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Young Scientist Award in JPS (invited talk)
- 2. 2 Footprints 2011-2014 Two-species atomic BEC @ Inouye lab., UTokyo (currently in Osaka City Univ.) 2014-2017 Cavity optomagnonics @ Nakamura-Usami lab., RCAST, UTokyo 2017-2019 QD + photonic crystal cavity @ Arakawa-Iwamoto lab., IIS, Utokyo 2019- Hybrid quantum systems @ Komaba Institute for Science, UTokyo （先進科学研究機構） Ion trap with vertically integrated cavity @ JST PRESTO ← “Alto Osada”で画像検索すると真っ先に出てくる…
- 3. 3 Indices • Cavity optomagnonics? • Magnon-Brillouin scattering and puzzles • Physics of cavity-optomagnonics system • Cavity optomagnonics and magnetic textures • Summary, acknowledgements and ads
- 4. 4 Optomagnonics T. Satoh et al. Nature Photon. 6, 662 (2012) T. Satoh et al. Nature Photon. 9, 25 (2014) S. O. Demokritov et al. Nature 443, 430 (2006) R. Hisatomi, AO et. al., PRB (2016) Interaction is weak (spin-orbit coupling) Enhancement by an optical cavity Cavity optomagnonics Condensed matter physics Quantum electronics
- 5. 5 Possible applications Y. Tabuchi et. al., Science (2015) SC qubit magnon 10 GHz microwave 200 THz light Microwave-to-optical photon converter I. Zutic and H. Dery Nature Materials 10, 647 Opto-spintronics Chiral photonics I. Sollner et al.,Nature Nanotech. 10, 775
- 6. 6 Al2O3 rod 1 mm Yttrium iron garnet (YIG) sphere Transparent for 1.5 µm light Ferrimagnetic Whispering gallery modes (WGMs) Walker modes A. Gloppe et al,. PRApplied 12, 014061 (2019). magnon-Brillouin scattering
- 7. 7 Indices • Cavity optomagnonics? • Magnon-Brillouin scattering and puzzles • Physics of cavity-optomagnonics system • Cavity optomagnonics and magnetic textures • Summary, acknowledgements and ads
- 8. Whispering gallery mode (WGM) • Resonance: 2𝜋𝑅 ⋅ 𝑛r = 𝑚𝜆 (𝑚 ∈ ℤ) • Geometrical birefringence 𝑓TE 𝑚 < 𝑓TM 𝑚 8 𝑚 − 1 𝑚 𝑚 𝑚 + 1 𝑚 + 1 Red = TM Blue = TE Mode index Frequency Transverse Magnetic Transverse Electric 𝑓TM 𝑚 − 𝑓TE 𝑚
- 9. Observation of WGMs in YIG 9 Q ~ 1×105 YIG sphere (diameter 1mm) Light beam
- 10. 10 Walker mode Magnetic field Kittel mode ( (1,1,0) Walker mode ) (4,3,0) Walker mode
- 11. 11 Walker mode YIG sphere Magnet • Several modes observed • fKittel = 7.42 GHz , QKittel ~ 1600 (7.28 GHz at 0.26 T, expected) Kittel mode (2,0,0) (4,1,1) (2,2,0) (3,3,0)
- 12. 12 Walker mode YIG sphere Magnet • Several modes observed • fKittel = 7.42 GHz , QKittel ~ 1600 (7.28 GHz at 0.26 T, expected) Kittel mode (2,0,0) (4,1,1) (2,2,0) (3,3,0)
- 13. 13 Walker mode YIG sphere Magnet • Several modes observed • fKittel = 7.42 GHz , QKittel ~ 1600 (7.28 GHz at 0.26 T, expected) Kittel mode (2,0,0) (4,1,1) (2,2,0) (3,3,0)
- 14. How to detect magnon-Brillouin scatt.
