Noise and decoherence in the Josephson Charge Qubits

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. 2e2 2e2 Cb Cb VgCg ng = e >> EJ Degeneracy - - - - + + + + The Josephson Charge Qubit Charging energy (for Cooper pair): >> kT Josephson energy: EJ Control gate Cg E Box Cb EJ 0 1 2 3 4 Reservoir Cb >> Cg ng =Vg Cg /e

4. The Hamiltonian Eigenstates Eigenenergies

5. -|0+|1 |0+|1 |-= |+= 2 2 -pulse: Jt =  Coherent Oscillations |1 E t = 0: t > 0: EJ |0 t P 1 q 0 t

6. ＳＱＵＩＤ Probe Junction Cooper-Pair Box 1mm Gate Al/AlOx/Al tunnel junctions Control pulse sequence Cooper- pair Box ＳＱＵＩＤ Probe Junction Tr Gate Pulse induced current in SQUID – box – probe junction circuit is measured 0+1 I = 2e ||2/Tr 0 1 t (ns)

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

8. Readout circuit Pulses I control: Cs SET readout: Cts Ct Trap t Cbt Readout gate Quasiparticle tanneling (when the trap is biased to 2D/e) Single-shot Readout qubit Reservoir Cb Box Control gate Coherent oscillations

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

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

11. -pulse Crossection Degeneracy Quantum Oscillations 0.95 0.90 P  = / 0.85 q (e) b t D 0.80 0.75 q 0.2 0.4 0.6 0.8 1 t (ns)

12. Relaxation to the reservoir td Control -pulse Reservoir SET Readout Trap Box Ntot = 327 220 exp(-t/288)+32 T1res = 288 ns

13. Relaxation to the Trap Control -pulse Reservoir SET Readout twidth Trap Box Teff = (1/T1res + 1/T1trap)-1 = 31 ns

14. Reservoir SET Trap Box Readout efficiency

15. EJ tan  = E Transitions Dephasing Two-level System as a Quantum Noise Spectrometer z Two-level system TLS E U transitions U Environment  dephasing U U EJ x Charge basis: Electrostatic energy noise E ( ) ( ) = - s - d s q + s q H U t cos sin Eigenbasis: z z x 2

16. SU() 1 = 22 SU Relaxation Excitation  Dephasing sin2 Relaxation rate: Dephasing: charge noise spectral density: Sq() Charge qubit q SU() = (2e/C)2Sq()

17. T1 time measurements E P(1)exp(-ta/T1) ng Control -pulse Adiabatic pulse ta time time readout pulse

18. T1 time vs Gate Voltage Degeneracy

20. EJ-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. 1 = SU(0) 22 The noise derived from 1 time sin2

24. T2-2

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

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 E kT

27. Low frequency 1/f noise

28. Temperature dependences of the 1/f noise

29. Standard qubit on 400 nm thick Si3N4

31. 1/f noise in superconducting – normal SETs

32. SET on GaAs substrate

33. SET island Al2O3 Al Si SET on Al2O3

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()  1/g 

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

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

39. Qubit relaxation (excitation) 3 2 1

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) Environment at T > 0 2 12 1 g0 High frequency cutoff f noise:    1/f noise:  << kT   1010  1011 Hz  < 105 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 T2 dependence of the 1/f noise has been observed