光 - マグノン - マイクロ波 - 超伝導量子ビットのリンクあるいは量子ピタゴラスイッチ

Transcription

1 光 - マグノン - マイクロ波 - 超伝導量子ビットのリンクあるいは量子ピタゴラスイッチ 東大先端研 宇佐見康二

2 Quantum optics with collective excitations in solid Koji Usami RCAST, the University of Tokyo

3 Wonderful world of quantum optics Cavity QED Atom Photon Ion Trap Ion Phonon Cavity QED with Rydberg atom Rydberg atom Microwave photon H.J. Kimble, Nature 453, 1023 (2008). F. Schmidt-Kaler, et al., Nature 422, 408 (2003). S. Gleyzes, et al., Nature 446, 297 (2007)

4 Nobel Prize in Physics 2012 David J. Wineland Serge Haroche

5 Individual quantum systems charge photon spin atom

6 Collective excitations charge surface plasmon polariton photon photon spin atom magnon phonon

7 Macroscopic quantum systems Superconductivity surface plasmon polariton photon magnon phonon Ferromagnetism Lattice order

8 Collective excitations Spontaneous breaking of symmetry : Nambu-Goldstone bosons Superconductivity surface plasmon polariton photon magnon phonon Ferromagnetism Lattice order

9 Phonons and nano-mechanics

10 Atomic chain Potential: Equation of motion: Coupled equations

11 Continuum limit (a 0) Coupled equation of motion: (1+1)-D boson field equation:

12 Continuum limit (a 0) (1+1)-D boson field equation: Dispersion relation in continuum limit: Sound velocity: Elastic constant Continuum limit Mass density

13 Boundary conditions make the discrete modes Type A (linear dispersion) Type B (quadratic dispersion) Doubly-clamped cantilevers Free-free cantilevers

14 Ferromagnets and magnons

15 Interacting particles Atomistic viewpoint (microscopic) Mechanics (Phonons) Covalent/molecular/ionic bonding Magnets (Magnon) Exchange interaction

16 Interacting particles Atomistic viewpoint (microscopic) Mechanics (Phonons) Covalent/molecular/ionic bonding Magnets (Magnon) Exchange interaction

17 Continuum limit (k 0 limit) Atomistic viewpoint (microscopic) Continuum field viewpoint (macroscopic) Mechanics (Phonons) Magnets (Magnon)

18 Continuum limit (k 0 limit) Atomistic viewpoint (microscopic) Continuum feild viewpoint (macroscopic) Mechanics (Phonons) Magnets (Magnon) Elastic rigidity (elastic constant) Magnetic rigidity

19 that is, Harmonic potential Atomistic viewpoint (microscopic) Continuum feild viewpoint (macroscopic) Mechanics (Phonons) Magnets (Magnon) 1D lumped system (spring) Rigidity neglect equilibrium

20

21 Wonderful world of quantum optics Cavity QED Atom Photon Ion Trap Ion Phonon Cavity QED with Rydberg atom Rydberg atom Microwave photon H.J. Kimble, Nature 453, 1023 (2008). F. Schmidt-Kaler, et al., Nature 422, 408 (2003). S. Gleyzes, et al., Nature 446, 297 (2007)

22 Superconductivity and Josephson atoms

23 Elementary excitation in metals Superconducting state Joyez, Thesis (1995) CEA Saclay

24 Superconducting LC circuit Rydberg atom Microwave photon 中村泰信 日本物理學會誌 57(11), ,

25 Josephson effect (lossless nonlinearity) number n phase difference B. D. Josephson 1962 Cooper-pair tunneling -2e Eel n E 2E J n= /p Tight-binding model in 1d lattice Bloch band

26 energy Superconducting qubits artificial atoms in electrical circuit small large Charge qubit Flux qubit Phase qubit Josephson energy E J = confinement potential charging energy E C = kinetic energy typical qubit energy typical experimental temperature