- 15. How to detect magnon-Brillouin scatt. magnon frequency ~ 7-8 GHz
- 16. How to detect magnon-Brillouin scatt. magnon frequency ~ 7-8 GHz
- 17. How to detect magnon-Brillouin scatt. magnon frequency 𝑓Kittel ~ 7-8 GHz Polarization modulation at 𝑓Kittel
- 18. How to detect magnon-Brillouin scatt. magnon frequency 𝑓Kittel ~ 7-8 GHz Amplitude modulation at 𝑓Kittel
- 19. 19
- 20. 20
- 21. There must be something! K. Usami (superviso r) There can be some difference if we invert WGM circulation! Man…
- 24. x 100 ! 25 Brillouin scattering interchange
- 25. 26 Indices • Cavity optomagnonics? • Magnon-Brillouin scattering and puzzles • Physics of cavity-optomagnonics system • Cavity optomagnonics and magnetic textures • Summary, acknowledgements and ads
- 27. 28 Model |𝑔〉 |𝑒〉 𝑔/𝑒, 𝑛 = |electronic state, number of magnons〉 ~1550 nm
- 28. 29 Model • Single magnon = single-spin flip |𝑔, 𝑛〉 |𝑔, 𝑛 + 1〉 |𝑒, 𝑛〉 |𝑒, 𝑛 + 1〉 |𝑒, 𝑛 − 1〉 |𝑔, 𝑛 − 1〉 𝜎− 𝜎+ 𝜋 𝜋 𝜎+ 𝜎− 𝑔/𝑒, 𝑛 = |electronic state, number of magnons〉 Magnetic field
- 29. 30 Polarizations of WGMs Magnetic field = 𝜋 polarization = 𝜎+ and 𝜎− polarizations Spin-Hall effect of light M. Onoda et al., PRL 93, 083901 (2004). “Rays of the two (transverse) spin components shift” ~ 4 µm
- 30. Spin-Hall effect of light div𝐸 = 𝜕⊥ 𝐸⊥ + 𝜕𝑧 𝐸𝑧 = 0 𝜕⊥ 𝐸⊥ = −𝑖𝑘𝐸𝑧 x 0 ≠ z
- 31. 32 Polarizations of WGMs TE TM (CCW) TM (CW) ±𝑚 𝜋 𝑚 − 1 𝜎− + 𝑚 + 1 𝜎+ −(𝑚 − 1) 𝜎+ + −(𝑚 + 1) 𝜎− CW or CCW Inner component or outer component Spin- and orbital-angular-momentum conservation for…
- 32. 33 Nonreciprocal Brillouin scattering |𝑔, 𝑛〉 |𝑔, 𝑛 + 1〉 |𝑒, 𝑛〉 |𝑒, 𝑛 − 1〉 |𝑔, 𝑛 − 1〉 𝜎− 𝜎+ 𝜋 |𝑔, 𝑛〉 |𝑔, 𝑛 + 1〉 |𝑒, 𝑛〉 |𝑒, 𝑛 − 1〉 |𝑔, 𝑛 − 1〉 𝜎− 𝜎+ 𝜋 CW & inner component almost resonant! Nonreciprocity!
- 33. 34 Resonant enhancement Yoke (iron) Electromagnet Inject the laser Magnon freq. Cavity enhancement ~ x20 compared with R. Hisatomi, AO et al., PRB 93, 174427 (2016).
- 34. 36 Indices • Cavity optomagnonics? • Magnon-Brillouin scattering and puzzles • Physics of cavity-optomagnonics system • Cavity optomagnonics and magnetic textures • Summary, acknowledgements and ads
- 37. 39 Winding numbers 0 2ππ φ φ 0 2ππ φ 0 2ππ OAM 0 1 2
- 38. 40 Nonreciprocal Brillouin scattering 0 2 0 1
- 39. 41 Nonreciprocal Brillouin scattering 0 2 0 1 3𝑔Kittel 12𝑔Kittel2𝑔Kittel𝑔Kittel
- 40. 3𝑔Kittel 12𝑔Kittel2𝑔Kittel𝑔Kittel 42 Nonreciprocal Brillouin scattering 0 2 0 1 Different OAM of magnon reciprocal/non-. Interplay with spin-Hall effect of WGM! [AO et al., PRL 116, 223601 (2016).] [AO et al., PRL 120, 133602 (2018).] [AO et al., NJP 20, 103018 (2018).]
- 41. 43 Indices • Cavity optomagnonics? • Magnon-Brillouin scattering and puzzles • Physics of cavity-optomagnonics system • Cavity optomagnonics and magnetic textures • Summary, acknowledgements and ads • （時間が余ったら）博士取得後の珍事
- 42. 44 Summary • Brillouin scatterings of WGM light by Walker modes were investigated • OAM of magnon and photon result in nontrivial reciprocal/nonreciprocal Brillouin scattering • Cavity enhancement of the Brillouin scattering was examined K. Usami Y. Nakamura Great thanks to all the co-workers!
