10cm @ MIT
a h R B r
Jeff Ba
detection in zero-field region!
Φa(t) = gaγγ p 2ρDM cos(mat) × (BmaxV Gtoroid)
geometric factor, ~0.1 for r = R = a = h/3 gap (or overlap) for return current in MQS regime
VB
Optimization of dc SQUID Voltmeter and Magnetometer Circuits 411
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
~2RL,
[(yvT+ T )Iz=i
2o~2ywV,~LT(I + Xi ] +ot4y,L2V~T]
GL- R L--E,J J
(11) 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 the 4He temperature range, since TA~-IK and yv~8. Equation (11) becomes
w2RLiT Ri
2toL\ 2 / 1 2
TN :2 2LRiV~
{YV[L\(--+wLi -4--R-DD)
+ ~1 2~_,,C; ) ]
4 r2T12~2aEyvjLV,~(1
1 ) a "/IL v~[ + R \ m 2L---~-
R 2 J (12) (a) (b) I_p
f
Cc) (d) (a) Tuned voltmeter, (b) untuned voltmeter, (c) untuned magnetometer, (d) tuned magnetometer.
Optimization of dc SQUID Voltmeter and Magnetometer Circuits 419
characteristic of ideal dc SQUIDS. Since the performance of real devices is 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 characterized by a noise temperature TN which is so much smaller than the ambient temperature that the voltage measurement is always limited by Johnson noise in the input circuit. In this frequency range, there seems little need to use the tuned voltmeter, especially as the large values of capacitance and inductance involved would make these elements rather cumbersome. However, at higher frequencies, TN oc ~, and the noise temperature of the untuned voltmeter may become comparable with the ambient temperature. In this limit the lower noise temperature offered by the tuned voltmeter may be significant. In the same way, the untuned magnetometer is preferable to the tuned magnetometer at low frequencies. However, at frequencies above a few hundred Hz the tuned magnetometer offers a clear improvement in sensi- tivity, provided that feedback is used properly to improve the frequency
used in future applications where high sensitivity in a relatively restricted bandwidth is required.
ACKNOWLEDGMENT
One of us (JC) gratefully acknowledges the hospitality of the Institute fur Theorie der Kondensierten Materie, University of Karlsruhe, West Germany, during the preparation of this manuscript.
REFERENCES
MAG-13, 240 (1977).
47, 428 (1978)].
39, C6-1213 (1978).
(1979).
[Clarke, Tesche, and Giffard, 1979]
We will see crossover frequency is temperature-dependent, but broadband is advantageous for lightest axions
100 mT prepolarized Static field Conventional Faraday SQUID tuned gradiometer SQUID untuned gradiometer SQUID tuned magnetometerSQUID magnetometry: Low-field MRI:
[Myers et al., 2007]
been added in quadrature to the detector noise. As dis- cussed above, prepolarized SQUID untuned detection is the optimal detection modality at frequencies below 50 kHz. Between 50 kHz and 4 MHz, prepolarized
pickup loop input coil SQUID superconducting = SQUID noise dominates thermal noise Inductance matching: Li ≈ Lp =
⇒ ΦSQUID ≈ α 2 s L Lp Φpickup
huge area = amplification
≈ 0.01 Optimal coupling*:
1 2 Z B2 dV = Φ2 2Lp
*thanks to K. Irwin for pointing this out
S/N ∼ |ΦSQUID| (tτ)1/4/S1/2
Φ,0
R = r = a = h/3: tall toroid increases B-field energy improves at low masses from coherence time
t τ
If , S/N improves like Our regime is : t < τ √ t (random walk)
gaγγ > 6.3 × 10−18 GeV−1 ✓ ma 10−12 eV 1 year t ◆1/4 5 T Bmax × ✓0.85 m R ◆5/2 s 0.3 GeV/cm3 ρDM S1/2
Φ,0
10−6Φ0/ √ Hz
Take data for time : t
irreducible resistance (resistance in series rather than parallel)
Q = 1 R r LT C
can use feedback to match circuit bandwidth to signal
New source of noise: thermal noise in pickup RLC circuit, dominates at T = 0.1 K up to Q = 108 LT = Lp + Li
PS = Q0 maΦ2
pickup
2LT , PN = kBT r ma 2πte−fold
each e-fold of frequency scanned for equal time (note: other scanning strategies possible!)
