Frequency and Quantum Metrology Research Group Research Staff - - PowerPoint PPT Presentation

SLIDE 1

Frequency and Quantum Metrology Research Group

• Research Staff
• Michael Tobar
• Eugene Ivanov
• John McFerran
• Alexey Veryaskin
• Sascha Schediwy
• Maxim Goryachev
• Jeremy Bourhill
• Students
• Ben McAllister
• Akhter Hoissan
• Graeme Flower
• Scott Hardie
• Lewis Teixeira
• Catriona Thomas

1

SLIDE 2

Modified Axion Electrodynamics and the BEAST Experiment

• Axion modified electrodynamics as a magnetization

and polarization of the vacuum

• Polarizations and magnetisations induced by a DC

Magnetic Field

• Magnetizations and polarizations induced by a DC

Electric Field

• Broadband low-mass experiments
• Inductor in DC Electric Field
• Capacitor in DC Magnetic Field
• Broadband Electric Axion Sensing Technique

(BEAST)

SLIDE 3

Modified Axion Electrodynamics

⃗ ∇ ⋅ ⃗ D = ρf + gaγγ ϵ0 μ0 ⃗ B ⋅ ⃗ ∇a ⃗ ∇ × ⃗ H = ⃗ Jf + ∂ ⃗ D ∂t − gaγγ ϵ0 μ0 ( ⃗ B ∂a ∂t + ⃗ ∇a × ⃗ E) ⃗ ∇ ⋅ ⃗ B = 0 ⃗ ∇ × ⃗ E = − ∂ ⃗ B ∂t ⃗ D = ϵ0 ⃗ E + ⃗ P ⃗ H =

⃗ B μ0 −

⃗ M

SLIDE 4

Vair &,tMI: 5H

4 MAY 1987

• Nt. MHFR

1H

Two Applications

• f Axion Electrodynamics

Frank Wilczek

institute for Theoretical

Physics, University of California,

Santa Barbara, Santa Barbara, California 93106

(Received 27 January

1987) The equations

• f axion

electrodynamics are studied. Variations

in the axion

field can give rise to

peculiar distributions

• f charge

and current.

These eAects provide a simple

understanding

• f the frac-

tional electric charge

• n dyons

and of some recently discovered

• ddities

in the electrodynamics

• f anti-

phase boundaries

in PbTe. Some speculations

regarding the possible occurrence of related phenomena

in

• ther solids are presented.

PACS numbers: 14.80.Gt, 05.30.Fk, 14.80.Hv, 71.50.+t

Whether

• r not axions'

have any physical

reality, their

study can be a useful intellectual

exercise.

For by having

a field which

modulates the eA'ects of anomalies

and in-

stantons

and calculating

the consequences

• f its variation

in space and time,

we can get some intuitive

feeling

for these important,

but

• ften

subtle and

• bscure,

things. Also, it is (I shall argue) not beyond the realm of possi- bility

that

fields whose

properties partially mimic those

• f axion

fields can be realized

in condensed-matter

sys-

tems.

In this spirit, I will consider

in this paper two situ-

ations

where

the equations

• f axion

electrodynamics

seem to illuminate

• therwise

surprising phenomena, and then speculate briefly on potential

generalizations.

To begin,

let us recall the equations

• f axion electro-

dynamics. They are generated

by adding to the ordinary

Maxwell Lagrangean

an additional

term

hL=xaE 8,

where

• K. is a coupling

constant. The resulting

equations are

al VaxE+aB.

The

form

• f these

terms reflects the discrete symmetries

• f a: a is P and T odd.

Also, these terms depend

• nly
• n space-time

gradients

• f the axion

field. This

is because

with a =const, hX in Eq. (1) be-

comes a perfect derivative,

and does not aAect the equa- tions of motion. Dyon

• charge. —

Consider

a magnetic monopole sur- rounded

by a spherical

ball

in which a=O, modulating

within a thin shell into a =0 at large distances

(Fig. l).

Now because of the axion term

in (2) one finds that the

domain

wall carries electric charge

density —

• KVa. B, or

charge/unit

length

—

tcVaC& when

integrated

• ver direc-

tion, where @ is the magnetic flux.