- 43. 45 Recent activities in Usami’s group Induction tomography of Walker modes A. Gloppe et al., arXiv:1809.09785 • Two-magnon process • “Bizarre” Brillouin scattering - Umklapp process joins - Looks like spin non- conserving! R. Hisatomi et al., arXiv:1905.0401 8 Magnonic crystal S. Baba et al., arXiv:1905.0468 3
- 44. 46 余談 宣伝 東京大学 大学院総合文化研究科 先進科学研究機構 野口研究室 超伝導量子回路による量子光学実験 電子のPaulトラップ イオントラップ実験も始まるかも？ 長田はイオンを使っ たcavity QEDの実験 を粛々と立ち上げ中。
Editor's Notes
- Thank you for the kind introduction and I am grateful to the organizers who invited me o such a celebrated, awesome conference. Here I will talk about the cavity optomagnonics with quasivortices which was one of the topics I dealt with in my PhD study.
- Well we should first note that there are a numerous number of works aiming at controlling spin waves or its quantum, magnon, by electromagnetic waves. By microwave it’s been done from long ago, and current topic is to address or detect magnons by optical means, to access the k-space information held by the magnon. However, it’s quite hard. Quite hard because the light-magnon interaction is inevitably mediated by the spin-orbit interaction of the electron in the material. Our idea was to enhance this inherently weak interaction using the optical cavity. That’s the idea of cavity optomagnonics, which has the same spirit as the cavity optomechanics.
- Well we should first note that there are a numerous number of works aiming at controlling spin waves or its quantum, magnon, by electromagnetic waves. By microwave it’s been done from long ago, and current topic is to address or detect magnons by optical means, to access the k-space information held by the magnon. However, it’s quite hard. Quite hard because the light-magnon interaction is inevitably mediated by the spin-orbit interaction of the electron in the material. Our idea was to enhance this inherently weak interaction using the optical cavity. That’s the idea of cavity optomagnonics, which has the same spirit as the cavity optomechanics.
- The system stimulates us to apply it to the Microwave-to-optical photon converter that can possibly be used to the quantum interface, or some device made up of the combination of spintronic and optical technologies. Another interesting thing is the chiral photonic devices useful for the nanophotonic circuits.
- Okay, then given such an idea, we want nice magneto-optical material that makes it feasible. And in most cavity optomagnonics activities the yttrium iron garnet sphere is adopted. It is ferrimagnetic on one hand to exhibit magnetostatic modes of rich spin textures. On the other hand YIG is highly transparent at telecom wavelength and the sphere supports whispering gallery modes. The light can circulate the periphery to form the optical resonance. Here’s the situation we want. Walker mode magnons can be addressed by the optical resonator!
- ウィスパリングギャラリーモードは光が誘電体の中を全反射しながら周回する共振モードで、共振条件は光路長が波長の整数倍という条件です。偏光に関して二つのモードがあり、電場が軌道面に垂直なTEモードと軌道面内にあるTMモードがあります。そしてこれら二つの偏光モードは試料界面での境界条件の違いにより周波数が異なることが知られています。横軸を周波数に、ウィスパリングギャラリーモードの状態密度を可視化するとこのように、赤のTMと青のTEモードがそれぞれ周期的にあり、二つは周波数がずれています。さて、偏光によりこのように異なるスペクトルが期待されるわけですが、ウィスパリングギャラリーモードの観測はこの球の表面から外側に漏れ出す光に、同じく染み出し光を用いて結合します。
- ともかく、プリズムを用いてYIG球に置けるウィスパリングギャラリーモードを観測しましょう。まず1.5ミクロンのレーザーをプリズムで全反射するように入射させておきます。入射偏光は面内がTM、面直がTEモードに結合するようなものになります。そしてプリズムの表面のどこかで全反射している光の染み出しスポットを、YIG球を動かしながら地道にさがしていきます。ひとたびウィスパリングギャラリーモードが見つかれば、このようにTMモードとTEモードのそれぞれのスペクトルが得られます。このスペクトルから共振の間隔が40.2GHz、そしてTEとTMの周波数の差が32GHzと見積もることができます。理論的には44GHzと39GHzで、少しすれていますが位置関係という点では理論通りになっています。またQ値は、10^5という比較的高い値となることがわかりました。
- Okay, let’s move on to the experiment. We have a YIG sphere of diameter 1mm and the magnons are excited by the microwave through the loop coil. The excited magnons are in this experiment detected by the WGM light injected evanescently through this prism. Since we are interested in creating or annihilating magnons by light, the Brillouin scattering is concerned here, namely the energy and the angular momenta of the magnon should be transferred to or retracted from the WGM. These facts requires the scattered light to possess the frequency shifted by magnon frequency, about 7 GHz, and the polarization rotated. So here we detect the fluctuation of the output light polarization by the fast photodetector to get the sideband signal at 7 GHz. The optical sideband is beaten down to the microwave regime by taking heterodyne signal. In the network analyzer the simplest, uniform magnetostatic mode, the Kittel mode, is observed as the dip in the reflection signal of the loop coil and the Brillouin-scattered light is detected like this yellow signal.
