Probing axion dark matter with magnon

Asuka Ito (Kobe Univ. Japan)

with Tomonori Ikeda, Kentaro Miuchi, Jiro Soda, Hisaya Kurashige,
Dany Lachance-Quirion, Yasunobu Nakamura, Yutaka Shikano

2019 5/14

Talk plan1.

Axion :

axion DM, axion-electron interaction

2.

Magnon as collective spin excitation of electrons

3.

Experimental upper limit on theaxion-electron coupling constantTalk plan1.

Axion :

axion DM, axion-electron interaction

2.

Magnon as collective spin excitation of electrons

3.

Experimental upper limit on theaxion-electron coupling constantAxionQCD axion : a Nambu-Goldstone boson of the broken Peccei-Quinn symmetry(for resolving the strong CP problem)

Invisible axion models

The KSVZ model

J.E.Kim (1979),
M.A.Shifman, A.Vainshtein, V.I.Zakharov (1980)

The DFSZ model

M.Dine, W.Fischler, M.Srednicki (1981),
A.Zhitnitsky (1980)(QCD) axion is a strong candidate for dark matter.
How can we detect ?

Axion-electron interaction

An axion can interact with the electron:

KSVZ: loop level
DFSZ: tree level,

In the non-relativistic limit,

Hint '<latexit sha1_base64="k5cMcq4WTW4YJIA3KIbqpbCqasg=">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</latexit>

|e|
µB =
: Bohr magneton ,2mgaee ~
ˆ · ra =2me

2µB Ŝ ·

⇣g

aee

e

Ŝ i =

rai

2: spin⌘eﬀective magnetic ﬁeld

Reﬂecting the nature and distribution of the axion DM

Axion DM

V (a)Axions can behave as DM if it oscillates
around the bottom of the potential :a

The equation of state parameter w = 0

a(x) = a0 cos(!tcorresponding to theabundance of the axion DM

kx)

determined by the axion mass

( ! = ma )※In the case of the QCD axion, the axion mass around µeV is favored for DM.

ma ⇠ µeV

scale of cavity experiments(cm, GHz)

Eﬀective magnetic ﬁeld

gaee
Ba =
ra
e
<latexit sha1_base64="7bWuTOt5AftwrLjVV51AJccogkU=">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</latexit>
sha1_base64="LHaWa1pNUSD+ZPLNPPJeBOn4MV4=">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</latexit>

If gradient of the axion DM is non-zero, it acts as magnetic ﬁelds.
We assume that the axion DM forms clumps in the Galaxy
as a stable solution of the Shrodinger-Poisson equation.

de Broglie
wave lengthv ⇠ the virial velocity<latexit sha1_base64="l82Q5mSDAZsCGDbSqoZf5vah044=">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</latexit>in the Galaxy

Eﬀective magnetic ﬁeld

When a clump of axion DM is going through us, we feel “axion-wind”

Thenra ⇠ ma va

and the coherence time isEﬀective magnetic ﬁeld

We can estimate the amplitude of the eﬀective magnetic ﬁeld as<latexit sha1_base64="t0n/N8XkFT+LQ2mh8PmAeWTl4dA=">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</latexit>

gaee is tiny, how can we measure such small magnetic ﬁeld?
Axion-electron resonance caused by coherent oscillation of axion DM
Use so many electrons (magnon)

Talk plan1.

Axion :

axion DM, axion-electron interaction

2.

Magnon as collective spin excitation of electrons

3.

Experimental upper limit on theaxion-electron coupling constantMagnonWe consider a ferromagnetic sample which has N electronic spinsin an external magnetic ﬁeld B .
<latexit sha1_base64="+97El6ztDdg4MDgQtAVAoiGsebM=">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</latexit><latexit

It is well described by the Heisenberg model:

i = 1...N

specify the sites of electrons.