The total charge seen

by observers

far from the monopole

is q = —

rc&k

(6)

The Witten eflect, that

in a 0 vacuum

magnetic mono-

poles become dyons with fractional

charge to their mag-

netic charge and to 0, is essentially contained

in (6). By

• ur

introducing axions, and allowing

0 to become

a

V E=p —

xVa B,

V x E = —

BB/Bt,

• V. B=0

V x 8 =BE/Bt +j+ rc(a B+Va x E),

(3) (4)

(s)

where

P,j are the

• rdinary

(nonaxion) charge

and

current. We see that there

is an extra charge

density proportional

to —

Va B, and current density

proportion-

• FIG. l.

Monopole surrounded

by a shell of axion

domain

wall

1987 The American

Physical

Society

1799 Vair &,tMI: 5H

4 MAY 1987

• Nt. MHFR

1H

Two Applications

• f Axion Electrodynamics

Frank Wilczek

institute for Theoretical

Physics,

University of California,

Santa Barbara, Santa Barbara, California 93106

(Received 27 January

1987)

The equations

• f axion

electrodynamics are studied. Variations

in the axion

field can give rise to

peculiar distributions

• f charge

and current.

These eAects provide a simple

understanding

• f the frac-

tional electric charge

• n dyons

and of some recently discovered

• ddities

in the electrodynamics

• f anti-

phase boundaries

in PbTe. Some speculations

regarding the possible occurrence of related phenomena

in

• ther solids are presented.

PACS numbers:

14.80.Gt, 05.30.Fk, 14.80.Hv, 71.50.+t

Whether

• r not axions'

have any physical

reality, their

study can be a useful intellectual

exercise.

For by having

a field which

modulates the eA'ects of anomalies

and in-

stantons

and calculating

the consequences

• f its variation

in space and time,

we can get some intuitive

feeling

for

these important, but

• ften

subtle and

• bscure,

things. Also, it is (I shall argue) not beyond the realm of possi- bility

that

fields whose

properties partially mimic those

• f axion

fields can be realized

in condensed-matter

sys-

tems.

In this spirit, I will consider

in this paper two situ-

ations

where

the equations

• f axion

electrodynamics

seem to illuminate

• therwise

surprising phenomena, and then speculate briefly on potential

generalizations.

To begin,

let us recall the equations

• f axion electro-

dynamics. They are generated

by adding to the ordinary

Maxwell

Lagrangean

an additional

term

hL=xaE 8,

where

• K. is a coupling

constant. The resulting

equations are

al VaxE+aB.

The

form

• f these

terms reflects the

discrete

symmetries

• f a: a is P and T odd.

Also, these terms

depend

• nly
• n space-time

gradients

• f the axion

field.

This

is because

with a =const, hX in Eq. (1) be-

comes a perfect derivative,

and does not aAect the equa- tions of motion. Dyon

• charge. —

Consider

a magnetic monopole sur- rounded

by a spherical

ball

in which a=O, modulating

within a thin shell into a =0 at large distances

(Fig. l).

Now because of the axion term

in (2) one finds that the

domain

wall carries electric charge

density —

• KVa. B, or

charge/unit

length

—

tcVaC& when

integrated

• ver direc-

tion, where @ is the magnetic

flux.

The total charge seen

by observers

far from the monopole

is q = —

rc&k

(6)

The Witten eflect, that

in a 0 vacuum

magnetic

mono-

poles become dyons

with fractional

charge to their mag-

netic charge and to 0, is essentially contained

in (6). By

• ur

introducing axions, and

allowing

0 to become

a

V E=p —

xVa B,

V x E = —

BB/Bt,

• V. B=0

V x 8 =BE/Bt +j+ rc(a B+Va x E),

(3)

(4)

(s)

where

P,j are the

• rdinary

(nonaxion) charge

and

current. We see that there

is an extra charge

density proportional

to —

Va B, and current

density

proportion-

• FIG. l.

Monopole surrounded

by a shell of axion

domain

wall

1987 The American

Physical

Society

1799 VOLUME 58, NUMBER 18

PHYSICAL REVIEW LETTERS

4 MAY 1987

"Im

rn

la

+

/

6 Arg

rn= Tr

—

—

—

+—

—

—

y

g—

— —

E.—

—

——

6 Arg m= —

Tr

Re m

• FIG. 3. Expectation
• f the current

in a background

field is

derived from the vacuum

polarization.

