1. Noise and decoherence in the Josephson Charge Qubits Oleg Astafiev, Yuri Pashkin, Tsuyoshi Yamamoto, Yasunobu Nakamura, Jaw-Shen Tsai RIKEN Frontier Research System NEC Fundamental Research Laboratories

2. Outline The Josephson charge qubit Single-shot readout with charge trap Measurements of energy relaxation Charge fluctuators and energy relaxation

3. The Josephson Charge Qubit Charging energy (for Cooper pair): Josephson energy: EJEJ EJEJ C b >> C g E n g =V g C g /e         Reservoir Box CbCb CgCg 2e22e2 CbCb Control gate n g = VgCgVgCg e Degeneracy >> kT 2e22e2 CbCb >> E J 02314

4. The Hamiltonian Eigenstates Eigenenergies

5. |0  |1  t = 0: t > 0: Coherent Oscillations P tt 1 0 E tt   |1  2   |1  2  -pulse:  J  t =  q EJEJ

6. Cooper-Pair Box GateGate ＳＱＵＩＤＳＱＵＩＤ ProbeJunctionProbeJunction 1m1m ProbeJunctionProbeJunction Cooper- pair Box Cooper- GateGate ＳＱＵＩＤＳＱＵＩＤ Al/AlO x /Al tunnel junctions Pulse induced current in SQUID – box – probe junction circuit is measured  0  +  1  I = 2e |  | 2 /T r TrTr Control pulse sequence  t (ns) 0 1

7. 2e Cooper-pair box Final state read-out A pair of qusiparticles tunnels through the probe junction biased to V b  2  /e e e + probe

8. Single-shot Readout Coherent oscillations Quasiparticle tanneling (when the trap is biased to 2  /e) Reservoir Box Control gate qubit CbCb C ts SET Readout circuit CsCs I C bt Trap Readout gate CtCt t readout: control: Pulses

9. Measurement circuit is electrostatically decoupled from the qubit Final states are read out after termination coherent state manipulation

10. Reservoir Box SET Trap gate Readout with control  -pulses Readout pulse Control  -pulse ngng I

11. 0.20.40.60.81 0.75 0.80 0.85 0.90 0.95 tt (ns) b P Quantum Oscillations  q (e)  =  /   -pulse Degeneracy Crossection tt qq

12. Relaxation to the reservoir Readout tdtd Control  -pulse 220 exp(-t/288)+32 T1 res = 288 ns N tot = 327 Reservoir Box SET Trap

13. Relaxation to the Trap Control  -pulse t width T eff = (1/T 1 res + 1/T 1 trap ) -1 = 31 ns Readout Reservoir Box SET Trap

14. Readout efficiency Reservoir Box SET Trap

15. Two-level System as a Quantum Noise Spectrometer Two-level system TLS Environment Electrostatic energy noise Charge basis: Eigenbasis: tan  = EJEJ E UU EJEJ  UU z x transitions dephasing Dephasing Transitions UU UU   sincos 2 xzz tU E H  E

16. Charge qubit qq charge noise spectral density: S q (  ) S U (  ) = (2e/C) 2 S q (  )  1 = 2222  SU() SU() Relaxation rate: sin 2  Dephasing: SUSU Dephasing Relaxation Excitation 

17. T 1 time measurements ngng E tata P(1)  exp(-t a /T 1 ) time readout pulse Control  -pulse Adiabatic pulse

18. Degeneracy T 1 time vs Gate Voltage

20. E J -dependences Degeneracy Off degeneracy

21. Coupling to Environment through Electrical Leads Coupling to gates: Coupling to SET: Measured relaxation time can not be explained by coupling to the external environment through electrical leads

22. Effect of the measurement SET

23. The noise derived from  1 time  1 = 2222  SU(0) SU(0) sin 2 

24. T 2 -2

25. Classical  Quantum Noise Quantum f-noise (  > 0): Classical 1/f-noise:   (kT eff ) 2  Do low frequency 1/f and high frequency f noises have common origin?  1/f  f SU()SU() kT/   emissionabsorption

26. Relaxation through Fluctuators Dephasing is caused by 1/f noise of charge fluctuators with activation energy less than kT Fluctuators with activation energy of   (   >> kT) accept qubit excess energy kT EE

27. Low frequency 1/f noise

28. Temperature dependences of the 1/f noise

29. Standard qubit on 400 nm thick Si 3 N 4

31. 1/f noise in superconducting – normal SETs

32. SET on GaAs substrate

33. SET on Al 2 O 3 Si Al Al 2 O 3 SET island

34. Large area SETs

35. 1/f noise properties from experiments does not depend on substrate type noise appears in oxide of Al(?) scales with SET size (area?) saturation level at low temperatures depends on current

36. Basic properties of the 1/f noise caused by bistable fluctuators    S()S()

37. Qubit TLS (fluctuators) Environment at T > 0  Qubit island TLS fluctuators The qubit is coupled to environment through charge degree of freedom

38. 1/f noise  23  13 1 2 3 Environment at T > 0 high frequency cutoff of the 1/f noise If, then

39. 1 2 3 Qubit relaxation (excitation)

40. 1/f low frequency noise: f high frequency noise: Crossover frequency:

41. Same fluctuators contribute in the 1/f noise and the quantum f noise Constant distribution of two energy parameters for the fluctuators is required

42. Two energy parameters: Single energy:

43. Single energy (TLS)  12 1 2 Environment at T > 0 00 High frequency cutoff 1/f noise:  << kT f noise:     < 10 5 Hz   10 10  10 11 Hz Different TLS contribute in 1/f and f noises

44. Conclusion  We have demonstrated single-shot readout using charge trap  Energy relaxation of the qubit has been measured  The energy relaxation is caused by quantum f noise which has crossover frequency with 1/f noise at kT/   Nearly T 2 dependence of the 1/f noise has been observed