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Hideaki Takayanagi NTT Basic Research Laboratories, NTT Corporation, Japan

Superconducting Flux Qubit as a Macroscopic Artificial Atom. Hideaki Takayanagi NTT Basic Research Laboratories, NTT Corporation, Japan. NTT 物性科学基礎研究所. 髙 柳 英 明. Outline. Quantum Information Research at NTT Fux Qubit Single-Shot Measurement Multi-Photon Absorption Rabi Oscillation

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Hideaki Takayanagi NTT Basic Research Laboratories, NTT Corporation, Japan

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  1. Superconducting Flux Qubit as a Macroscopic Artificial Atom Hideaki Takayanagi NTT Basic Research Laboratories, NTT Corporation, Japan NTT物性科学基礎研究所 髙 柳 英 明 Outline • Quantum Information Research at NTT • Fux Qubit • Single-Shot Measurement • Multi-Photon Absorption • Rabi Oscillation • Conclusions

  2. QIT Project in NTT Basic Research Laboratories Head: H. Takayanagi About 20 researchers participate to the project which consists of five sub-projects. Four qubit-research projects and a quantum cryptography one.

  3. Solid-State Qubits Four Kinds of Qubit Coupled QDs (artificial molecule) Exciton in QDs SQUID Rabi oscillation Single-shot measurement Multi-photon absorption Rabi oscillation Quantum gate operation cooled atom Atom Chip

  4. Bob Testing Alice Counter Photon 0 Detector 3 waveguide 50%-50% Beam Splitter Space filter Half-wavelength ¼ wavelength Titanium-Sapphire Laser Helium Cryostat 電気光学 変調器 Splitter Detector 4 Beam Splitter Mirror Attenuator Beam Splitter Single-mode fiber Grating lens Quantum dot Lens Detector 1 Pin-hole Lens Detector 2 時間間隔 解析器 Amp Gene- rator 時間間隔 解析器 Quantum cryptography with a single photon Nature, 420 (2002) 762

  5. aEJ g = + + = g g g g g g , g1 , g2 , g3 g g g g q 1 1 1 3 1 2 2 2 U U U EJ EJ =1.0 =1.0 =1.0 2f U U U U p - - - - - Josephson Energy : ( 2 a cos ( ) ) EJ + a cos cos = U U U U U j j j m m p =0.8 =0.8 =0.8 =0.8 U 2f p 1 g + g =0.6 =0.6 =0.6 =0.6 j = ( ) 1 g 2 p 2 2 1 j = ( ) g - g m 1 2 2 =0.8 j p Josephson persistent current Qubit J. E. Mooij et al.,Science285, 1036 (1999). Phase difference Fqubit = f F0 B f = Fqubit / F0 f = Fqubit / F0 = 0.5

  6. Schematic qubit energy spectrum D = m = m a = E 1055 eV, E 30 . 44 eV, 0 . 80 J C 15 100 10 5 Energy (GHz) Energy (GHz) 0 0 -5 -10 -100 0.4 0.5 0.6 0.49 0.50 0.51 F F / 0 qubit Fqubit F0 /

  7. EJ ; C 3 • Coupling energy (1 junction): EC = e2/ 2C • Flux quantization: EJ C 1 2 EJ C ext= f0 • Josephson Energy (1 junction): Three-Josephson-junction Loop:Description 0<<1.0 Josephson Energy: J.E. Mooij､et al (1999)

  8. U Three-Josephson-junction Loop:Energy Diagram f=0.5 2 minima in each unit cell. Top View

  9. Three-Josephson-junction Loop: Dependence of the Potential f=0.5 U U U =0.6 =0.8 =1.0 • If  increases, the barrier height : • increases between the two minima of one unit cell • decreases between the minima of adjacent cells

  10. Classical states = persistent currents of opposite sign. Degenerated atf= 0.5 Quantum tunnelling “anti-crossing” Level splitting E0 (1) E <Iq>/Ip /0 Symmetric and antisymmetric superposition of the macroscopic persistent currents Classical states Quantum ground state |0> Quantum first excited state |1> Three-Josephson-junction Loop:Flux Dependence of the States

  11. Sample Fabrication • e-beam lithography • Shadow evaporation • Lift-off Josephson junctions Al / Al2O3 / Al Junction area SQUID : 0.1 x 0.08m2 Qubit : 0.1 x L m2, ( a = 0.8 ) L = 2 ~ 0.2 Loop size SQUID ~ 7 x 7m2 Qubit ~ 5 x 5m2 Mutual inductance M ~ 7 pH Qubit and a detector dc-SQUID NTT Atsugi

  12. e-beam lithography suspended-bridge & shadow evapolation

  13. Sample and Cavity DC measurement NTT Atsugi To mixing chamber Microwave line Thermometer Vm line Ibias line Samples A loop Cavity