• FIG. 2. Phase changes

through

~ n depending

• n the sign
• f the imaginary

part.

will

depend

• n

small

perturbations —

including

both terms, such as Zeeman splitting,

not retained

in the mod-

el Lagrangean

(9), and effects of impurities

and doping

—

when the Fermi level is near midgap.

For

truly

complex-valued masses the mechanism

whereby

charges

and currents

are generated

need not be

connected

with

the

existence

• f 0 modes,
• r

midgap

states.

For

instance,

if

I m (x) I

is constant,

and

its phase varies

slowly

in

the sense

that

I Bm/9x I/Im I

(

I m I, then the local magnitude

• f the gap will remain

—

2

I m I

everywhere.

Nevertheless, the charges

and

currents

discussed above will be produced; they are asso-

ciated

with

the behavior

• f the

Fermi sea as a whole.

Their magnitude

in this case is robust.

The current associated

with an electric field

in the

plane of the wall is so remarkable

that it deserves further

discussion.

First, let us note its properties:

(i) Since j~E, the current

is voltage controlled

(ii)

Since jJ E, the

current

is

nondissipative Of. course

I have ignored

impurities,

etc., so that this state-

ment

is only approximate.

At the level of analysis

in this

paper many-body eAects

have been

ignored,

and

the

current

is not a supercurrent.

(iii) The direction

• f the current

is determined

by the unit vector B/I BI. This form follows from time-reversal

symmetry.

It indicates

that the direction

• f current

can

reverse, ideally,

in response

to changes

in magnetic

fields

• f tiny magnitude.

This peculiar

dependence

is associat-

ed, in the axion picture

[Eq. (12)], with

the fact that a change

in the sign of the mass is ambiguous;

it can mean

3,=+z or —

z across the wall.

And

now let me discuss

in more detail how these prop-

erties arise.

I will

first discuss

the case where

m is an

• dd, real function
• f z and m(~) is positive.

1 use the

conventions

• f Bjorken and Drell.

The zero-mode

solu- tions of the Dirac equation

are then of the form

p2

y=exp

J~

m(z)dz [Z~f(x,y)+Ezg(x, y)l,

(13a)

Other

modes

have

energy

—

I m(~) I

and

can

be

neglected.

The

eff'ective

two-dimensional dynamics

• f

the low-energy modes

are described

by

the efrective

Hamil ton ian

AH

P(73,

P ~xk,

as we see by sandwiching

the eAective coupling

(i4)

03

Q

3

3,

in (is).

So in this case the interaction

• f the low-energy

modes

with

a planar

electric

field reduces

to a problem

in the

electrodynamics

• f (2+ 1)-dimensional

massive

fer-

mions. Now there

is a peculiarity

in the vacuum

polar-

ization

• f (2+1)-dimensional

electrodynamics

that

is

relevant

• here. '

That

is,

the current induced

by an

external

field, calculated

from the Feynman

diagram

in

• Fig. 3, is of the form

H =io3cr 8

acting on the two-component

spinor

ri =(gI). A magnetic

field normal

to the wall leads to a series of Landau

levels

at energies n(eB/2~) 'i

with degeneracy

eB/2x per unit

• area. If the Fermi

level is slightly

above 0, then one has

charge accumulated

• n the wall, as discussed

above, be-

cause the n =0 mode is composed half of positive-energy

and

half of negative-energy states

relative

to the free

(i.e., no domain

wall) Hamiltonian.

The independence

• f the magnitude
• fj on the magnitude
• f B is now easi-

ly understood

heuristically as follows.

The basic

phe- nomena

is a drift of the zero-mode

plasma

in crossed

electric

and

magnetic

fields. In this situation,

the drift

velocity of a charged

particle

is proportional

to E and in-

versely proportional

to 8. But since the number

• f states

in the

zero-mode plasma, as discussed above,

is itself

proportional

to 8 this dependence cancels out.

An infinitesimal

complex

(3+ 1)-dimensional

mass, i.e., an effective axion

field, generates

a (2+1)-dimen- sional mass p, leading

to similar

results. Indeed, the

efIect of the axion field in the z direction

is simply to in-

duce an effective mass term

where

j,

(p/

I u I )~..

.