- Okay, let’s move on to the experiment. We have a YIG sphere of diameter 1mm and the magnons are excited by the microwave through the loop coil. The excited magnons are in this experiment detected by the WGM light injected evanescently through this prism. Since we are interested in creating or annihilating magnons by light, the Brillouin scattering is concerned here, namely the energy and the angular momenta of the magnon should be transferred to or retracted from the WGM. These facts requires the scattered light to possess the frequency shifted by magnon frequency, about 7 GHz, and the polarization rotated. So here we detect the fluctuation of the output light polarization by the fast photodetector to get the sideband signal at 7 GHz. The optical sideband is beaten down to the microwave regime by taking heterodyne signal. In the network analyzer the simplest, uniform magnetostatic mode, the Kittel mode, is observed as the dip in the reflection signal of the loop coil and the Brillouin-scattered light is detected like this yellow signal.
- では実際にウィスパリングギャラリーモードの偏光状態がどういうものかについて、まあこういった観点ではほとんど解析されてこなかったんですけれども、私が得た結論について述べます。まずTE偏光は光の軌道面内に垂直に電場が振動するπ偏光です。そしてもう一つ考えたい自由度が軌道角運動量で、モード指数がmのとき、TEモードの軌道角運動量もmであることがわかります。そしてウィスパリングギャラリーモードの宗愛方向によってプラスかマイナスかがきまる。一方TMモードでは印可磁場に垂直な偏光で、一般にはこれはσ+とσ-の重ね合わせになります。ここでウィスパリングギャラリーモードは動径方向に非常に強く局在している効果で、二つのスピン成分が片方は外側に、片方は内側にずれてしまいます。そして速さが同じで半径が大きい外側の成分は軌道角運動量はmより少し大きくなってm+1、内側は少し小さくなってm-1という風になっています。この偏光成分による重心のずれは光のスピンホール効果と呼ばれており、電場が波数ベクトルに直交であれという条件が光のスピン軌道相互作用とみなせるということが知られております。よって例えば反時計回りの時には下向きスピンが外、上向きスピンが内にあり、また時計回りの時には軌道角運動量は全体にマイナスが付くだけなんですけどもスピン部分に関しては反時計回りの時と内と外が入れ替わります。
- では実際にウィスパリングギャラリーモードの偏光状態がどういうものかについて、まあこういった観点ではほとんど解析されてこなかったんですけれども、私が得た結論について述べます。まずTE偏光は光の軌道面内に垂直に電場が振動するπ偏光です。そしてもう一つ考えたい自由度が軌道角運動量で、モード指数がmのとき、TEモードの軌道角運動量もmであることがわかります。そしてウィスパリングギャラリーモードの宗愛方向によってプラスかマイナスかがきまる。一方TMモードでは印可磁場に垂直な偏光で、一般にはこれはσ+とσ-の重ね合わせになります。ここでウィスパリングギャラリーモードは動径方向に非常に強く局在している効果で、二つのスピン成分が片方は外側に、片方は内側にずれてしまいます。そして速さが同じで半径が大きい外側の成分は軌道角運動量はmより少し大きくなってm+1、内側は少し小さくなってm-1という風になっています。この偏光成分による重心のずれは光のスピンホール効果と呼ばれており、電場が波数ベクトルに直交であれという条件が光のスピン軌道相互作用とみなせるということが知られております。よって例えば反時計回りの時には下向きスピンが外、上向きスピンが内にあり、また時計回りの時には軌道角運動量は全体にマイナスが付くだけなんですけどもスピン部分に関しては反時計回りの時と内と外が入れ替わります。
- In the last part I will talk about the effect of the presence of the cavity.