27 Superconducting qubits artificial atoms in electrical circuit 中村泰信 日本物理學會誌 57(11), ,

28 Advances of superconducting qubits Artificial quantum system in electrical circuits Strong coupling with microwave Design flexibility, integrability Improved coherence time R. Barends et al. Nature (2014) UCSB Courtesy of S. Kono Courtesy of W. Oliver and P. Welander (MIT-LL)

29 Quantum transducers

30 Linking superconducting qubits Superconducting Qubit Quantum circuits Dilution fridge (10mK) X Quantum optics R. Barends et al. Nature (2014). Optical photons (~200THz) H.J. Kimble, Nature 453, 1023 (2008).

31 Linking single-atom qubits D.L.Moehring, et al., Nature 449, 68 (2007).

32 Quantum transducer for linking single-atom qubits Spin-orbit interaction Electric-dipole interaction Hyperfine interaction Nuclear spin (n) Hyperfine interaction Electron spin (s) Spin-orbit coupling Orbital (l) Electric-dipole interaction light D.L.Moehring, et al., Nature 449, 68 (2007).

33 Quantum transducer architecture Superconducting Qubit circuit QED Phonons nano mechanics Microwave photon collectively-enhanced coupling ferromagnets Magnons Superconducting qubit circuit QED Microwave collectively-enhanced coupling Magnon/phonon collectively-enhanced coupling light collectively-enhanced coupling Optical photons

34 Circuit QED

35 Number of modes Purcell enhancement Fabry-Perot cavity Free space Angular frequency

36 Jaynes-Cummings Hamiltonian Einstein Hamiltonian Fermi s golden rule Jaynes-Cummings Hamiltonian Rabi oscillation

37 QED systems Cavity QED Atom Photon Ion Trap Ion Phonon Cavity QED with Rydberg atom Rydberg atom Microwave photon H.J. Kimble, Nature 453, 1023 (2008). F. Schmidt-Kaler, et al., Nature 422, 408 (2003). S. Gleyzes, et al., Nature 446, 297 (2007)

38 Variants of cavity QED systems Cavity QED Atom Photon Cavity QED with Rydberg atom Rydberg atom Microwave photon Superconducting Circuit Artificial atom Microwave photon H.J. Kimble, Nature 453, 1023 (2008). S. Gleyzes, et al., Nature 446, 297 (2007) R. J. Schoelkopf and S. M. Girvin, Nature 451, 664 (2008).

39 Circuit QED Superconducting Circuit Artificial atom Microwave photon Fundamental limit of the coupling strength: for cavity volume of R. J. Schoelkopf and S. M. Girvin, Nature 451, 664 (2008).

40 Collectively-enhanced coupling

41 Angular Momentum addition Young s Tableau = S=1/2 S=1/2 S=1 S=0 = 3 state 1 state Triplet (totally symmetric) Singlet (totally anti-symmetirc)

42 S=1, m=1 S=0, m=0 S=1, m=0 S=1, m=-1

43 Permutation Symmetry - in case of 4 spin-1/2 particles - S=1/2 S=1/2 S=1/2 S=1/2 = 5 state 3 state 3 state 3 state 1 state 1 state S=2 S=1 S=0 m = 2 m = 1 m = 0 m = -1 m = -2 (totally symmetric) degeneracy 3 degeneracy 2 Bosonic symmetry

44 2, 2 m S ) ( 2 1 1, 2 m S ) ( 6 1 0, 2 m S ) ( 2 1 1, 2 m S 2, 2 m S (CSS) (Dicke, W) (Dicke, W) (CSS) (Super-radiant) Second Quantization of Spin

45 Collective enhancement J N N, m N N N J, m 1 J, m N/2 N/2-1 0 N 2 N 2 0 N J ˆ aˆ aˆ N 1 N 1 J ˆ aˆ aˆ N 0 N J ˆ aˆ aˆ 1 N 1 N 2 N ( 2 N N 1) Collective enhancement Superradiance