F.,

(is)

1

(i3b)

This gives us the current

discussed above, with the prop-

erties (i)- (iii). Note that the (2+1)-dimensional

mass p is P and T

• dd; it is this which

explains

how it can be proportional

1801

SLIDE 5

⃗ B ⋅ ⃗ ∇a = ⃗ ∇ ⋅ (a ⃗ B) + a( ⃗ ∇ ⋅ ⃗ B) ⃗ ∇a × ⃗ E = ( ⃗ ∇ × (a ⃗ E)) − a( ⃗ ∇ × ⃗ E )

Vector Identities Modified Gauss’ Law and Ampere’s Law

⃗ ∇ ⋅ ⃗ D = ρf + gaγγ ϵ0 μ0 ⃗ ∇ ⋅ (a ⃗ B) ⃗ ∇ × ⃗ H = ⃗ Jf + ∂ ⃗ D ∂t − gaγγ ϵ0 μ0 ( ∂(a ⃗ B) ∂t + ⃗ ∇ × (a ⃗ E)) ⃗ ∇ ⋅ ⃗ B = 0 ⃗ ∇ × ⃗ E = − ∂ ⃗ B ∂t

SLIDE 6

Reformulate Modified Electrodynamics

⃗ ∇ ⋅ ⃗ Da = ρf ⃗ ∇ × ⃗ Ha = ⃗ Jf + ∂ ⃗ Da ∂t ⃗ ∇ ⋅ ⃗ B = 0 ⃗ ∇ × ⃗ E = − ∂ ⃗ B ∂t

Modification in the Constitutive Relations

⃗ Da = ϵ0 ⃗ E + ⃗ P + ⃗ Pa ⃗ P a = − gaγγ ϵ0 μ0 (a ⃗ B) ⃗ Ha = 1 μ0 ⃗ B − ⃗ M − ⃗ Ma ⃗ Ma = gaγγ ϵ0 μ0 (a ⃗ E)

Similar to Standard Model Extension Modifications for Lorentz Invariance Violations

SLIDE 7

Signals for Lorentz violation in electrodynamics

• V. Alan Kostelecky

´ and Matthew Mewes

Physics Department, Indiana University, Bloomington, Indiana 47405 Received 20 May 2002; published 23 September 2002 investigation is performed of the Lorentz-violating electrodynamics extracted from the PHYSICAL REVIEW D 66, 056005 2002

• H

0D 0,

• D

0,

• E

0B 0,

• B

0.

D

• H

1DE DB HE 1HB E

• B

,

New methods of testing Lorentz violation in electrodynamics

Michael Edmund Tobar,1,* Peter Wolf,2,3 Alison Fowler,1 and John Gideon Hartnett1

1University of Western Australia, School of Physics, M013, 35 Stirling Highway, Crawley 6009 WA, Australia 2Bureau International des Poids et Mesures, Pavillon de Breteuil, 92312 Se

`vres Cedex, France

3BNM-SYRTE, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, France

(Received 1 September 2004; published 7 January 2005) PHYSICAL REVIEW D 71, 025004 (2005)

D H

• 0e

r DE

• q

DB

• q

HE 1

0 e

r1 HB B @ 1 C A E B

• :

at gaγγa nvariance

, DB is dis-

• r HE.

~

Axion Interaction similar to odd parity Lorentz Invariance Violation

SLIDE 8

www.physics.indiana.edu/~kostelec/

Sidereal Modulations of Constant Background Fields

Oscillating Background Fields Create EM Radiation

Axion is similar to an oscillating odd parity background SME Lorentz invariance violation field. Cannot shield against these type of violations -> Source Terms.

SLIDE 9

arXiv:hep-th/9609099 v1 11 Sep 1996

Asymptotic Freedom

⋆

Frank Wilczek

†

School of Natural Sciences Institute for Advanced Study Olden Lane Princeton, N.J. 08540 1.2. Antiscreening as Paramagnetism: The Importance of Spin

Vacuum acts as Dielectric and Paramagnet!