<latexit sha1_base64="bHZjBtbNeEcHqPBt1DgEoXM4+Gw=">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</latexit>ｚ

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sha1_base64="fkeVbA7hEeDt2jAX/I91v85wpWg=">AAACfnichVG9SsNQGD2N/63a6iS4FKXiVL64WJwEF8dabSu0UpJ41atpEpLbghZfwMlN1EnBQXwAH8DFF3DwEcRRwcXBL2lAVNQvJPfcc7/z3RyO6dkyUESPCa2nt69/YHAomRoeGU1nxoYrgdvyLVG2XNv1100jELZ0RFlJZYt1zxdG07RF1dxbCs+rbeEH0nXW1L4nNprGtiO3pGUopip1tSOU0chMU56iyv4EegymEVfRzdyijk24sNBCEwIOFGMbBgJ+atBB8JjbQIc5n5GMzgUOkWRti7sEdxjM7vF3m3e1mHV4H84MIrXFt9j8+qzMIkcPdE0vdE839ETvv87qRDPCf9nn1exqhddIH02svv2ravKqsPOp+kNhcvffnhS2UIi8SPbmRUzo0urObx+cvKwulHKdGbqkZ/Z3QY90xw6d9qt1tSJK50hyQPr3OH6Cylxep7y+QhjEJKYwyzHMYxHLKKLM1+3iGKc401KarhW6UWqJONNxfClt4QNi/ZEm</latexit>
sha1_base64="VmOmcsvgSXOUOKwMcqq8CbtnwM0=">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</latexit>

B<latexit sha1_base64="+97El6ztDdg4MDgQtAVAoiGsebM=">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</latexit><latexit,

Ba = (Ba sin ✓, 0, Ba cos ✓) ' (Ba sin ✓, 0, 0)<latexit sha1_base64="MK/mo8K/p4qrKzs7vwAGQvKNRuU=">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</latexit>

Holstein-Primakoﬀ transformation
Spin operators can be rewritten in terms of bosonic operators
by using the Holstein-Primakoﬀ transformation:

where

A spin ﬂip corresponds to creation of a boson.

Bz

Bz
=

no boson,=a bosonFurthermore, we can move on to Fourier space :A bosonic operator of“spin wave”=
MagnonMagnon

Holstein-Primakoﬀ transformation

⇣
⌘
p
B
sin
✓
a
†
H ' 2µB Bz ĉk=0 ĉk=0 + 2µB
N ĉ†k=0 e i!a t + ĉk=0 ei!a t
4<latexit sha1_base64="SvvCQkLC9yzUHMuUwYbVpB8Ygy4=">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</latexit>+<latexit sha1_base64="DTlfnVkf1HwSluLtryqF+9XcHm0=">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</latexit>X

i=1..NH(ĉk=i )The coupling constantis eﬀectively increased bypp
Typically, N ⇠ 1020 ⇠ 1010 .

p<latexit sha1_base64="g9qf3InP12/ulRPlwgfau7EE6rI=">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</latexit>N.

The axion DM excites the uniform mode of the magnon!

Talk plan1.

Axion :

axion DM, axion-electron interaction

2.

Magnon as collective spin excitation of electrons

3.

Experimental upper limit on theaxion-electron coupling constantExperiment
We measured the quantum state of a magnon with qubit
qubit:

A two-state system

We can see the quantum state of the magnon by observing qubit spectrum!

Qubit spectrum!m : magnon frequency!q : qubit frequency<latexit sha1_base64="kmKmjwIPP3rnsD4adCYo+3Q3rks=">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</latexit><latexit sha1_base64="xvG7GoZoexaWY4rTQGDKsFOYZ24=">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</latexit><latexit sha1_base64="Xv70BESpW+v5j6XI7fpQF273eHE=">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</latexit>

gq m : magnon-qubit coupling constantgef f: magnon-axion coupling constant<latexit sha1_base64="+Y2yA8OBurTaLdqugy1rpX8A6DA=">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</latexit>

This system is approximately solvable and we can obtain the qubit spectrum:Magnon state and qubit spectrum

Upper limit

We observed the qubit spectrum and found no evidence of the axion DM.

oratma = 33 μeV<latexit sha1_base64="dqsrScXKUpmarqjzmQkkFdSK1kY=">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</latexit>Upper limitSummary

Axion is a strong candidate for DM

Axion DM can induce resonant spin precession of electrons

Axion-magnon coupling get eﬀective factor

p

N⇠

p

1020 ⇠ 1010

We measured the quantum state of a magnon and gave
an upper limit
ma = 33 μeVat<latexit sha1_base64="dqsrScXKUpmarqjzmQkkFdSK1kY=">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</latexit>