Cavity Optomagnonics Silvia Viola Kusminskiy
optical fiber classical technologies
quantum technologies superconducting quantum circuit state preparation • info processing • communication • Martinis group UCSB and Google (2015) optical fiber classical technologies
quantum technologies superconducting quantum circuit state preparation • info processing • communication • need hybrid Martinis group UCSB and Google (2015) systems optical fiber classical technologies
Hybrid Systems for Quantum Technologies photonic crystal optomechanics nano/micro scale systems Safavi-Naeini et al, PRL 2012 (Caltech) microwave optomechanics electromechanics Benyamini et al, Nature Physics 10, 151 (2014) optomagnonics Teufel et al, Nature 2011 (NIST) use collective excitations Osada et. al PRL 116, 223601 (2016)
Optomagnonics quantum photons optics solid magnons state Picture form Tabuchi et al, PRL 113, 083603 (2014)
Magnons and the Kittel mode Microwave regime Optomagnonics Optically induced spin dynamics Outlook and Summary
Magnons and the Kittel mode Microwave regime Optomagnonics Optically induced spin dynamics Outlook and Summary
Magnonics magnon elementary magnetic excitation (quantum of spin wave)
Magnonics magnon elementary magnetic excitation (quantum of spin wave) Robust Low Power Tunable
Magnonics Kittel mode homogeneous magnetic mode M ( r ) = M spin wave with k=0
Magnonics Kittel mode macrospin Ω ∝ H homogeneous tunable precession frequency magnetic mode M ( r ) = M Ω ∼ GHz for 30mT spin wave with k = 0
Landau-Lifschitz-Gilbert Equation Dynamics of the macrospin damping constant η G ⇣ ⌘ S = − Ω e z × S + η G ˙ ˙ S × S S S phenomenological damping term (Gilbert damping) Ω ∝ H precession frequency
Magnons and the Kittel mode Microwave regime Optomagnonics Optically induced spin dynamics Outlook and Summary
Microwave Regime Magnons Microwaves Strong coupling demonstrated in 2014 (a) 1 mm Tabuchi et. al PRL 113, 083603 Zhang et. al PRL 113, 156401 • • (Nakamura’s group, Tokyo) (Hong Tang’s group, Yale)
YIG YIG Yttrium Iron Garnet Y 3 Fe 5 O 12 • ferrimagnetic • insulator • transparent in the infrared Picture form Tabuchi et al, PRL 113, 083603 (2014)
Microwave Regime Magnons Microwaves Strong coupling demonstrated in 2014 0.3 (a) (a) 10.7 frequency (GHz) Kittel mode Kittel mode Frequency (GHz) 0.2 10.6 Cavity mode MW Mode 0.1 10.5 10.4 0.0 -4 -3 -2 -1 0 1 2 3 4 Magnetic field Current I (mA) 1 mm Tabuchi et. al PRL 113, 083603 Zhang et. al PRL 113, 156401 • • (Nakamura’s group, Tokyo) (Hong Tang’s group, Yale)
Microwave Regime Magnons Microwaves Strong coupling demonstrated in 2014 0.3 Resonant (a) (a) 10.7 frequency (GHz) coupling Kittel mode Kittel mode Frequency (GHz) 0.2 10.6 a † ˆ a + ˆ S + ˆ S − ˆ Cavity mode MW Mode 0.1 10.5 ˆ ˆ S a 10.4 ∼ 50MHz 0.0 -4 -3 -2 -1 0 1 2 3 4 Magnetic field Current I (mA) Cooperativity 1 mm C = 3 × 10 3 Tabuchi et. al PRL 113, 083603 Zhang et. al PRL 113, 156401 • • (Nakamura’s group, Tokyo) (Hong Tang’s group, Yale)
Microwave Regime Magnons Microwaves QUANTUM INFORMATION (Science 2015) YIG 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 Nakamura 1,2 SC Qubit MW Cavity
Coupling to Optics? light MW magnon process communicate THz GHz information information wavelenght converter Motivation: magnon as a transducer
Magnons and the Kittel mode Microwave regime Optomagnonics Optically induced spin dynamics Outlook and Summary
Faraday Effect (1846) polarizer u n material p o l a r i no light z e d t h l g i g i l h d t e z i r a l o p Glass Oil Lamp
Faraday Effect (1846) polarizer S N θ F L L Faraday rotation Glass Oil Lamp
Faraday Effect (1846) polarizer S N θ F L L Faraday rotation Glass Oil Lamp Phil. Trans. R. Soc. Lond. 1846 136 , 1-20 Before Maxwell equations (1860)!