SLIDE 10

Axion-Photon Interaction as Oscillating Vacuum Polarization and Magnetization Fields

*Vacuum polarizations and magnetisation cause running of the fine structure constant * Magnetic anti-screening and Electric screening gives =1/137 at low energy and 1/128 at 90 GeV

α α

*Tiny oscillating refractive index or fine structure constant * Similar to Brillouin scattering in media nonlinear -> Frequency Shift Goryachev (Tomorrow)

SLIDE 11

⇢a = ga r ✏0 µ0 ~ r · (a ~ B)

~ Ja = ga r ✏0 µ0 @(a ~ B) @t .

r · ~ Ja = @⇢a @t

by ~ Ja = @ ~

Pa @t .

~ Jba = ~ r ⇥ ~ Ma = ga r ✏0 µ0 ~ r ⇥ (a ~ E).

~ Ek

1 − ~

Ek

2 = 0,

~ B?

1 − ~

B?

2 = 0.

~ D?

a1 − ~

D?

a2 = 0,

~ Hk

a1 − ~

Hk

a2 = 0,

Axion Induced Virtual Bound Charges and Currents

Virtual Particle Bound Charge Virtual Particle Polarizarion Current Satisfies the Continuity Equation Virtual Particle Bound Current

Boundary Conditions

Calculate from integral form of modified Maxwell’s equations (no free charges and currents)

SLIDE 12

R,

Axion induced Polarization and Magnetization Fields under DC Magnetic Field tion with ~ B = B0ˆ z

• ~

E = 0

I

C

~ Mφa · d~ l = − @ @t Z Z

S

~ Pa · d~ S.

~ Beff

a = −µ0µr ~

Mφa = −gaγγ µr c @a @t r 2B0 ˆ .

1) Assume Infinite Solenoid

~ Eeff

a = ~

Pa/(✏0✏r) = −gaγγa c ✏r B0ˆ z,

~ Pa = −gaγγ r ✏0 µ0 aB0ˆ z.

~ Mφa = gaγγ @a @t r ✏0 µ0 r 2B0 ˆ .

Effective/Pseudo Fields

~ Bφa = −gaγγ @a @t 1 c R 2 B0 ˆ (r = R)

~ Bφa(r) = −gaγγ @a @t 1 c R2 2r B0 ˆ (r > R),

~ Hk

a1 − ~

Hk

a2 = 0,

= -

~ Bφa µ0

~ Mφa

Match Boundary Conditions Calculate Vacuum Magnetization

SLIDE 13

DC Solenoid of Finite Length

X X X X X X X X

Ma

B

0z

P

az

z

• r
• FIG. 1: A sketch of a finite solenoid, showing the the

static magnetic field (green) and the axion-induced fields (blue and red).

X X X X X X X X

B

0z

P

az

Ma

z r

• Ba

Eaz

• FIG. 2: A finite solenoid with idealised field cancelation

above and below the inner region together with the static magnetic field (green), the axion-induced

• scillating ~

Pa and ~ Ma fields (blue and red) and the axion induced oscillating ~ Ea and ~ Ba fields outside the DC magnetic field (pink and orange).

2) Finite Solenoid->Dipole Field 3) Finite Solenoid with ideal Field Cancelation Above and Below

SLIDE 14

Axion induced Magnetization and Polarization Fields under DC Electric Field

axion. as ~ B = 0, ~

1) Assume Infinite Capacitor no Fringing Field

, ~ E = aginary For E0ˆ z,

~ Mza = ( −ga q

✏0 µ0 aE0ˆ

z, r < R, 0, r > R.

R,

Kba ˆ = ga r ✏0 µ0 aE0 ˆ

• At boundary r=R

SLIDE 15

P

a

E0z

Maz z

• r

Positive T erminal

Ground T erminal

• FIG. 3: A pair of capacitor plates, showing the the

static electric field (green) and the axion-induced fields (blue and red).

DC E-field from Finite Length Capacitor

Jba ˆ = ~ r ⇥ ~ Ma = @Pa @t ˆ .

~ r ⇥ ~ Ma = ga r ✏0 µ0 a(t)~ r ⇥ ~ E(r, z).

SLIDE 16

Inductor in a DC Electric Field

, ~ E = aginary For E0ˆ z,

DC field will indu ga q

✏0 µ0 aE0ˆ

z

• n Maz =

Φa = µ0µrAMaz = ga µr c AaE0.

axion. as ~ B = 0, ~

ia = NΦ L = ga µr c AN L aE0.

va = ga µr c AN da dt E0

g a = a0 cos(!at)

large number of a0 = q

2⇢a c ¯ h ma

V RMS

a

= gaµrANE0 p⇢ac.

