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)

22

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

23

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)

24

One-pole resonator implementation: axion

• Hidden photon effective ac current penetrates superconductors

25

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)

26

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

28

DM Radio pathfinder experiment

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Toroidal Nb sheath and parallel-plate capacitors

30

Nb shield & SQUID amplifier

31

DM Radio pathfinder

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DM Radio Pathfinder

33

34

• 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

35

DM Radio status

36

Conclusions

37

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

42

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

43

How to measure effective axion current

• Screening currents in superconductor flow to cancel field in bulk

Meissner Effect

44

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