The Dark Matter Radio
Kent Irwin for
the DM Radio Collaboration
DM Radio Pathfinder
• Field-like dark matter: axions and hidden photons
• Fundamental limits on the detection of axions and hidden photons through coupling to electromagnetism
• Optimal impedance-matching (Broadband? One-pole resonator? Multi-pole?)• Optimal coupling to quantum-limited amplifier• Optimal scan strategy given different priors (QCD, neutral, etc.)• Science reach of electromagnetic searches for axions and hidden photons• Extension to photon counting and non-classical measurements
• The Dark Matter Radio (DM Radio)• Design• Status of Pathfinder experiment• Science reach and plans for Stage II and Stage III
Outline
• Number density is small (small occupation)
• Tiny wavelength
• No detector-scale coherence
• Look for scattering of individual particles
Heavy Particles Light Fields
• Number density is large (must be bosons)
• Long wavelength
• Coherent within detector
• Look for classical, oscillating background field
Detector Detector
3
Particle-like and field-like dark matter
• Strong CP Problem
• Can be detected via inverse Primakoff effect – coupling to electromagnetism
• Frequency: ɋெ = మ
• Bandwidth: οɋெ~10ɋெ
Neutron Electric Dipole Moment
Why is it so small?Solution:
is a dynamical field(Peccei-Quinn solution, the axion)
4
gaɶɶaxion
dc magnetic field
photon
Leslie J Rosenberg PNAS 2015;112:12278-12281
Dark matter candidate: axion (spin 0)
ADMX
“Hidden” photon: generic vector boson (spin 1)
Hidden photon DM drives EM currentsCMB photon Hidden Photon DM
(oscillating E’ field)
P. Graham et al., “Vector Dark Matter from Inflationary Fluctuations,” arxiv:1504.02102
• A new photon, but with a mass, and weak coupling• Couples to ordinary electromagnetism via kinetic mixing
• Vector dark matter can be generated in observed dark matter abundance by inflationary fluctuations
Frequency: ɋெ = ଶ/Bandwidth: οɋெ~10ɋெ
peV neV �eV meV
10-18
10-16
10-14
10-12
10-10
kHz MHz GHz THz
ma
g���
[GeV
-1 ]
f =ma/2�
QCD axion
ADMX
Axion
Haloscopes
CAST
SN 1987a �-ray
Widerangeofunexploredparameterspace
6
Axions: plenty of room at the bottom
peV neV �eV meV
10-16
10-14
10-12
10-10
10-8
10-6
kHz MHz GHz THz
m�'
�
f =m�'/2�
CMB (���') precisionEM
stellarproduction
CMB(�'��)
Axion
HaloscopesADMX
Widerangeofunexploredparameterspace
7
Hidden photons: plenty of room at the bottom
First: standard quantum limit – measure both quadratures of the electromagnetic field.
• Minimum 1 photon of “noise” from Heisenberg
• Also include thermal noise associated with residual dissipation in practical measurement (~ 1 m3 volume at ~10 mK )
• What is the limit on the science reach set by the optimal impedance and noise match to a quantum-limited amplifier?
• What is the fundamental limit on coupling to the dark matter field?
• What is the optimal scan strategy with different priors (QCD, neutral, etc.)?
• Paper: Chaudhuri et al., Oct. 19, 2017
Extension: photon counting and non-classical measurements of field (squeezing, entanglement) with the above machinery
The fundamental limit on detection axions and hidden
photons through electromagnetic coupling
Pow
erFrequency
610~ �'QQ
Pierre Sikivie (1983)
Primakoff Conversion
Expected Signal
Amplifier
Magnet
Cavity
Thanks to John Clarke
Resonant conversion of axions into photons
ADMX experiment
Workshop Axions 2010, U. Florida, 2010
Idea for subwavelength, lumped-element experiment
Workshop Axions 2010, U. Florida, 2010
Also: Sikivie, P., N. Sullivan, and D. B. Tanner. "Physical review letters 112.13 (2014): 131301.
Also useful for hidden photons:Arias et al., arxiv:1411.4986Chaudhuri et al., arxiv: 1411.7382v2
SIGNAL SOURCE
1) Inductive/capacitive element coupling to dark matter
2) Residual loss and associated thermal noise
3) Zero-pointfluctuation noise
Amplifier or photon counter
( Phase-insensitiveamplifier must add imprecision noise / backaction )
READOUTMATCHING NETWORK
Examples:1) Single-pole LC resonator2) Broadband inductive 3) Multi-pole resonator
Model for electromagnetic axion / hidden photon detector
Standard Quantum Limit (SQL): Heisenberg uncertainty when both quadraturesof the field are measured.• Manifests in: vacuum noise, imprecision noise, backaction.• Can do better with photon counting or non-classical states (squeezing,
entanglement)
• Equivalent circuit model for resonant detector in scattering mode. Resonator tuned by changing capacitance.