IRMS

a

= ga r ✏0 µ0 ⇣ c !a ⌘ d N E0 p⇢ac.

coil of length y L = µ0µrN 2A

d

by

SLIDE 17

Modified Axion Electrodynamics as Oscillating Polarization and Magnetization of the Vacuum

Michael E. Tobar,1, ∗ Ben T. McAllister,1 and Maxim Goryachev1

1ARC Centre of Excellence For Engineered Quantum Systems,

Department of Physics, School of Physics and Mathematics, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia. (Dated: August 23, 2018) We present a reformulation of modified axion electrodynamics where the four Maxwell’s equations maintain a similar form to the unmodified versions, with all modifications redefined within the constitutive relations between the ~ D, ~ H, ~ B and ~ E fields. In this reformulation the axion induced bound charge density, polarization current density and bound current density are identified along with the associated axion induced vacuum polarization and magnetization, which are shown to satisfy the charge-current continuity equation. This representation is consistent with Wilczek’s

• riginal calculations from the polarization of vacuum fields. The reformulation is important when

considering conversions of axions into photons, relevant in many experimental contexts. For example, when a DC ~ B-field is applied, oscillating bound vacuum charges and polarization currents are induced at a frequency equivalent to the axion mass. In contrast, when a large DC ~ E field is applied, an oscillating bound current or magnetization of the vacuum is induced at a frequency equivalent to the axion mass. Moreover, the integral forms of the equations can be used to clearly define the boundary conditions between distinct media either with or without axion induced vacuum polarization or magnetization. This provides clarity when considering experiments sensitive to axion induced electric and/or magnetic effects inside or outside the high DC field region. For example, a capacitor in a high DC magnetic field can act as a detector for low-mass axions without suppression

• f of the signal due to electromagnetic shielding.

Also, we calculate the voltages and currents induced by axions in an inductive sensor under a DC electric field, which is the dual experiment to a capcitive sensor under a DC magnetic field.

Paper to be Posted on ArXiv Very Soon

SLIDE 18

FACULTY OF SCIENCE

Perth, Australia

Broadband Electric-field Axion Sensing Technique


(BEAST)


BT McAllister, M Goryachev, J Bourhill, EN Ivanov, ME Tobar

SLIDE 19

Broadband Axion Dark Matter Haloscopes via Electric Sensing

Ben T. McAllister,1, ∗ Maxim Goryachev,1 Jeremy Bourhill,1 Eugene N. Ivanov,1 and Michael E. Tobar1, †

1ARC Centre of Excellence For Engineered Quantum Systems,

Department of Physics, School of Physics and Mathematics, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia. (Dated: August 21, 2018) The mass of axion dark matter is only weakly bounded by cosmological observations, necessitating a variety of detection techniques over several orders of magnitude of mass ranges. Axions haloscopes based on resonant cavities have become the current standard to search for dark matter axions. Such structures are inherently narrowband and for low masses the volume of the required cavity becomes prohibitively large. Broadband low-mass detectors have already been proposed using inductive mag- netometer sensors and a gapped toroidal solenoid magnet. In this work we propose an alternative, which uses electric sensors in a conventional solenoidal magnet aligned in the laboratory z-axis, as implemented in standard haloscope experiments. In the presence of the DC magnetic field, the in- verse Primakoff effect causes a time varying electric vacuum polarization (or displacement current) in the z-direction to oscillate at the axion Compton frequency. We propose non-resonant techniques to detect this oscillating polarization by implementing a capacitive sensor or an electric dipole an- tenna coupled to a low noise amplifier. We present the theoretical foundation for this proposal, and the first experimental results. Preliminary results constrain gaγγ >∼ 2.35 × 10−12 GeV−1 in the mass range of 2.08 × 10−11 to 2.2 × 10−11 eV, and demonstrate potential sensitivity to axion-like dark matter with masses in the range of 10−12 to 10−8 eV.