46 Cavity QED and collective enhancement Cavity QED Rydberg atom Collective enhancement Coherent coupling rate Single-atom decay rate Micro cavity Cavity decay rate Cooperativity (SNR)

47 Magnon transducer architecture Superconducting Qubit circuit QED Microwave photon collectively-enhanced coupling ferromagnets Magnons Superconducting qubit circuit QED Microwave collectively-enhanced coupling Magnon collectively-enhanced coupling light collectively-enhanced coupling Optical photons

48 Paramagnetic spin ensemble quantum transducers Circuit QED Collective enhancement where single-spin coupling strength: A. Imamoglu, Phys. Rev. Lett. 102, (2009).

49 Experiments

50 Superconducting qubit- magnon coupling SUPERCONDUCTING QUBIT(TRANSMON) FERROMAGNET CRYSTAL

51 Coupling superconducting qubit with magnon

52 Magnon Qubit Excitation Energy Magnon cavity - qubit hybrid system Magnon-qubit coupling mediated by cavity ω r g m ω FMR g eff g q ω q Effective coupling Ground state

53 Readout Energy Magnon Vacuum Rabi Splitting 2g/2π = 22.7 MHz ω r Qubit g m g q ω q ω FMR Ground state = Magnetic field (applied locally to YIG sphere)

54 SUMMARY 1 - Strong magnon-photon coupling - Strong magnon-qubit coupling - Tunable coupling by parametric driving - Time-domain control & reaout magnons - Non-classical magnon control - Magnon-state tomography - Coupling to light

55 Magnon-light coupling

56 Collective enhancements Microwave photon (Resonant) collective enhancement where single-spin coupling strength: ferromagnets Raman collective enhancement (DLCZ) Optical photons A. Imamoglu, Phys. Rev. Lett. 102, (2009).

57 Collective enhancements Microwave photon (Resonant) collective enhancement where single-spin coupling strength: ferromagnets Raman collective enhancement (DLCZ) Optical photons A. Imamoglu, Phys. Rev. Lett. 102, (2009); L.-M. Duan et al., Nature 414, 413 (2001).

58 Light-magnon coupling scheme Faraday interaction: Collective spin operator Stokes operator Evolution of Stokes operator: (Faraday rotation) Light Ferromagnetic magnon Microwave cavity mode 1-D Transmission line

59 Light-magnon coupling scheme N Laser S Light Faraday interaction Ferromagnetic magnon Microwave cavity mode 1-D Transmission line

60 Sideband appear at normal mode frequencies

61 Magnon-cavity coupling probed by light Microwave cavity mode Magnon

62 Microwave-light transducer Strong coupling Ferromagnetic magnon Microwave cavity mode 1-D Transmission line

63 Microwave-light transducer Strong coupling Light Ferromagnetic magnon Microwave cavity mode 1-D Transmission line

64 SUMMARY 2 S. C. qubit Realization of strong coupling magnon and M.W. Observation of the coupling system using light Realization of coherent m.w. generation using light Microwave Ferromagnetic magnon Light

65 Why microwave? Small dissipation (superconductivity) Strong nonlinearity (Josephson effect) Strong confinement (ultra-small mode volume)

66 Why collective excitations? Large dimensions Easy mode-matching Collectively-enhanced coupling

67 Overview of Research activities Superconducting Qubit Microwave photon Y. Nakamura Y. Tabuchi Mechanics Phonons nano mechanics ferromagnets Spin Magnons Sir. Ishino Optics A. Noguchi R. Yamazaki K. Sato Optical photons R. Hisatomi

68 Overview of Research activities Optomechanics-NMR Cavity cooling of magnon Waseda Iwase lab UEC Hakuta lab M. Okada Kyoto Takeda lab A. Osada Tokyo Nomura lab

69 Thank you!

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