MAD MAX

Javier RedondoUniversidad de Zaragoza (Spain)Max Planck Institute für Physik

Axions are necessarily dark matter

0 ⇡�⇡

time

n

nCoherent oscillations

=Dark Matter Axions

Energy

~ One parameter theory

axion mass✓(t, x) = a(t, x)/fa

ma = 6meV109 GeV

fa

Measured today |✓| < 10�10 (strong CP problem)

- is it a dynamical field? ✓(t,x)generated by QCD!

✓(t) = ✓0 cos(mat)

Relic density as function of mass

- Random IC (after a phase transition)- One Universal IC (inflation smoothens the axion field)

�⇡

✓

⇡

Theta evolution, Averaged SCENARIO I

DM dominated by string radiation

- Axion DM scenarios

Excluded (too much DM) ok sub

Phase transition (N=1)strings+unstable DW’s

Axion dark matter

Initial conditions set by :

Excluded (too much DM) ok sub

Phase transition (N=1)strings+unstable DW’s

- Axion DM scenarios

oktuned (anthropic?) tuned

Inflation smooth⌦aDMh2 ' ✓2I

✓80µeV

ma

◆1.19

Excluded

Axion dark matter

Initial conditions set by :

Detecting Axions

⇢aDM = 0.3GeV

cm3

✓0 = 3.6⇥ 10�19

⇢a =1

2(a)2 +

1

2m2

aa2 =

1

2m2

af2a✓

20

V✓✓

Cavities Mirrors LC-circuit

Spin precession Atomic transitions Optical

Axion experiments (target areas)

osc. EDM

LC

only one running

not DM

test bench

Axion Dark Matter eXperiment (Seattle, Yale...)

Excluded

IAXO?

SCENARIO I

ADMXADMX-HF

QUAX

?

ARIADNE✓0QCD > 10�14?

CAPP

osc. EDM only one running

baby bornMunich Axion Dark MAtter “eXperience”

not DM✓0QCD > 10�14?

Excluded

IAXO?

SCENARIO I

ARIADNE✓0QCD > 10�14?

QUAX

?LC

MADMAX

Axion experiments (target areas)

ADMXADMX-HF

CAPP

- In a static magnetic field, the oscillating axion field generates EM-fields

B-field

- Electric fields - Oscillating at a frequency

(amp independent of mass!)

Axion DM in a B-field

LI = �Ca�↵

2⇡

a

faB ·E

LI = �Ca�↵

2⇡✓(t)B

ext

·E

source

! ' ma

Ea = Ca�↵B

ext

2⇡✓0

cos(mat)

10-7 10-6 10-5 10-4 10-310-1

1

10

102

10310-1 1 10 102

10-1

1

10

102

103

c�KSVZ

DFSZ

AD

MX

RBF

UF

AD

MX AD

MX

2 AD

MX

-HF

CARR

ACK

?

ma[µeV]

⌫[GHz]

IAXO

- Haloscope (Sikivie 83) “Amplify resonantly the EM field in a resonant cavity”

- Signal (V / m�3a ) P

out

/ V ma ⇠ 1

m2

a

- Noise Pnoise

= Tsys

�⌫a / m2

a

P ⇠ Q|Ea|2(V ma)G

Resonant cavity experiments

Output EM power

on resonance ⌫res =ma

2⇡

Ca�

ma[eV]

30 cm 0.6 cm

spherical reflecting dish

pre MADMAX (dish antenna)- Do not give up volume -> Area

D � 1

ma

P ⇠ |Ea|2A

Radiation from a dielectric interface ...

Emitted EM-wave

E(t) =c�↵✓0B

2⇡✏cos(mat) E(t) =

c�↵✓0B

2⇡cos(mat)

Boundary conditions!E||1 = E||2Emitted EM-wave

Radiation from a magnetised mirror : Power

Emitted EM-wave

MIR

ROR

Power

Area

⇠ 2.2⇥ 10

�27Watt

m

2

✓Ca�

2

B||

5T

◆2

Many dielectrics : MADMAX at MPP Munich

Emitted EM-waves from each interface

+ internal reflections ......

- Emission has large spatial coherence; adjusting plate separation -> coherence

boost factorP

Area⇠ 2.2⇥ 10�27 W

m2

✓Ca�

B||

10T

◆2

⇥ �2(!)

0 1 2 3 4

0.2

0.4

0.6

0.8

1.0

One dielectric

Axion emission (boost factor) (n=2,3,4)

⌫/⌫00 1 2 3 4

0.2

0.4

0.6

0.8

1.0

transmission coefficient

⌫/⌫0

�0

2= d

- Frequency response

Close to nu0, many layers

18 19 20 21 22

20

40

60

80

100

120

140

Emitted EM-waves from each interface

+ internal reflections ......

boost factor (N=10,40,80; n=3,nu0=20 GHz)

⌫[GHz]

�N ⇠ N ⇥ �1

Nice boost, excellent bandwidth!

mirror

n = 1, �

n, �n

20 40 60 80 1000

1

2

3

4

5

6

z

z=4.5, 4, 3.5, 3, 2.5 mm

zn

zn=0.65 mmn=3

⌫[GHz]

[...]

�

When dielectrics are non-transparent, mild resonances appear that allow higher boosts

Close to 2nu0, cavity effects

Maximum effect for z =�

2, zd =

�0

4=

�

4n

tuning

Distances between layers allow tuning (transfer matrix formalism)

JCAP 1701 (2017)

Broadband vs narrowband central frequency

Potential reach

A = 1 m^2B-field = 10 T80disk n=5

whys

- why can it work?

Large volume + (relatively) simple tuning long measurements broadbandshort measurements narrowband

- What can go wrong?

- 10T dipole-like Magnet, 1 m^2 aperture !- 1 m^2 dielectrics (tiling smaller pieces)- Tolerances (several micron distances)- difraction

Conclusions

- Strong CP problem and dark matter motivate Axions

- Most predictive model (N=1) mass~ 0.1 meV (fa ~ 10^11 GeV)

- Many experimental efforts, solid player missing in that range

- MW emission from interfaces is weak , make layered haloscope

- Munich Axion Dark MAtter eXperiment