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

2. Cooper-pair Box Coupled to an SET Box SET VgVg V ge CgCg CcCc C ge V ds BoxSET Electrometer Superconducting tunnel junction Qubit Quantum state readout Quantum spectrum analyzer Cooper-pair Box SET Transistor Nonequilibrium noise source or

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

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

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

6. E Cooper-Pair Resonance Spectroscopy V app 01 0.5  =38 GHz CgCg V app =V g +V ac sin  t 1 0 38 GHz 2-photon Peak

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

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

9. absorptionemission Emission and Absorption due to Environment Box

10. CgCg Spontaneous Emission into Environment estimate: Excited-state lifetime, T 1 VgVg

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

12. Relaxation by Electrometer? Peak Height (e) Electrometer Operating Point ( V ge ) 0 0.6 0.3 CgCg 2e2e SET VgVg CcCc e-e- V ge Peaks saturate when

13. V ds Charging Diagram of SET Electrometer C g V ge /e eV ds V ge Electrometer SET: R = 150 k  E C ~  ~ 2.4 K 44 2E c 0 1e Electrometer operating pt. on “DJQP” feature

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

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

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

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

19. Cooper-pair Staircase vs. Electrometer Bias Theory: Cooper-pair box ground state 2e 1e 0 0.5 0 1 1 sweep gate @ 2e per 100  s Data: V ds = 350  V V ds = 275  V V ds = 250  V

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

21. Peak height 0 -2 1 2 B “SQUID box” to vary E J Charge States Coupled by E J V app Peak location 32 GHz 35 GHz 38 GHz

22. n e =-1n e =0n e =1 EcEc E 0-0.50.5 Single-electron Box: Coulomb Staircase e e Coulomb Staircase Thermally broadened kT/E c 1 500 mK 200 mK 50 mK 0 1 First demonstrated by Lafarge et al, ’91 (CEA Saclay) E c /4

23. Temperature Dependence in Normal State

24. 0.235 0 Peak width Decoherence Time of Box 0.265 74 GHz78 GHz 0.2

25. DJQP Noise, Off-resonance 00.511.52 0 2  Γ  > Γ  Population inversion in the qubit. Ω / E CS Avg. Qubit Charge Move away from the center of the resonance by increasing V DS … NBNB

28. Peak height 0 -2 1 2 E B “SQUID box” to vary E J Charge States Coupled by E J V app

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

30. Box State Depends on Electrometer Bias V ds (  V) 250 290 1200 0 420 470 760

31. CgCg 2e2e SET Box Environment Spontaneous Emission VgVg CcCc V ds E Relaxation

32. Backaction of SET on Box t CmCm CgCg Z env

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

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

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

36. 0 The Quantum Spectrum Analyzer C meas ? V bias Measures all Noise Classical (symmetric) Quantum (asymmetric)

37. Quantum Computing Scalable Coherent Controllable Measurable Cooper-pair box SQUID’s Ion Traps Liquid State NMR Nuclear Spins in Semiconductors How coherent is a Cooper-pair box?

38. 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

39. Microwaves Small, Cold and Fast 1  m Dilution refrigerator T = 15 mK Millikelvins Nanometers

40. Experiment Diagram

41. Quantum Shot Noise of DJQP* Process 00.511.52 0 2 Avg. Qubit Charge -0.500.51 10 -15 10 -10 Hertz NBNB Ω / E CS ExcitationRelaxation Ω= -E CS Ω= E CS  Qubit acts like a spectrum analyzer of the SET quantum noise! *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat 0203338) (see also Aguado & Kouwenhoven, 2000 for double dot)

42. Single Spin ½Quantum Measurement NMR of a Single Spin Box SET V gb V ge C gb CcCc C ge V ds

43. e nene The Single-Electron Box n e to n e +1 electrons VgVg island C j R j CgCg n e =-1n e =0n e =1 EcEc E E c /4 Normal tunnel junction

44. n e =-1n e =0n e =1 EcEc E 0-0.50.5 Single-electron Box: Coulomb Staircase e e Coulomb Staircase Thermally broadened kT/E c 1 500 mK 200 mK 50 mK 0 1 First demonstrated by Lafarge et al, ’91 (CEA Saclay) E c /4

45. C ge V ge V ds I ds V ds 10 nA 1 mV Single-electron Transistor: Electrometer Electrometer input gate drain source SET

46. Quantum Shot Noise of DJQP* Process -0.500.51 10 -15 10 -10 Hertz Ω / E CS ExcitationRelaxation  Sharp thresholds due to opening & closing of transport channels ΓΓ *Double Josephson-quasiparticle cycle: (A. Clerk et al. cond-mat/0203338)

47. 10 -5 e/Hz 1/2 charge noise Sub-electron sensitivity for > 100 MHz bandwidth Electrometer input gate Transformer SET RF Reflected power Measure RF power reflected from LC transformer Schoelkopf et al., (Science 1998) Radio-Frequency Single Electron Transistor (RF-SET) Response to step in V ge single time trace

48. e nene The Single-Electron Box n e to n e +1 electrons VgVg island C j R j CgCg n e =-1n e =0n e =1 EcEc E E c /4 Normal tunnel junction

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

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