~ Eeff

a = ~

Pa/(✏0✏r) = −gaγγa c ✏r B0ˆ z,

Paper rewritten with respect to Axion Modified Electrodynamics as discussed previously Vacuum polarisation term, not E-field, so low-mass signals not suppressed

SLIDE 20

Geometry Comparison with ABRACADABRA

ABRACADABRA (Axion Magnetic Dipole) BEAST (Axion Electric Dipole)

What causes the Axion induced Jeff?

• > No conduction electrons
• > Caused by small oscillations of

vacuum polarization

• > Bound Displacement Current

E fields inside antenna conductors are due to oscillating free currents: J = σ E σ (metal conductivity)

B

Jeff

Ea

J Similar to a Loop Antenna Similar to Hertzian Dipole Antenna

SLIDE 21

A=πR2 (DC field) +

• The BEAST Experiment

Measure with SQUID (current) or High Impedance Amplifier (HIA) (voltage) Measure Currents and Voltages v To improve sensitivity with SQUID -> Large Plate Area To improve sensitivity with HIA -> Large Plate Separation

~ Ja = @ ~ Pa @t = gaγγ r ✏0 µ0 ~ B0 @a @t .

~ Pza = gαγγ r ✏0 µ0 aB0ˆ z = ✏0✏r ~ Ea eff.

q VaRMS = 1 ✏r gad c !a

• B0

p ⇢ac3.

IaRMS = gaA r ✏0 µ0 B0 p ⇢ac3,

tion with ~ B = B0ˆ z

• ~

E = 0

~ Mφa = gaγγ r ✏0 µ0 r 2B0 @a @t ˆ = 1 µ0µr ~ Ba eff

g a = a0 cos(!at)

large number of a0 = q

2⇢a c ¯ h ma

SLIDE 22

Built Experiment With a SQUID

DC SQUID in a copper holder to be attached to the “cold finger” of the pulse-tube dilution fridge Calibration: Use resistors instead of capacitors

• > Derive SQUID transimpedance ~ 1.2 MΩ
• 3dB low pass bandwidth of 2.1 MHz

SQUID RMS current spectral density, ~ pA

Hz

SLIDE 23

7 T Magnet (10 cm bore) SQUID Large Area Capacitor Plate 7.5 x 7 cm 7 T field at 4 K for 8 days of

• bservation time

SLIDE 24

Possible to discriminate against these spurious signals with the flux line, which is susceptible to spurious RF signals in the lab. This spectra do not have the requisite to resolution to resolve axion signals with an effective line width of 10-6ωa

Beast Spectral Density

SLIDE 25

BEAST: First Limits

Higher resolution search was conducted around 5 kHz, with the minimal spectral resolution of 4.5 mHz (increasing at higher frequencies) All sharp peaks greater than 4.4 standard deviations from the mean originating from the SQUID were able to be excluded, due to a similar signal appearing in the flux line Using this data, we may place the 95 % confidence exclusion limits on axion-photon coupling

SLIDE 26

• HIA VRMS readout
• > A unimportant
• > d important

Suggests many long and skinny “noodle” capacitors to improve sensitivity

• SQUID IRMS readout
• > A important
• > d unimportant

Suggests many long flat “pan cake” capacitors to improve sensitivity Element cross capacitance stray capacitance and grounding needs to be modeled carefully

Possible Improvements

SLIDE 27

Long “Noodle” Capacitors not likely: Wire dipole antennas instead? Response of a Conductor to Axion Conversion?

d A

Bo (DC field) Basically governed by Ohms law with current and voltage in phase Minimizes stray capacitances Noodle BEAST

~ Jfa = ga r ✏0 µ0 ~ B0 @a @t .

Free current density induced in a conductor due to axion

⇢fa = ga r ✏0 µ0 ~ B0~ r · a.

IaRMS = gaA r ✏0 µ0 B0 p ⇢ac3, VaRMS = ga d  r ✏0 µ0 B0 p ⇢ac3.

e current throu y Ifa = Jfa ⇤ A,

p e conductivity of the wire, 

SLIDE 28

Frequency and Quantum Metrology Research Group

• Research Staff
• Michael Tobar
• Eugene Ivanov
• John McFerran
• Alexey Veryaskin
• Sascha Schediwy
• Maxim Goryachev
• Jeremy Bourhill
• Students
• Ben McAllister
• Akhter Hoissan
• Graeme Flower
• Scott Hardie
• Lewis Teixeira
• Catriona Thomas

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