• HEMT, resonant dc SQUID, parametric amplifier (used in ADMX/HAYSTAC)
• How well can the output impedance of the resonator be matched to the input/noise impedance of the amplifier?
Scattering mode impedance matching
Image of new JPA
10 mPCastellanos-Beltran et al., Nature Physics (2008).
Parametric amplifier with 0.04 photons of added noise. (similar devices deployed in HAYSTAC)
Scanned, one-pole resonant RLC input circuit read out by SQUID. (e.g. ADMX, Haystac)
Op-amp mode impedance matching
Broadband LR circuit. (Kahn et al, PRL 117, 141801 (2016) )
Can we do better with a more complex (multi-pole) matching structure?
dc SQUID: “op-amp mode” flux amplifier
• Maximize integrated sensitivity across search band, between ɋland ɋh
• Figure of merit for scattering system with quantum-limited amplifier:
= න
ɋ
|ଶଵ ɋ |ଶ
|ଶଵ ɋ |ଶ ɋ + 1
ଶ
n(ɋ)= cavity thermal occupation number, “1” is standard quantum limit
• Includes vacuum noise, amplifier imprecision noise and backaction
• Similar calculation for op-amp mode
Figure of merit for integrated sensitivity
Amplifier noise floor
Resonator line shape/ Thermal noise
Resonator bandwidthSensitivity bandwidth
Example: One-pole LC resonator output noise spectrum. Figure of merit integrates sensitivity at all relevant frequencies. There is significant information outside of the resonator bandwidth, depending on amplifier noise floor.
Apples-to-apples• Assumes same volume, cavity temperature 10 mK.• Assumes optimally matched amplifier at standard quantum limit.• Assumes optimal scan strategy (not described in this talk).• Assumes same total integration time over full science bandwidth.
• One-pole resonator is better at all frequencies where a resonator can be practically constructed (>~100 Hz)
• But a one-pole resonator is not optimal.
One-pole scanned resonator vs. broadband
Ratio of minimum detectable coupling for one-pole resonant resonant (R) and broadband (B) plotted vs rest mass frequency.
Value < 1 implies resonator limit stronger than broadband limit
A one-pole resonator is always more sensitive than a broadband measurement when it can be built. But a multi-pole resonator can be better still. How much better?
• Constraint provided by Bode-Fano criterion for matching LR to a quantum-limited amplifier with a real noise impedance:
න
ɋ
1|ଶଶ ɋ |
ܮ2
1Ͷ(ɋ)
ܮ
, (ɋ) ب 1
0.41ܮ
, (ɋ) ا 1
• An optimal single-pole resonator can have a figure of merit U that is ~75% of the fundamental limit of a multi-pole circuit (pretty good!)
