Probing Axion Dark Matter with Magnon

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 plan

1. Axion : axion DM, axion-electron interaction

2. Magnon as collective spin excitation of electrons

3. Experimental upper limit on the axion-electron coupling constant Talk plan

1. Axion : axion DM, axion-electron interaction

2. Magnon as collective spin excitation of electrons

3. Experimental upper limit on the axion-electron coupling constant Axion

QCD 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

KSVZ: loop level An axion can interact with the electron: DFSZ: tree level

e i In the non-relativistic limit, µB = | | : Bohr magneton , Sˆi = : spin 2m 2

gaee~ gaee int ˆ a = 2µBSˆ a

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 '2me · r · e r 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)=a cos(!t kx) 0

corresponding to the determined by the axion mass abundance of the axion DM ( ! = 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 = a

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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 length

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 the virial velocity ⇠ in the Galaxy Eﬀective magnetic ﬁeld

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

Then a m va and the coherence time is r ⇠ a Eﬀective magnetic ﬁeld

We can estimate the amplitude of the eﬀective magnetic ﬁeld as

is tiny, how can we measure such small magnetic ﬁeld? 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 gaee

Axion-electron resonance caused by coherent oscillation of axion DM

Use so many electrons (magnon) Talk plan

1. Axion : axion DM, axion-electron interaction

2. Magnon as collective spin excitation of electrons

3. Experimental upper limit on the axion-electron coupling constant Magnon

We consider a ferromagnetic sample which has N electronic spins

in an external magnetic ﬁeld 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 . It is well described by the Heisenberg model:

specify the sites of electrons. 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 =1...N

ｚ B (t)=B cos(!t) 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 a a

✓AAACiXichVG7SgNBFD2urxhfURvBRgyKVbgrgiFVMI1lEs0DTJDdddTVze6yOwnE4A9Y2YlaKViIH+AH2PgDFn6CWEawsfBmsyAq6h1m5syZe+7M4equZfqS6KlH6e3rHxiMDEWHR0bHxmMTk0XfqXuGKBiO5XhlXfOFZdqiIE1pibLrCa2mW6KkH2Q696WG8HzTsTdk0xXVmrZrmzumoUmmihW5J6S2FYtTgoKY/QnUEMQRRtaJ3aGCbTgwUEcNAjYkYwsafB6bUEFwmauixZzHyAzuBY4QZW2dswRnaMwe8LrLp82QtfncqekHaoNfsXh6rJzFPD3SDbXpgW7pmd5/rdUKanT+0uRd72qFuzV+PL3+9q+qxrvE3qfqD4XO2X97kthBMvBisjc3YDoujW79xuFpez2Vn28t0BW9sL9LeqJ7dmg3Xo3rnMhfIMoNUr+34ycoLiVUSqi55Xh6NWxVBDOYwyL3YwVprCGLAr+7jxOc4VwZVlQlqaS6qUpPqJnCl1AyH7jrkhs=sha1_base64="dO1RVWgbv0QBXFnWGIM/DJuxBX8=">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_base64="fkeVbA7hEeDt2jAX/I91v85wpWg=">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_base64="VmOmcsvgSXOUOKwMcqq8CbtnwM0=">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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 boson

Furthermore, we can move on to Fourier space : A bosonic operator of “spin wave” =

Magnon Magnon

Holstein-Primakoﬀ transformation

Ba sin ✓ p i!at i!at 2µBBzcˆk†=0cˆk=0 +2µB N cˆk†=0e +ˆck=0e 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 ' 4 ⇣ ⌘ + (ˆc ) H k=i 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 i=1X..N

The coupling constant is eﬀectively increased by p . 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 N Typically, pN p1020 1010 . ⇠ ⇠ The axion DM excites the uniform mode of the magnon! Talk plan

1. Axion : axion DM, axion-electron interaction

2. Magnon as collective spin excitation of electrons

3. Experimental upper limit on the axion-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

: magnon frequency !AAACi3ichVG9SsNQGD2N/9XaqovgIhbFqXxRQSkOogiOVu0P2FKSeFtD80eSFrT4Ao4uDrooOIgP4AO4+AIOPoI4Krg4+DUNiBbrF3Lvued+50sOR3UM3fOJniNST29f/8DgUHR4JDYaT4yN5zy77moiq9mG7RZUxROGbomsr/uGKDiuUEzVEHm1ttG6zzeE6+m2tecfOaJkKlVLr+ia4jNVKNqmqCpls5xIUoqCmu4EcgiSCGvbTtyjiAPY0FCHCQELPmMDCjx+9iGD4DBXQpM5l5Ee3AucIMraOncJ7lCYrfFa5dN+yFp8bs30ArXGXzH4dVk5jVl6olt6o0e6oxf6/HNWM5jR+pcj3tW2Vjjl+Onk7se/KpN3H4ffqi4Klbu7e/JRwUrgRWdvTsC0XGrt+Y3j87fd9M5sc46u6ZX9XdEzPbBDq/Gu3WTEzgWiHJD8O45OkFtIyZSSM0vJtfUwqkFMYQbznMcy1rCFbWSDHM5wgUspJi1KaWm13SpFQs0EfpS0+QWfFpLu m ! : qubit frequency

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 q g 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 q m : magnon-qubit coupling constant g : magnon-axion coupling constant 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 eff

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.

at μeV mAAACjHichVG7SgNBFD2u7/hI1EawWQwRq3BXBUUJiIJY+kpUNITddaJL9sXuJhCDP2BrYaEWChbiB/gBNv6AhZ8glgo2Ft5sFkTFeIeZOXPmnjtzuJprGn5A9NQitba1d3R2dcd6evv644mBwZzvlD1dZHXHdLwtTfWFadgiGxiBKbZcT6iWZopNrbRYv9+sCM83HHsjqLoib6n7tlE0dDVgatsqqHJGnpyUC4kkpSkM+TdQIpBEFCtO4g672IMDHWVYELARMDahwuexAwUEl7k8asx5jIzwXuAIMdaWOUtwhspsidd9Pu1ErM3nek0/VOv8isnTY6WMFD3SDb3SA93SM338WasW1qj/pcq71tAKtxA/Hl5//1dl8R7g4EvVRKFxdnNPAYqYCb0Y7M0NmbpLvVG/cnj6uj67lqqN0RW9sL9LeqJ7dmhX3vTrVbF2hhg3SPnZjt8gN5FWKK2sTiXnF6JWdWEEoxjnfkxjHstYQZbftXCCc1xI/dKUNCdlGqlSS6QZwreQlj4BohGR9w== a = 33 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 pN p1020 1010 ⇠ ⇠

We measured the quantum state of a magnon and gave an upper limit at μeV 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 a = 33