Magnonics in the quantum regime - uni-mainz.de · Microwave cavity. 1mm sphere. H. static. H. ac....
Transcript of Magnonics in the quantum regime - uni-mainz.de · Microwave cavity. 1mm sphere. H. static. H. ac....
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