- 磁場を変化させたときに得られた、キッテルモードによるブリルアン散乱の信号がこちらに羅列してあります。下から上に向かって磁場が大きくなっており、磁場が大きくなるにつれて信号が大きくなっています。これは共鳴に近づいている兆候です。そしてある磁場の大きさからは別のモードがキッテルモードを横切ってきて、ファノ的な干渉が見られます。この効果をきちんとフィットしてキッテルモードによる寄与のみを抽出すると、横軸磁場、縦軸ピークの高さでこのようなプロットが得られます。データ店は丸と四角がありますが、これは電磁石だけでは十分な範囲で磁場を変えられなかったために磁石のペアを変えてとったことを示しています。青のローレンチアンはフィットですが、パラメータは高さのみです。位置と太さは入出力のウィスパリングギャラリーモードの周波数差と線幅かを用いました。このプロットから、磁場を振ることによってたしかに共鳴的な兆候が見られました。この振る舞いはCambridgeのグループによっても観測されています。
- What is astonishing is that when the direction of the WGM light is clockwise, indicated by blue, the Brillouin scattering can be observed, however, when counterclockwise, indicated by red, the signal disappears! The phenomenon is nonreciprocal. This is not as usual as simple Faraday effect because the Brillouin scattering is dynamical effect. This nonreciprocity was revealed to be due to the interplay among energy and spin angular momentum conservation, and the spin-orbit coupled nature of the WGM. We do not dive into the great detail in this talk. Let us see further mystery we encountered in the experiment. That is, when you see the higher-order magnons located at the higher frequency, you see the nonreciprocal or reciprocal nature is strongly dependent on those modes.
- Let’s take a look at these magnon modes. The leftmost is the Kittel mode, the uniform mode. And others can be identified by checking their frequencies for variable magnetic fields. These are the transverse magnetization distributions and you can see various textures exhibited by these, for example the 401 mode possesses the spiral texture at some instance. What makes these textures different from each other is resolved by examining the winding number of these vector fields. In order to do so we shall track the transverse magnetization in the vicinity of the perimeter.
- First, the Kittel mode and 311 mode the transverse magnetization points the same direction all along the circumference, therefore the winding number reads 0. For the 401 mode, it is up here, rotates by 180 degree on the other side and goes back. The total amount of rotation is 2pi, which yields the winding number of 1. And for 31bar1 mode, from its pattern we see the magnetization is up here, down here, up, down, up, and rotated all the way by 4pi in total. Thus the winding number is 2. Since such rotations are the spatial variation of the phase, we can interpret them as the orbital angular momenta.
- Okay, then let’s have a look back. Now the orbital angular momenta are assigned to the Walker modes. And we notice that for magnons with vanishing OAM, the clockwise cases are more prominent than the counterclockwise cases. If the magnon have OAM of 1, the Brillouin scattering appears to be reciprocal. If 2, in this case the counterclockwise scattering is superior to the clockwise one. These results are in a quite nice agreement with the theory that take in to account the energy and angular momenta conservation.
- Okay, then let’s have a look back. Now the orbital angular momenta are assigned to the Walker modes. And we notice that for magnons with vanishing OAM, the clockwise cases are more prominent than the counterclockwise cases. If the magnon have OAM of 1, the Brillouin scattering appears to be reciprocal. If 2, in this case the counterclockwise scattering is superior to the clockwise one. These results are in a quite nice agreement with the theory that take in to account the energy and angular momenta conservation.
- Okay, then let’s have a look back. Now the orbital angular momenta are assigned to the Walker modes. And we notice that for magnons with vanishing OAM, the clockwise cases are more prominent than the counterclockwise cases. If the magnon have OAM of 1, the Brillouin scattering appears to be reciprocal. If 2, in this case the counterclockwise scattering is superior to the clockwise one. These results are in a quite nice agreement with the theory that take in to account the energy and angular momenta conservation.