Magnonics in the quantum regime

Koji UsamiResearch Center for Advanced Science and Technology (RCAST)

University of Tokyo

Yasunobu Nakamura

K.C. Schwab and M.L. Roukes, Physics Today 58, 7, 36 (2005)

J.D.Teufel et al., Nature 475, 359 (2011)

J.Chan et al., Nature 478, 89 (2011)

10MHz oscillator (10mK)

3GHz oscillator (4K)

Putting Magnonics into Quamtum Magnonics

New possibility of optomagnonics

Cavity (circuit) quantum magnonics

Posters

A. Gloppe Y. Nakata

Magnetic quasi-vortex Magnonic crystal

New possibility of optomagnonics

Cavity (circuit) quantum magnonics

Magnons

Exchange interaction

Holstein-Primakoff transformation:

ZeemanExchange

Paramagnet

Ferromagnet

Exchange Zeeman

Magnetostatic (Walker) modes

Maxwell equations

Landau-Lifshitz equation

Walker equations

Inside:

Outside:

L. R. Walker, Phys. Rev. 105, 390 (1957)

Continuum limit

Magnetostatic (Walker) modes(1, 1, 0)

”Kittel mode”

(2, 2, 0) (3, 3, 0)

(2, 0, 0)

P. C. Fletcher and R. O. Bell, J. Appl. Phys. 30, 687 (1959)

Ferromagnetic resonance

Yttrium Iron Garnet (YIG)

Kittel mode

Ferromagnetic resonance (FMR)

YIG single crystal

Microwave cavity

1mm sphere

Hstatic

Hac

Rectangular TE101 modeFrequency ~ 10.5 GHzQ factor ~ 104

Hybridizing magnons and microwave photons

Y. Tabuchi et al., Phys. Rev. Lett. 113, 083603 (2014)

Harmonic oscillator + harmonic oscillator

Harmonic oscillator

Energy

.....

+Harmonic oscillator

.....

Energy

..... .....

→

ResonanceNormal mode splitting

Linear energy level structure

Experimant: Y. Tabuchi et al., Science 349, 405 (2015) Proposal: A. Imamoglu, Phys. Rev. Lett. 102, 083602 (2009).

Meta cavity QED

Superconducting qubit

LC circuit

.....

Capacitor with Josephson junction

.....

Flux:Phase:

Superconducting qubit

LC circuit

.....

Capacitor with Josephson junction

.....

Flux:Phase:

Experimant: Y. Tabuchi et al., Science 349, 405 (2015) Proposal: A. Imamoglu, Phys. Rev. Lett. 102, 083602 (2009).

Meta cavity QED

Meta cavity QED

+Qubit Cavity (harmonic oscillator)

Energy

.....

+Magnon (harmonic oscillator)

.....

Circuit QED

M1+

Virtual photon

Y. Tabuchi et al., Science 349, 405 (2015).

+ →

Artificial Atom Magnon (Harmonic oscillator) Jaynes-Cummings ladder

EnergyEnergy

.....

..... .....

Virtual photon

Resonance

Magnon-vacuum Rabi splitting

Y. Tabuchi et al., Science 349, 405 (2015).

Qubit

Magnon-vacuum Rabi splitting

Resonant coupling

D. Lachance-Quirion et al., Sci. Adv. 3, e1603150 (2017)

Dispersive coupling

D. Lachance-Quirion et al., Sci. Adv. 3, e1603150 (2017)

+Artificial Atom Magnon (Harmonic oscillator)

Energy

.....

Virtual photon

Off - resonance

“Magnon-polariton” shift

D. Lachance-Quirion et al., Sci. Adv. 3, e1603150 (2017)

“Magnon-polariton” shift

New developments of quantum magnonics

Magnon linewidth vs. temperature

Y. Tabuchi et al., Phys. Rev. Lett. 113, 083603 (2014)

Resonant TLSMagnon-magnon

Slow relaxationMagnon-phonon

Relaxation and dephasing

Dephasing

Total linewidth

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

Tomography of magnon states

From coil current to ac-Stark drive

Idea from Patrice Bertet, thanks!

