Cavity Optomagnonics Silvia Viola Kusminskiy optical fiber - - PowerPoint PPT Presentation

Cavity Optomagnonics

Silvia Viola Kusminskiy

classical technologies

• ptical fiber

quantum technologies

superconducting quantum circuit Martinis group UCSB and Google (2015)

classical technologies

• ptical fiber
• state preparation
• info processing
• communication

quantum technologies

superconducting quantum circuit Martinis group UCSB and Google (2015)

classical technologies

• ptical fiber
• state preparation
• info processing
• communication

need hybrid systems

Hybrid Systems for Quantum Technologies

photonic crystal optomechanics

Safavi-Naeini et al, PRL 2012 (Caltech)

microwave optomechanics

Teufel et al, Nature 2011 (NIST)

Benyamini et al, Nature Physics 10, 151 (2014)

electromechanics nano/micro scale systems

• ptomagnonics

Osada et. al PRL 116, 223601 (2016)

use collective excitations

Picture form Tabuchi et al, PRL 113, 083603 (2014)

photons magnons

solid state quantum

• ptics

Optomagnonics

Microwave regime Optomagnonics Outlook and Summary Optically induced spin dynamics Magnons and the Kittel mode

Microwave regime Optomagnonics Outlook and Summary Optically induced spin dynamics Magnons and the Kittel mode

magnon

elementary magnetic excitation (quantum of spin wave) Magnonics

magnon

elementary magnetic excitation (quantum of spin wave) Magnonics Robust Tunable Low Power

Kittel mode

homogeneous magnetic mode M(r) = M

spin wave with k=0 Magnonics

Kittel mode

homogeneous magnetic mode M(r) = M

Ω ∝ H

tunable precession frequency

Ω ∼ GHz for 30mT macrospin

Magnonics spin wave with k = 0

Dynamics of the macrospin

Ω ∝ H

S ˙ S = −Ωez × S + ηG S ⇣ ˙ S × S ⌘ ηG

phenomenological damping term (Gilbert damping) damping constant precession frequency

Landau-Lifschitz-Gilbert Equation

Optomagnonics Outlook and Summary Optically induced spin dynamics Microwave regime Magnons and the Kittel mode

Microwaves Magnons

Strong coupling demonstrated in 2014

• Tabuchi et. al PRL 113, 083603

(Nakamura’s group, Tokyo)

• Zhang et. al PRL 113, 156401

(Hong Tang’s group, Yale)

(a)

1 mm

Microwave Regime

Picture form Tabuchi et al, PRL 113, 083603 (2014)

YIG

Yttrium Iron Garnet

Y3 Fe5 O12

• ferrimagnetic
• insulator
• transparent in the infrared

YIG

Microwaves Magnons

Strong coupling demonstrated in 2014

• Tabuchi et. al PRL 113, 083603

(Nakamura’s group, Tokyo)

• Zhang et. al PRL 113, 156401

(Hong Tang’s group, Yale)

(a)

1 mm

Current I (mA) Frequency (GHz) 0.0 0.1 0.2 0.3

• 4
• 3
• 2
• 1

1 2 3 4 10.4 10.5 10.6 10.7 Cavity mode Kittel mode (a)

frequency (GHz) Magnetic field

MW Mode Kittel mode

Microwave Regime

Microwaves Magnons

Strong coupling demonstrated in 2014

• Tabuchi et. al PRL 113, 083603

(Nakamura’s group, Tokyo)

• Zhang et. al PRL 113, 156401

(Hong Tang’s group, Yale)

(a)

1 mm

Current I (mA) Frequency (GHz) 0.0 0.1 0.2 0.3

• 4
• 3
• 2
• 1

1 2 3 4 10.4 10.5 10.6 10.7 Cavity mode Kittel mode (a)

frequency (GHz) Magnetic field

MW Mode Kittel mode

Resonant coupling ˆ S+ˆ a + ˆ S−ˆ a† ˆ a ˆ S

∼ 50MHz

Cooperativity

C = 3 × 103 Microwave Regime

QUANTUM INFORMATION

Coherent coupling between a ferromagnetic magnon and a superconducting qubit

Yutaka Tabuchi,1* Seiichiro Ishino,1 Atsushi Noguchi,1 Toyofumi Ishikawa,1 Rekishu Yamazaki,1 Koji Usami,1 Yasunobu Nakamura1,2

(Science 2015)

YIG SC Qubit MW Cavity

Microwaves Magnons Microwave Regime

light

magnon

MW

GHz THz Motivation: magnon as a transducer wavelenght converter process information communicate information Coupling to Optics?

Optomagnonics Outlook and Summary Optically induced spin dynamics Microwave regime Magnons and the Kittel mode

Oil Lamp Glass

polarizer

no light material p

• l

a r i z e d l i g h t u n p

• l

a r i z e d l i g h t

Faraday Effect (1846)

Glass

N S

polarizer

θFL

Faraday rotation

L

Oil Lamp

Faraday Effect (1846)

Before Maxwell equations (1860)!