  14. DC measurement RF line 1 2 3 4 5 10 nF connectors HP 20dB R.T. 2.4mm connectors 4.2K Through capacitor Flexible coaxial cable HP 10dB 1.2K attenuator 0.8K resistance 0.4K 10mK Heat anchor for outer shield Twisted Constantan wire 100  • No on-chip capacitor and resistor • No on-chip control line • Change twisted wires to thin coaxial cables to introduce dc-pulse 200  200  200  Sample box Loop antenna ~ 1mm above the sample

  15. DC measurement I b Vm qubit Readout through a dc-SQUID Record each switching when Vm = Vth~ 30 mV as a function of Isw Sweep Ib ( 140 Hz ) Tilt SQUID potential I b ~ 100 nA Isw Isw Isw 4~6 nA Isw t 0 70 ~ 100 μsec Vm ~ 7 ms Vth(~30μV) t 0

  16. DC measurement Current is swept Isw(/ 0) curve I(V) curve Magnetic field is swept Readout with a dc-SQUID

  17. DC measurement Step on the Isw(/ 0) Qubit switches its current sign Flux in SQUID changes through M SQUIDIsw changes Φ M Qubit dc-SQUID Qubit step in the SQUID Isw Fqubit / F0

  18. Parameter dependence of the qubit step ( D, Ej, Ec ) SQUID I Lqubit LSQUID Qubit Josephson junctions : Al / Al2O3 / Al Junction area : SQUID0.2 x 0.2 m2 qubit 0.2 x L m2, L=0.3, 0.5, 1.0 Loop size : Lqubit= 5.1, 9.7, 19.0 (m)LSQUID= 6.3, 10.9, 20.2

  19. Two energy scale Ec, EJ energy energy Pair tunneling superconductor -p p superconductor Number of tunneled pair n Phase difference Tunnel barrier H = Ec - EJcos g - Iexg [n,g]=i Josephson energy : EJ charging energy : Ec =(2ne)2/(2CJ ) kBT << EJ<< Ec < D→charge qubit kBT << Ec<< EJ < D→phase、flux qubit

  20. QB# 6 Junction area = 0.2 m2 Loop size : Lqubit = 9.7 m LSQUID = 10.9 m QB# 5 Junction area = 0.1 m2 Loop size : Lqubit = 9.7 m LSQUID = 10.9 m QB# 4 Junction area = 0.06 m2 Loop size : Lqubit = 9.7 m LSQUID = 10.9 m ( D ~ 2GHz > kBT ) ( D ~ 0.4GHz ~ kBT ) ( D ~ 2MHz << kBT ) Fqubit / F0 Fqubit / F0 Fqubit / F0 QB# 8 Junction area = 0.1 m2 Loop size : Lqubit = 19.0 m LSQUID = 20.2 m QB# 7 Junction area = 0.06 m2 Loop size : Lqubit = 19.0 m LSQUID = 20.2 m QB# 3 Junction area = 0.2 m2 Loop size : Lqubit = 5.1 m LSQUID = 6.3 m Fqubit / F0 Fqubit / F0 Fqubit / F0 D Qubit energy splitting kBT~25mK

  21. Calculated qubit energy level D=0.4 GHz D=2 GHz D=2 MHz Ej=280 GHz Ec=3.2 GHz Ej/Ec=87 Ej=130 GHz Ec=5.4 GHz Ej/Ec=24 Ej=544 GHz Ec=1.6 GHz Ej/Ec=338

  22. Optimal operation point for SQUID Qubit signals appear at half-integer Sensitivity of dc-SQUID depends on magnetic fields We can achieve excellent resolution at f = 1.5 ↓ ↑

  23. Spectroscopy EJ = 312 GHz, EC = 3.8, a = 0.7 D = 2.6 GHz after averaging w/o averaging 0.001 F0 M2.4 GHz

  24. DC measurement Qubit signals at different SQUID modulation S/N depends on SQUID Isw design qubit and SQUID to be crossed at small Isw |> |> |> |> T = 25 mK

  25. Level splitting E0 (1) E <Iq>/Ip /0 Classical states Quantum ground state |0> Quantum first excited state |1> f=

  26. Level splitting E0 (1) E <Iq>/Ip /0 Classical states Quantum ground state |0> Quantum first excited state |1> Boltzman Distribution

  27. Schematic qubit energy spectrum D = m = m a = E 1055 eV, E 30 . 44 eV, 0 . 80 J C 15 100 10 5 Energy (GHz) Energy (GHz) 0 0 -5 -10 -100 0.4 0.5 0.6 0.49 0.50 0.51 F F / 0 qubit Fqubit F0 /