Bode-Fano Limit on Impedance Match
Bode-Fano
Bode-Fano-limited U
Dark Matter Radio science: axions
AXIO
N-P
HOTO
N C
OU
PLIN
GFREQUENCY
MASS
HIDD
EN P
HOTO
N-P
HOTO
N
MIX
ING
ANGL
E
Dark Matter Radio science: hidden photons
FREQUENCY
MASS
Stanford: Arran Phipps, Dale Li, Saptarshi Chaudhuri, Peter Graham, Jeremy Mardon, Hsiao-Mei Cho, Stephen Kuenstner, Carl Dawson, Richard Mule, Max Silva-Feaver, Zach Steffen, Betty Young, Sarah Church, Kent IrwinBerkeley: Surjeet RajendranCollaborators on DM Radio extensions:Tony Tyson, UC DavisLyman Page, Princeton
Stanford: Arran Phipps, Dale Li, Saptarshi Chaudhuri, Peter Graham, Jeremy Mardon, Hsiao-Mei Cho, Stephen Kuenstner, Carl Dawson, Richard Mule, Max Silva-Feaver, Zach Steffen, Betty Young, Sarah Church, Kent IrwinBerkeley: Surjeet RajendranCollaborators on DM Radio extensions:Tony Tyson, UC DavisLyman Page, Princeton
Distance Coherence E Coherence freq
0 km
3 km 300 neV 70 MHz
40 km 20 neV 5 MHz
120 km 7 neV 2 MHz
5,000 km 0.2 neV 40 kHz
Cross-section
Superconducting shield
Hollow, superconductingsheath (like a hollow donut)
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Block EMI background with a superconducting shield
• In the subwavelength limit of DM Radio, you can approximate the signal from axions and hidden photons as an effective stiff ac current filling all space, with frequency f = mc2/h (the “interaction basis”)
• To detect this signal, we need to block out ordinary photons with a superconducting shield
• Toroidal coil produces DC magnetic field inside superconducting cylinder
• Axions interact with DC field, generates effective AC current along direction of applied field(B0 toroid inside cylinder)
Top-Down Cross-section
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Field from effective axion current
• Add a tunable lumped-element resonator to ring up the magnetic fields sourced by local dark matter
• Tune DM Radio over frequency with insertibledielectric (sapphire)
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One-pole resonator implementation: axion
• Hidden photon effective ac current penetrates superconductors
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Field from effective hidden photon current
• Add a tunable lumped-element resonator to ring up the magnetic fields sourced by local dark matter
• Tune DM Radio over frequency with insertibledielectric (sapphire)
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One-pole resonator implementation: hidden photon
HIDD
EN P
HOTO
N-P
HOTO
N
MIX
ING
ANGL
E
DM Radio Pathfinder science reach
FREQUENCY
MASS
750 mL Pathfinder now being tested
• T=4K (Helium Dip Probe)
• Frequency/Mass Range: 100 kHz – 10 MHz 500 peV – 50 neV
• Coupling Range: 10-9 – 10-11
• Readout: DC SQUIDs
4K Dip Probe
Detector inside superconductingshield
Inserts intoCryoperm-linedhelium dewar
67 inches
9.5 inchesDesign Overview of the DM Radio Pathfinder ExperimentM. Silva, arXiv:1610.09344, 2016
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DM Radio pathfinder experiment
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Toroidal Nb sheath and parallel-plate capacitors
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Nb shield & SQUID amplifier
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DM Radio pathfinder
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DM Radio Pathfinder
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• Superconducting toroidal sheath, superconducting shield, SQUID amplifier, capacitors, probe, electronics, shield, cryogenics: all in place.
• Broadband cryogenic operation verified: low SQUID noise, very good control over EMI within shield.
• Now: winding inductors, testing fixed resonators to evaluate Q, material properties. Finite element modeling of probe to determine constraints on coupling.
• Next: connect tunable dielectric and scan.
• Support for initial construction of Stage 2 (30 L experiment in dilution refrigerator) from Heising-Simons foundation.
• Stage 3 full science experiment (~1 m3) in planning stage
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DM Radio status
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Conclusions
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Conclusions
Hidden PhotonsAxions
Light-field dark matter is a boson1. Scalar field (spin-0)2. Pseudoscalar (spin-0, but changes sign under parity inversion) “axion”3. Vector (spin-1): “hidden photon”4. Pseudovector (spin-1, but changes sign on parity inversion)
DM mass:
Light (field) DM• Spin-0 scalar• Spin-1 vector• Higher spin (tensor) disfavored
Heavy (particle) DM• WIMPs• Etc. etc.
The dark matter zoo
• Hidden photon effective ac current penetrates superconductors
• Generates a REAL circumferential, quasi-static B-field
• Screening currents on superconductor surface flow to cancel field in bulk
Meissner Effect 40
How to measure effective hidden photon current
• Cut concentric slit at bottom of cylinder
• Screening currents return on outer surface
41
How to measure effective hidden photon current
• Cut concentric slit at bottom of cylinder
• Screening currents return on outer surface
• Add an inductive loop to couple some of the screening current to SQUID
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How to measure effective hidden photon current
• Toroidal coil produces DC magnetic field inside superconducting cylinder
• Axions interact with DC field, generates effective AC current along direction of applied field
• Produces REAL quasi-static AC magnetic field
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How to measure effective axion current
• Screening currents in superconductor flow to cancel field in bulk
Meissner Effect
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How to measure effective axion current
• Cut a slit from top to bottom of the superconducting cylinder
• Screening currents continue along outer surface
45
How to measure effective axion current
• Cut a slit from top to bottom of the superconducting cylinder
• Screening currents continue along outer surface
• Use inductive loop to couple screening current to SQUID
46
How to measure effective axion current