Glass

N S

polarizer

θFL

Faraday rotation

L

• Phil. Trans. R. Soc. Lond. 1846 136, 1-20

Oil Lamp

Faraday Effect (1846)

¯ UMO = θF r ε ε0 Z dr M(r) Ms · ε0 2iω [E∗(r) × E(r)] Optomagnonic Hamiltonian

• ptical

spin density magnetization density

Faraday rotation

¯ UMO = θF r ε ε0 Z dr M(r) Ms · ε0 2iω [E∗(r) × E(r)]

Quantize:

ˆ a

ˆ S

ˆ a† Optomagnonic Hamiltonian

¯ UMO = θF r ε ε0 Z dr M(r) Ms · ε0 2iω [E∗(r) × E(r)]

Quantize:

ˆ a

ˆ S

ˆ a† Optomagnonic Hamiltonian

two-photon process

¯ UMO = θF r ε ε0 Z dr M(r) Ms · ε0 2iω [E∗(r) × E(r)]

Quantize:

ˆ a

ˆ S

ˆ a† Optomagnonic Hamiltonian

two-photon process

Kittel mode

Ω ∝ H

Bloch sphere

ˆ S

M(r) = M

ˆ HMO = ~ X

jβγ

ˆ SjGj

βγˆ

a†

βˆ

aγ

Optomagnonic Hamiltonian Microscopic Hamiltonian

ˆ S ˆ a G

Parametric coupling

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

ˆ HMO = ~ X

jβγ

ˆ SjGj

βγˆ

a†

βˆ

aγ

Gj

βγ = −i"0f Ms

4~S ✏jmn Z drE∗

βm(r)Eγn(r)

−i θFλ 2π~S ε0ε 2

Optomagnonic Hamiltonian Microscopic Hamiltonian Optomagnonic coupling

ˆ S ˆ a G

Parametric coupling

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

ˆ HMO = ~ X

jβγ

ˆ SjGj

βγˆ

a†

βˆ

aγ

Gj

βγ = −i"0f Ms

4~S ✏jmn Z drE∗

βm(r)Eγn(r)

−i θFλ 2π~S ε0ε 2

Optomagnonic Hamiltonian Microscopic Hamiltonian Optomagnonic coupling

ˆ S ˆ a G

Parametric coupling

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
• verlap electric field

mode functions

ˆ HMO = ~ X

jβγ

ˆ SjGj

βγˆ

a†

βˆ

aγ

Gj

βγ = −i"0f Ms

4~S ✏jmn Z drE∗

βm(r)Eγn(r)

−i θFλ 2π~S ε0ε 2

Optomagnonic Hamiltonian Microscopic Hamiltonian Optomagnonic coupling

ˆ S ˆ a G

Parametric coupling

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

Faraday rotation

ˆ HMO = ~ X

jβγ

ˆ SjGj

βγˆ

a†

βˆ

aγ

Gj

βγ = −i"0f Ms

4~S ✏jmn Z drE∗

βm(r)Eγn(r)

−i θFλ 2π~S ε0ε 2

Optomagnonic Hamiltonian Microscopic Hamiltonian Optomagnonic coupling

ˆ S ˆ a G

Parametric coupling

number of spins

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

Magnons

Optical photons Coupling demonstrated in 2016

Cavity Optomagnonics

Magnons

Optical photons Coupling demonstrated in 2016

• Osada et. al PRL 116, 223601

(Nakamura’s group, Tokyo)

• Zhang et. al PRL 117, 123605

(Hong Tang’s group, Yale)

• Haigh et. al PRL 117, 133602

(Ferguson’s group, Cambridge)

Cavity Optomagnonics

in

• ptical fiber

magnetic field Whispering Gallery Modes YIG

• ut

H

A cavity enhances the effect

Magnons

Optical photons

• Osada et. al PRL 116, 223601

(Nakamura’s group, Tokyo)

Cavity Optomagnonics

Port 1 Port 2 Beat signal [arb. u.]

S i g n a l

Sidebands at the magnon frequency

Optomagnonics Outlook and Summary Optically induced spin dynamics Microwave regime Magnons and the Kittel mode

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

Ω

y z x

• ptical mode

ˆ a

(a) (b)

Kittel mode

Ω Cavity Optomagnonics: 1 optical mode

ˆ HMO = ~ X

jβγ

ˆ SjGj

βγˆ

a†

βˆ

aγ

acquires a simple form Coupling

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

H = −~∆ˆ a†ˆ a − ~Ω ˆ Sz + ~G ˆ Sxˆ a†ˆ a

∆ = ωlas − ωcav

driving laser detuning

Total Hamiltonian for one optical mode

Ω

y z x

• ptical mode

ˆ a

(a) (b)

Kittel mode

Ω Cavity Optomagnonics: 1 optical mode

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

H = −~∆ˆ a†ˆ a − ~Ω ˆ Sz + ~G ˆ Sxˆ a†ˆ a

∆ = ωlas − ωcav

driving laser detuning

Total Hamiltonian for one optical mode

Ω

y z x

• ptical mode

ˆ a

(a) (b)