Summary

Quantum magnonics with ferromagnet• Strong coupling with microwave cavity• Vacuum Rabi splitting• Magnon-number-resolving spectroscopy

In progress• Magnon-state tomography• Quantum magnon state generation

New possibility of optomagnonics

Cavity (circuit) quantum magnonics

Effective Hamiltonian

W. Happer and B.S. Mathur, Phys. Rev. 163, 12 (1967);J.M. Geremia, J.K. Stockton, and H. Mabuchi, PRA 73, 042112 (2006).K. Hammerer, A.S.Sorensen, and E.S.Polzik, Rev. Mod. Phys. 82, 1041 (2010).

Magnon

Photon

Cross section :A

Dielectric tensor

Symmetry requirements of

Hermiticity (losslessness):

( symmetric )

( anti-symmetric )

Symmetry requirements of

Reciprocity:

Symmetric part:

Anti-symmetric part:

even powers of M

odd powers of M

Dielectric tensor

Scalar light shift (symmetric)

Vector light shift (anti-symmetric)

Tensor light shift (symmetric)

Vector light shift (Faraday effect)

Rotation matrix

Tensor light shift (Cotton-Mouton effect)

Stress tensor Strain tensorStiffness matrix

For cubic crystal like YIG (H // 100)

DC response

DC response

Scalar light shift

Vector light shift (anti-symmetric tensor)

Tensor light shift (symmetric tensor)

One-magnon processes

One-magnon process

Scalar light shift

Vector light shift (anti-symmetric tensor)

Tensor light shift (symmetric tensor)

one-magnon processes

Stokes scatteringAnti-Stokes scattering

magnon

photon photon

magnon

photon photon

Cavity optomagnonics

J.A. Haigh et al., PRL 117, 133602 (2016)A. Osada et al., PRL 120, 133602 (2018)

X. Zhang et al., PRL 117, 123605 (2016)

Two-magnon processes

Two-magnon process

Scalar part

Vector part (anti-symmetric)

Tensor part (symmetric)

Two-magnon processes

magnon

photon photon

magnon

photon photon

magnon

magnon

magnon

photon photon

magnon

photon photon

magnon

magnon

What is it good for?

Magnon BEC

S.O. Demokritov et al., Nature 443, 430 (2006)

Magnon BEC

D.A. Bozhko et al., Nature Physics 12, 1057 (2016)

magnon

magnonmagnon

magnon

Magnon BEC

D.A. Bozhko et al., Nature Physics 12, 1057 (2016)

magnon

photon photon

magnon

Who have ever observed it?

P.A. Fleury et al., Phys. Rev. Lett. 17, 84 (1966)

Antiferromagnet

P.A. Fleury et al., Phys. Rev. Lett. 17, 84 (1966)

Optical magnon dispersion

One-magnon scattering

1.6 THz

P.A. Fleury et al., Phys. Rev. Lett. 17, 84 (1966)

Optical magnon dispersion

Two-magnon scattering

2.3 THz

What about ferromagnets?

One-magnon scattering

B field

y

x

z

PBSmagnetization

Fast photodiode

t

Voltage signal

YIG sphere

Laser: 1550 nm Driving B field

Two-magnon scattering

B field

PBSmagnetization

Fast photodiode

t

Voltage signal

YIG

Laser: 1550 nm

Driving B field

QWP

QWP

Sideband separation

Local oscillator

2 Kittel magnon scattering (100 // H)

2 Kittel magnon scattering (100 // H)

magnon

photon photon

magnon

photon photon

magnon

magnon

Two-magnon scattering

5 GHz

5 GHz

Two-magnon scattering

5 GHz

5 GHz

2-Kittel magnon scattering (111 // H)

Tensor light shift (Cotton-Mouton effect)

For cubic crystal like YIG (H // 100)

Tensor light shift (Cotton-Mouton effect)

Isotropic

Magnon-mode transfer

Dynamic Cotton-Mouton effect

B field

PBSmagnetization

Fast photodiode

t

Voltage signal

YIG

Laser: 1550 nm

Driving B field

QWP

QWP

(220)-magnons (110)-magnons

(220)-magnons (110)-magnons

(220)-magnon

photon photon

(220)-magnon

photon photon

(110)-magnon

(110)-magnon

Two-magnon scattering

(220)-magnon

photon photon

(110)-magnon

(220)-magnon (110)-magnon

Team

R. Hisatomi

Y. Nakamura Y. Tabuchi

S. Ishino

D. Lachance-Quirion

How large?

Look at one-magnon process again

“Intrinsic” sideband asymmetry

One-magnon process

Scalar part

Vector part (anti-symmetric)

Tensor part (symmetric)

Saturation magnetization

Two-magnon process

magnetization due to magnon