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The Cooper-pair Box as a Quantum Spectrum Analyzer

The Cooper-pair Box as a Quantum Spectrum Analyzer. Rob Schoelkopf. Depts. of Applied Physics & Physics Yale University. Yale. expt. K. Lehnert L. Spietz D. Schuster B. Turek. Chalmers University K.Bladh D. Gunnarsson P. Delsing. theory A. Clerk S. Girvin D. Stone.

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The Cooper-pair Box as a Quantum Spectrum Analyzer

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  1. The Cooper-pair Box as a Quantum Spectrum Analyzer Rob Schoelkopf Depts. of Applied Physics & Physics Yale University Yale expt. K. Lehnert L. Spietz D. Schuster B. Turek Chalmers University K.Bladh D. Gunnarsson P. Delsing theory A. Clerk S. Girvin D. Stone And discussions w/: M. Devoret & J. Martinis The David and Lucile Packard Foundation Funding:

  2. Vds Cg Cc Cge Box Vg Vge SET Cooper-pair Box Coupled to an SET Box SET Electrometer Superconducting tunnel junction SET Transistor Cooper-pair Box Quantum state readout Qubit or Nonequilibrium noise source Quantum spectrum analyzer

  3. Cooper-pair Box Vg Vg (e.g. Bouchiat et al., 98)

  4. Cooper-pair Box as Quasi-spin 1/2 Measure charge Ground state 1 b c a a b c Excited state 0 0.5 E a b c

  5. Continuous Measurement of a Single Spin Measured continuously by SET Theory: Cooper-pair box ground state 1 0.5 2e 1e 0 0 0.5 1 Measurement must cause additional dephasinguncertainty principle Measurement mayalso mix states, drive transitions from ground state

  6. Cooper-Pair Resonance Spectroscopy E Cg Vapp 38 GHz Vapp=Vg+Vacsinwt 2-photonPeak 1 w/2p=38 GHz 0 0 0.5 1

  7. Determination of Box Hamiltonian “SQUID box” to vary EJ Peak location 32 GHz 0.29 Vapp B 35 GHz 38 GHz 0.25 0 -2 2 -1 1 Fit parameters: E

  8. Effects of Voltage Noise on Pseudo-Spin dephasing slow fluctuations of mixing resonant fluctuations of

  9. Emission and Absorption due to Environment Box absorption emission

  10. Spontaneous Emission into Environment Cg Box Vg Excited-statelifetime, T1 estimate:

  11. Excited-state Lifetime Measurement of Box 1 follow peak height after shift 0 0 0.5 1 with continuous measurement Peak height (e) 0.3e 0 time 10 ms (@ 76 GHz)

  12. Relaxation by Electrometer? e- Cg Cc Vg Vge 2e SET Peaks saturate when 0.6 0.3 Peak Height (e) 0 Electrometer Operating Point (Vge)

  13. Charging Diagram of SET Electrometer Vge Vds 4D 2Ec eVds 0 Electrometer SET: R = 150 kW EC ~ D ~ 2.4 K 1e CgVge/e Electrometer operating pt. on “DJQP” feature

  14. Quantum Shot Noise of DJQP* Process *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat/0203338) Γ Excitation Relaxation Sharp thresholds due toopening&closingof transport channels

  15. Predicted Effects of DJQP on Box Charge (A. Clerk et al. cond-mat/0203338) SET noise spectrum Average box charge 1 Log[SV(w)] on resonance off resonance 0 Qubit acts like a spectrum analyzer of the SET quantum noise! (see also Aguado & Kouwenhoven, 2000 for double dot)

  16. Conclusions • RF-SET a good probe of the charge states of box • Spectroscopic determination of Hamiltonian of box • Inelastic lifetime is long > 1 ms : (and electrometer affects T1 !) • Cooper-pair box as a “quantum spectrum analyzer” Measures all NoiseClassical (symmetric) Quantum (asymmetric) 0

  17. Coulomb Staircase vs. Electrometer Bias Back-action increases with electrometer bias Supercurrent (Vds=0) DJQP (Vds= 400 mV) JQP (Vds= 800 mV) Gap rise (Vds= 1200 mV) T=20 mK

  18. Cooper-pair Staircase vs. Electrometer Bias Theory: Cooper-pair box ground state sweep gate @ 2e per 100 ms 1 Data: Vds= 350 mV Vds= 275 mV Vds= 250 mV 0.5 2e 1e 0 0 0.5 1

  19. Cooper-pair Staircase vs. Josephson Coupling Theory: Cooper-pair box w/ max EJ Data: maximum EJ minimum EJ 1 0.5 2e 1e 0 0 0.5 1

  20. Charge States Coupled by EJ Peak location “SQUID box” to vary EJ 32 GHz Vapp 35 GHz B 38 GHz Peak height 0 -2 2 -1 1

  21. Single-electron Box: Coulomb Staircase E First demonstrated by Lafarge et al, ’91(CEA Saclay) Ec Ec/4 ne=-1 ne=0 ne=1 Coulomb Staircase Thermally broadened 1 e e 500 mK200 mK 50 mK 0 kT/Ec -1 -1 -0.5 0 0.5 1

  22. Temperature Dependence in Normal State

  23. Decoherence Time of Box 74 GHz 78 GHz Peak width 0.2 0.235 0.265 0

  24. DJQP Noise, Off-resonance • Move away from the center of the resonance by increasing VDS… 2 Avg. Qubit Charge 0 0 0.5 1 1.5 2 NB Ω / ECS • Γ > Γ Population inversion in the qubit.