Kittel mode

Ω Cavity Optomagnonics G = 1 S c θF 4√εξ

mode overlap factor

(1µm)3

YIG

G ≈ 1Hz

H = −~∆ˆ a†ˆ a − ~Ω ˆ Sz + ~G ˆ Sxˆ a†ˆ a

∆ = ωlas − ωcav

driving laser detuning

Total Hamiltonian for one optical mode

Ω

y z x

• ptical mode

ˆ a

(a) (b)

Kittel mode

Ω Cavity Optomagnonics G = 1 S c θF 4√εξ

mode overlap factor

(1µm)3

YIG

G ≈ 1Hz

bopt ∼ 10−11T photon/(µm)3

Optical magnetic field density

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

˙ a = −i (GSx − ∆) a − κ 2 (a − αmax) ˙ S = (Ga∗a ex − Ω ez) × S + ηG S ( ˙ S × S)

Cavity decay rate initial light amplitude

Classical Equation of Motion Cavity Optomagnonics

˙ S = Beff × S + ηopt S ⇣ ˙ Sx ex × S ⌘

κ Ω Effective equation of motion for S:

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

integrate out the light field

Fast Cavity Limit

Bopt = G [( κ

2 )2 + (∆ − GSx)2]

⇣κ 2 αmax ⌘2 ex

˙ S = Beff × S + ηopt S ⇣ ˙ Sx ex × S ⌘

Beff = −Ωez + Bopt

effective field κ Ω Effective equation of motion for S:

• ptically induced
• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

integrate out the light field tunable by the external laser drive

Fast Cavity Limit

Bopt = G [( κ

2 )2 + (∆ − GSx)2]

⇣κ 2 αmax ⌘2 ex

˙ S = Beff × S + ηopt S ⇣ ˙ Sx ex × S ⌘

Beff = −Ωez + Bopt

effective field damping can change sign κ Ω Effective equation of motion for S:

2

− ⇣ ⌘ ηopt = −2GκS |Bopt| (∆ − GSx) [( κ

2 )2 + (∆ − GSx)2]2

• ptically induced
• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

integrate out the light field tunable by the external laser drive

Fast Cavity Limit

∆ = Ω , GS/Ω = 2 , κ/Ω = 5

ηopt ηopt

magnetic switching self-sustained

• scillations

Gα2

max/Ω = 0.6

Gα2

max/Ω = 0.8

Increasing light intensity

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

Fast Cavity Limit: Spin Dynamics

ηopt

magnetic switching

Fast Cavity Limit: Spin Dynamics

See experimental realization with cold atoms, Dan M. Stamper-Kurn Group

• Phys. Rev. Lett. 118, 063604

(2017)

(a) (b)

spin projection GSz/Ω chaos limit cycle period doubling coexistence

1.0

laser amplitude

• G|αmax|2/Ω

2 1

• 1
• 2

1.5

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

Full Nonlinear Dynamics

»Coherent

• ptical control

»Magnetic switching »Self-sustained

• scillations

»Optically induced route to chaos

spin projection GSz/Ω chaos limit cycle period doubling coexistence

1.0

laser amplitude

• G|αmax|2/Ω

2 1

• 1
• 2

1.5

Full Nonlinear Dynamics

• Florian Marquardt (Erlangen)
• Hong Tang (Yale)

Collaborators

Optomagnonics Outlook and Summary Optically induced spin dynamics Microwave regime Magnons and the Kittel mode

the state of the art optomagnonic coupling is too small Problem Outlook g ≈ 60 Hz C ≈ 10−7

Coupling per photon Cooperativity

ˆ S ˆ a

• S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)

Cavity Optomagnonics

(1µm)3

YIG

same form as the optomechanical Hamiltonian for small oscillations: spin harmonic oscillator

~G ˆ Sxˆ a†ˆ a ≈ ~G p S/2ˆ a†ˆ a(ˆ b + ˆ b†)

g0 = G p S/2 ≈ 0.1MHz

coupling per magnon

the state of the art optomagnonic coupling is too small Problem Outlook g ≈ 60 Hz C ≈ 10−7

Coupling per photon Cooperativity

Some solutions smaller systems better overlap of modes

(1µm)3

YIG

?

ˆ S ˆ a

Outlook smaller systems Magnetic textures Vortex in a micro disk

Outlook smaller systems better overlap of modes Vortex in a micro disk Magnetic textures

• ptical mode

mechanical mode Safavi-Naeini et al, PRL 2012 (Caltech)

Optomagnonic crystals?

• ptomechanical crystals

• Hybrid systems for quantum technologies
• Magnetic excitations: robust, designable, quantum
• Cavity optomagnonics: promising new field

Summary

Open positions starting January 2018! Erlangen, Germany New Max Planck Research Group “Theory of hybrid systems for quantum technologies”