improves at high masses improves at low temp
gaγγ > 9.0 × 10−17 GeV−1 ✓10−12 eV ma 20 days te−fold ◆1/4 × 5 T Bmax ✓0.85 m R ◆5/2 s 0.3 GeV/cm3 ρDM 106 Q0 T 0.1 K
γγ (-) ν=/π = = = = = = = = = = = =
With same experimental parameters, broadband for low frequencies, resonant for high frequencies Q = 106
IAXO
MQS breaks down (detailed sim. needed)
ADMX QCD axion
1 year total measurement time 1/f noise
~50 kHz crossover, scales as
T = 0.1 K T
A Broadband/Resonant Approach to Cosmic Axion Detection with an Amplifying B-field Ring Apparatus
Rin = 3 cm, Rout = 6 cm, h = 12 cm, V = 680 cm3, Bmax = 1 T, G = 0.085
Prototype specs:
MIT: Janet Conrad, Joe Formaggio, Sarah Heine, Joe Minervini, Jonathan Ouellet, Kerstin Perez, Alexey Radovinsky, Ben Safdi, Jesse Thaler, Daniel Winklehner, Lindley Winslow Princeton: YK
Now funded by NSF!
700 mK 50 mK 10 mK
Normally used for 0νββ Cryogen-free, can run weeks unattended Oxford Instruments Triton 400 dil fridge: 12 L working volume
25 cm 24 cm
Counter-wound superconducting NbTi coils* 12 cm 12 cm
*Need to be very careful of fringe fields!
Bmax ≈ 1 T finite wire separation acts as “gap”
Support “Donut” Assembled Support Donut wire to inject test signal
Superconducting pickup cylinder
Tall, thin walls: minimize inductance Gap to force current through SQUID
Superconducting pickup cylinder
Tall, thin walls: minimize inductance Gap to force current through SQUID
Pickup: looking to purchase a Magnicon SQUID current sensor Typical noise: 1.2 × 10-6 Φ0/(Hz)1/2 @ 4K, with 1/f corner at 3 Hz Amplifier: currently have a set of Magnicon SQUID amplifier arrays
(a) LIGO Livingston Observatory
What’s possible
Where we are now Vibrations source flux noise from fringe fields: S1/2
Φ
∼
vib
already below SQUID noise for prototype!
(measured at MIT lab) (LIGO)
γγ (-) ν=/π
Interesting physics with first-stage experiment!
broadband (T = 4 K) resonant (T = 0.1 K)
Expect data by end of 2017
Broadband/resonant readout
Lp Li L M
…full-scale experiment can probe GUT-scale axion! Zero-field pickup geometry
a h R B r
Prototype data in 2017…
γγ (-) ν=/π
Hot-DM ê CMB ê BBN
Telescope ê EBL
SN1987A
Burst Duration
SK Globular Clusters HgagL
HgaeL
White Dwarfs HgaeL
WD cooling hint
Solar Neutrino flux HgagL HgaeL
IAXO
Helioscopes
Beam Dump
ADMX-II ADMX
Cold DM
post-inflation PQ transition pre-inflation PQ transition Hnatural valuesL
10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 10 102 103 104 105 106 107
0.0 0.5 1.0 1.5 2.0
1014 1013 1012 1011 1010 109 108 107 106 105 104 103 102 101 1
ma@eVD fa@GeVD
1019
10−12 10−9
AD
10-
0.5
AD
10-
0.5
AD
10-
0.5
AD
10-
0.5
AD
10-
0.5
AD
10-
0.5
ADMX
Cold
PQ tr infla
10-7 10
0.5 0.0 0.5 1.0 1.5 2.0
ADMX
Cold
PQ tr infla
10-7 10
0.5 0.0 0.5 1.0 1.5 2.0
ADMX
Cold
PQ tr infla
10-7 10
0.5 0.0 0.5 1.0 1.5 2.0
ADMX
Cold
PQ tr infla
10-7 10
0.5 0.0 0.5 1.0 1.5 2.0
ADMX
Cold
PQ tr infla
10-7 10
0.5 0.0 0.5 1.0 1.5 2.0
1016
ADMX
Cold
PQ tr infla
10-7 10
0.5 0.0 0.5 1.0 1.5 2.0
CASPEr
ABRA- CADABRA
Many experiments needed to cover full parameter space!
[adapted from Essig et al., 1311.0029]
BH super- radiance
ARIADNE DM radio
solenoid toroid Borrow analysis of cryogenic current comparators
Q is not an appropriate variable to describe a purely inductive circuit
Li C R
Q = 1 R r LT C Q → 1, LT , C fixed
Lp
Li C R
Lp
Li C R
more noise, wider bandwidth
R, C → 0, LT fixed
Q = ∞?!
ω0 = ∞??
ω0 = 1 √ LC
~fT/(Hz)1/2 achievable
Superconducting shield ideal: looking into NbTi/Nb/Cu multilayer sheet
Axion Dark Matter 2016 ABRACADABRA December 6, 2016 A Broadband Search for Axion-Like Dark Matter
cooling power
contribute to the noise level
➡Can we cool the pickup loop and toroid to different
temperatures?
27
0.7 - 2K 100 mK