  25. Charge States Coupled by EJ “SQUID box” to vary EJ Vapp B Peak height 0 -2 2 -1 1 E

  26. dephasing slow fluct. of mixing resonant fluct. of Effects of Voltage Noise on Qubit z x

  27. Box State Depends on Electrometer Bias Vds (mV) 0 250 290 420 470 760 1200

  28. Spontaneous Emission Environment SET Box Vds Cc Cg Vg 2e SET E Relaxation

  29. Backaction of SET on Box Cm Cg Zenv t

  30. Who’s measuring whom? Measured continuously by SET Theory: Cooper-pair box ground state 1 2e 1e 0

  31. Can Electrical Circuits be ‘Quantum?’ Macroscopic Quantum Coherence: Cooper-pair boxY. Nakamura et al, Nature 1999 • New Challenges: • Understand and minimize decoherence • Develop efficient quantum readout • New Opportunities: • Create artificial atoms • Quantum computation

  32. Quantum Circuits for Quantum Computing Quantum bit (or “qubit”) Classical bit Information as state of a two-level quantum system , or values values 0 or 1 superposition: Prediction: a 2,000 bit quantum computer = a conventional computer the size of universe.

  33. Vbias Cmeas ? The Quantum Spectrum Analyzer 0 Measures all NoiseClassical (symmetric) Quantum (asymmetric)

  34. Quantum Computing Ion TrapsLiquid State NMR Nuclear Spins inSemiconductors Coherent Scalable ControllableMeasurable Cooper-pair boxSQUID’s How coherent is a Cooper-pair box?

  35. Outline • Charge quantization on a normal-metal island Single-electron Box • Superconducting island as quantum two-level system Cooper-pair Box • Spectroscopy of the Cooper-pair box Single-electron Tranistor (SET) measures box • Box Measures SET Quantum Spectrum Analyzer

  36. Small, Cold and Fast Microwaves Dilution refrigerator T = 15 mK 1 mm Millikelvins Nanometers

  37. Experiment Diagram

  38. Quantum Shot Noise of DJQP* Process *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat 0203338) -10 10 2 -1 Hertz Avg. Qubit Charge -15 10 0 -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 Ω / ECS NB Ω= -ECS Ω= ECS Excitation Relaxation • Qubit acts like a spectrum analyzer of the SET quantum noise! (see also Aguado & Kouwenhoven, 2000 for double dot)

  39. NMR of a Single Spin Single Spin ½ Quantum Measurement Vds Cgb Cc Cge Box Vgb Vge SET

  40. The Single-Electron Box island Cg Vg ne e Cj Rj Normal tunnel junction E Ec ne to ne+1 electrons Ec/4 ne=-1 ne=0 ne=1

  41. Single-electron Box: Coulomb Staircase E First demonstrated by Lafarge et al, ’91(CEA Saclay) Ec Ec/4 ne=-1 ne=0 ne=1 Coulomb Staircase Thermally broadened 1 e e 500 mK200 mK 50 mK 0 kT/Ec -1 -1 -0.5 0 0.5 1

  42. Single-electron Transistor: Electrometer SET drain Vds Cge Vge Ids 10 nA source Electrometer input gate Vds 1 mV

  43. Quantum Shot Noise of DJQP* Process *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat/0203338) Γ -10 10 -1 Hertz -15 10 -1 -0.5 0 0.5 1 Ω / ECS Excitation Relaxation • Sharp thresholds due to opening & closing of transport channels

  44. Radio-Frequency Single Electron Transistor (RF-SET) Response to step in Vge Transformer SET single time trace RF Reflected power Electrometer input gate Measure RF power reflected from LC transformer 10-5 e/Hz1/2 charge noise Sub-electron sensitivity for > 100 MHz bandwidth Schoelkopf et al., (Science 1998)

  45. The Single-Electron Box island Cg Vg ne e Cj Rj Normal tunnel junction E Ec ne to ne+1 electrons Ec/4 ne=-1 ne=0 ne=1

  46. Conclusions • Cooper-pair Box: A quantum two-level system worst-case coherence • Box Hamiltonian determined with spectroscopy • Long excited-state lifetime while continuously measured.

  47. Coulomb Staircase vs. Electrometer Bias Back-action increases with electrometer current Gap rise 500 pA Double JQP 300 pA Strong JQP 150 pA Weak JQP 100 pA Eye 100 pA T=20 mK

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