  28. DC measurement D Spectroscopy Pulse measurement excited state ground state

  29. Readout without averaging DC measurement Single shot measurement into { l0>, l1> } bases The <Iq> step shape does not change. Only the population changes. Fqubit / F0

  30. Close-up of Isw, T=25 mK DC measurement Histogram is well separated ! counts counts f Fqubit / F0 0.001 F0 M 2.4 GHz f = 1.50102

  31. Readout after averaging DC measurement Expected Current ( canonical ensemble average ) Fqubit / F0

  32. Experimental setup Pulse measurement 1 2 3 4 5 RF line SLP-1.9 R.T. 4.2K RFin : ２ attenuators RFout : terminator + attenuator DC : LP filter + Meander filter Flexible coaxial cable HP 10dB 1.2K 0.8K 0.4K I - I + V + V - 29mK Weinschell 10dB Thin coaxial cable f 0.33 mm Meander filters Sample cavity RF in RF in Terminator 50 W Sample cavity On-chip strip line

  33. Multi-photon transition Multi-photon transition between superposition of macroscopic quantum states ｰ ( ) /√21st excited state ＋ ( ) /√2ground state 3 3 2 2 1 1 3 1 2 2 3 1

  34. Multi-photon transition 3 2 １ 2 １ １ 3 RF : 3.8 GHz RF : 3.8 GHz 2 2 2 0 dBm -10 dBm 1 1 (nA) (nA) 2 0 0 １ SW SW d I d I -1 -1 -2 -2 1.504 1.496 1.498 1.500 1.502 1.496 1.498 1.500 1.502 1.504 F F / F F / qubit 0 qubit 0 Multi-photon spectroscopy SQUID readout D=0.86GHz 1-photon 2 -photon

  35. Multiphoton absorption at 9.1 GHz RF Power dependence double triple single off off off PRF = - 21 dBm 0 dBm 9.6 dBm 13.2 dBm 10 dBm 12 dBm 12 dBm

  36. Multi-photon transition Peak width vs MW intensity Bloch Kinetic Equation 9100MHz ----- (3) ------------------ (4)

  37. Pulse measurement Pulse measurement scheme repetition: 3kHz ( 333 ms) 180 ns ~1μs SQUID switch Ib DC pulse Non-switching time resonant microwave MW discrimination of the switching event Vout + Vout - V th I bias Fext Non-switching events Switching events Ibias + Ibias - SQUID Non-switching event Switching event

  38. Pulse measurement 030304_1 (1,2)FQB2 1st excited sate D 55 [%] 50 45 40 Probability 35 30 25 1 2 Relaxation time T1 15 9.1 GHz 1 ms pulse 10 data MW 5 exp-fit Energy (GHz) 0 m T = 1.6 s 1 -5 Ground state -10 0.49 0.50 0.51 Fqubit F0 / 500 ns 0 3 ms m Delay Time [ s] 1 ms delay time Ib pulse height 1.474 V, Trailing height ratio 0.6

  39. Pulse measurement switching probability ( % ) Rabi frequency ( MHz ) pulse width ( ns ) MW amplitude (a.u.) Quantum Oscillation : Rabi oscillations 11.4 GHz Dephasing time ~ 30 ns 150 ns 600 s Trailing height ratio 0.7 Resonant MW pulse width NTT Atsugi

  40. Summary • Spectroscopy of MQ artificial 2-level system • Qubit readout without averaging (DC) • Multi-photon transition between superposed MQ states • Coherent quantum oscillation ( Rabi oscillation ) • T1 ~1.6 ms, T2Rabi ~ 30 ns Future plan • Ramsey, Spin echo • Two qubit fabrication and operation • MQC with single shot resolution

  41. collaborators NTT Basic Research Laboratories Hirotaka Tanaka Shiro Saito Hayato Nakano Frank Deppe Takayoshi Meno Kouich Semba Tokyo Institute of Technology Masahito Ueda Yokohama National University Yoshihiro Shimazu Tomoo Yokoyama Tokyo Science University Takuya Mouri Tatsuya Kutsuzawa

  42. エネルギー固有状態をone-shot measurementで見た。 の時、 を測っている。 を測っているのではない。 これを測ると､ 0.5 と のsuperpositionは、生きている。 と の間のsuperpositionは死んでいる。

  43. 0.5 time domain で真ん中に出る理由 Qubitの磁場の量子力学的平均値を取っているから Qubitの磁場はszのはず（projection)。 を使って､time-dependentなSchrödinger 方程式を解き､SQUIDのswitching current を求めると、EJ/ECが小さくなると、ピークは １つ、反対にEJ/ECが大きくなると、ピークは ２つになる。 ピーク１つ ピーク２つ 0.5

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