Optomagnonic Hamiltonian optical Faraday spin density rotation r ε d r M ( r ) Z · ε 0 ¯ U MO = θ F 2 i ω [ E ∗ ( r ) × E ( r )] ε 0 M s magnetization density
Optomagnonic Hamiltonian r ε d r M ( r ) Z · ε 0 ¯ U MO = θ F 2 i ω [ E ∗ ( r ) × E ( r )] ε 0 M s a † ˆ ˆ ˆ S a Quantize:
Optomagnonic Hamiltonian r ε d r M ( r ) Z · ε 0 ¯ U MO = θ F 2 i ω [ E ∗ ( r ) × E ( r )] ε 0 M s a † ˆ ˆ ˆ S a Quantize: two-photon process
Optomagnonic Hamiltonian r ε d r M ( r ) Z · ε 0 ¯ U MO = θ F 2 i ω [ E ∗ ( r ) × E ( r )] ε 0 M s a † ˆ ˆ ˆ S a Quantize: two-photon process Bloch sphere Kittel mode ˆ S M ( r ) = M Ω ∝ H
Optomagnonic Hamiltonian Microscopic Hamiltonian S j G j a † Parametric X ˆ ˆ H MO = ~ a γ βγ ˆ β ˆ coupling j βγ ˆ S G ˆ a S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Optomagnonic Hamiltonian Microscopic Hamiltonian S j G j a † Parametric X ˆ ˆ H MO = ~ a γ βγ ˆ β ˆ coupling j βγ ˆ S Optomagnonic coupling G βγ = − i " 0 f M s Z − i θ F λ ε 0 ε G j d r E ∗ β m ( r ) E γ n ( r ) ˆ ✏ jmn a 4 ~ S 2 π ~ S 2 S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Optomagnonic Hamiltonian Microscopic Hamiltonian S j G j a † Parametric X ˆ ˆ H MO = ~ a γ βγ ˆ β ˆ coupling j βγ ˆ S Optomagnonic coupling G βγ = − i " 0 f M s Z − i θ F λ ε 0 ε G j d r E ∗ β m ( r ) E γ n ( r ) ˆ ✏ jmn a 4 ~ S 2 π ~ S 2 overlap electric field mode functions S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Optomagnonic Hamiltonian Microscopic Hamiltonian S j G j a † Parametric X ˆ ˆ H MO = ~ a γ βγ ˆ β ˆ coupling j βγ ˆ S Optomagnonic coupling G βγ = − i " 0 f M s Z − i θ F λ ε 0 ε G j d r E ∗ β m ( r ) E γ n ( r ) ˆ ✏ jmn a 4 ~ S 2 π ~ S 2 Faraday rotation S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Optomagnonic Hamiltonian Microscopic Hamiltonian S j G j a † Parametric X ˆ ˆ H MO = ~ a γ βγ ˆ β ˆ coupling j βγ ˆ S Optomagnonic coupling G βγ = − i " 0 f M s Z − i θ F λ ε 0 ε G j d r E ∗ β m ( r ) E γ n ( r ) ˆ ✏ jmn a 4 ~ S 2 π ~ S 2 number of spins S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Cavity Optomagnonics Magnons Optical photons Coupling demonstrated in 2016
Cavity Optomagnonics Magnons Optical photons Coupling demonstrated in 2016 in optical fiber out H magnetic YIG field Whispering Gallery Modes A cavity enhances the effect Osada et. al PRL 116, 223601 • (Nakamura’s group, Tokyo) Haigh et. al PRL 117, 133602 Zhang et. al PRL 117, 123605 • • (Ferguson’s group, Cambridge) (Hong Tang’s group, Yale)
Cavity Optomagnonics Magnons Optical photons Beat signal [arb. u.] Port 1 Port 2 l a n g i S Osada et. al PRL 116, 223601 • Sidebands at the magnon frequency (Nakamura’s group, Tokyo)
Magnons and the Kittel mode Microwave regime Optomagnonics Optically induced spin dynamics Outlook and Summary
Cavity Optomagnonics: 1 optical mode Coupling optical mode (a) S j G j a † X ˆ ˆ H MO = ~ a γ βγ ˆ β ˆ j βγ z acquires a simple form x y Ω Kittel mode (b) Ω ˆ a S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Cavity Optomagnonics: 1 optical mode optical mode (a) Total Hamiltonian for one optical mode a † ˆ a − ~ Ω ˆ S z + ~ G ˆ a † ˆ H = − ~ ∆ ˆ S x ˆ a z ∆ = ω las − ω cav driving laser detuning x y Ω Kittel mode (b) Ω ˆ a S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Cavity Optomagnonics optical mode (a) Total Hamiltonian for one optical mode a † ˆ a − ~ Ω ˆ S z + ~ G ˆ a † ˆ H = − ~ ∆ ˆ S x ˆ a z ∆ = ω las − ω cav driving laser detuning x y Ω Kittel mode (b) Ω ˆ a c θ F G = 1 YIG 4 √ εξ (1 µm ) 3 G ≈ 1Hz S mode overlap factor S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
Cavity Optomagnonics optical mode (a) Total Hamiltonian for one optical mode a † ˆ a − ~ Ω ˆ S z + ~ G ˆ a † ˆ H = − ~ ∆ ˆ S x ˆ a z ∆ = ω las − ω cav driving laser detuning x y Ω Kittel mode (b) Ω ˆ a c θ F G = 1 YIG 4 √ εξ (1 µm ) 3 G ≈ 1Hz S mode overlap factor Optical magnetic field density 10 − 11 T b opt ∼ photon / ( µ m) 3
Cavity Optomagnonics Classical Equation of Motion Cavity decay rate initial light amplitude a = − i ( GS x − ∆ ) a − κ ˙ 2 ( a − α max ) S = ( Ga ∗ a e x − Ω e z ) × S + η G ˙ S ( ˙ S × S ) S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, PRA 94, 033821 (2016)
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