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Measuring Quantum Coherence in the Cooper-Pair Box

Measuring Quantum Coherence in the Cooper-Pair Box. Konrad Lehnert. Depts. of Applied Physics & Physics Yale University. Yale Lafe Spietz Ryan Held Ben Turek Rob Schoelkopf. Chalmers University Kevin Bladh David Gunnarsson Per Delsing. And discussions w/:

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Measuring Quantum Coherence in the Cooper-Pair Box

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  1. Measuring Quantum Coherence in the Cooper-Pair Box Konrad Lehnert Depts. of Applied Physics & Physics Yale University Yale Lafe Spietz Ryan Held Ben Turek Rob Schoelkopf Chalmers University Kevin Bladh David Gunnarsson Per Delsing And discussions w/: M. Devoret, S. Girvin, A. Clerk, K. Nguyen The David and Lucile Packard Foundation Funding:

  2. 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

  3. 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.

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

  5. Single Electron Transistor Measuring Box Vds Box SET Electrometer Cg Cc Cge Box Vg Vge SET Superconducting tunnel junction Al/AlOx/Al junctions; 50 x 50 nm e-beam lithography; double-angle evaporationTc ~ 1.5 K

  6. Cooper-pair Box Vg Vg

  7. 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

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

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

  10. 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)

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

  12. Experiment Diagram

  13. 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

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

  15. 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

  16. Saturation of the Cooper Pair Resonance Photon Peak Height 0.5 37 GHz 39 GHz 0.2 0 0.235 0.265 Peak width Peak height 50% saturated 0

  17. Excited-state Lifetime 0 t<0 t>0 0.15 e time t=20ms 0 10 ms 1e 0.3e t=1.6 ms t<0 t=0.4 ms Peak height (e) 0 0.5 1 time 0 10 ms

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

  19. Spontaneous Emission into Environment Spontaneous Emission:Fermi’s golden rule Cg Box Vg 2e

  20. Electrometer Input Impedance Cg Cc Cg Cc Vg 2e 2e 2e SET 0.6 185 W Peak Height (e) 0.3 370 740 0 Electrometer Operating Point (Vg)

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

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

  23. Conclusions • RF-SET measures charge states of box • Spectroscopic determination of Hamiltonian of box • Dephasing time ~ 1 ns : (w/ continuous measurement) • Long Excited-state lifetime >1 ms : • Electrometer affects T1

  24. 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

  25. 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

  26. Single-electron Box: Coulomb Staircase E First demonstrated by Lafarge et al, ’91(Saclay) Ec Ec/4 ne=-1 ne=0 ne=1 200 mK 16 mK Coulomb Staircase Thermally broadened 1 e e 0 kT/Ec -1 -1 -0.5 0 0.5 1

  27. Cooper-pair Box Spectrum: Electrostatic and Josephson E EJ Ec n=-1 n=1 n=0 Condition:Two level System EJ /4Ec 2e 2e -0.5 0 0.5

  28. Cooper-pair Box as Spin 1/2 Time scales w01 Larmor frequency 10-40 GHz T1 Excited state lifetime 0.1-10 ms WR Rabi frequency T2* Ensemble decoherence time

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

  30. Cooper-pair Box Spectrum: Electrostatic and Quasi-particle E n=1.5 n=-0.5 n=0.5 Ec n=0 n=1 n=-1 Odd: single q.p. Even: no q.p. kT/4Ec 2e 2e-periodic Cooper-pair Staircase 2e -0.5 0 0.5

  31. Cooper-Pair Resonance Spectroscopy E Cg Vapp Vapp=Vg+Vacsinwt 1 38 GHz 35 GHz 0 0 0.5 1

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