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Technological Issues in Superconducting Charge Qubits: A Comprehensive Overview

Explore technological challenges and advancements in superconducting charge qubits with detailed discussions on electrostatic coupling, readout methods, and measurements of T1 and T2. The paper delves into Cooper-pair box models, gate charge states, and coherent oscillations. It also covers the Hamiltonian of charge qubits and quantum beatings experiments. Discover the operational points, quantum beatings, and theoretical expectations for charge qubits. Learn about single-shot readout techniques, coherent evolution, and the significance of no-quasiparticle relaxation. Gain insights into probing, trap and SET readouts, and control of superconducting charge qubits. Find out about novel materials, qubit control methods, and the impact of substrate materials on T1 and T2. Future directions and considerations for advancing superconducting charge qubits are also discussed.

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Technological Issues in Superconducting Charge Qubits: A Comprehensive Overview

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  1. NEC Tsukuba Quantum Technologies 2004 Vancouver, Canada Technological issues of superconducting charge qubits Yuri Pashkin RIKEN Oleg Astafiev Tsuyoshi Yamamoto Yasunobu Nakamura Jaw-Shen Tsai Dmitri Averin - RIKEN - SUNY at Stony Brook 30 March 2004

  2. Outline • introduction • electrostatic coupling • single-shot readout • T1 and T2 measurement • technological issues

  3. Cooper-pair box M. Büttiker, 1987 V. Bouchiat et al, 1995 • a single artificial two-level system • ~108 conduction electrons in the box E = (CgVg – 2ne)2/2C box reservoir Cooper-pair tunneling - - - - n=0 1 ++++ gate

  4. charge states: , coherent oscillations initial state Charge qubit based on Cooper-pair box Y. Nakamura et al, 1999 eigenstates: energy EJ gate voltage initialization coherent superposition read-out final state

  5. e e + probe Final state read-out Josephson-quasiparticle cycle (Fulton et al., 1989) 2e Cooper-pair box • detect the state • initialize the system to

  6. reservoir 2 reservoir 1 probe 1 probe 2 qubit 2 qubit 1 Cross Section dc gate 1 dc gate 2 pulse gate (common) box 2 box 1 1 m capacitive coupling I2 I1 Vb2 Vb1 Vg2 Vp Vg1 Capacitively coupled charge qubits standard e-beam lithography + angle evaporation I1 and I2 give info on charge states

  7. I00> I10> I01> I11> I00> I10> I01> I11> Hamiltonian charge basis EJ1,2 ~ Em < Ec1,2 initial state I00> Ec1, Ec2, Em EJ1, EJ2 En1n2= Ec1(ng1–n1)² + Ec2(ng2–n2)² + Em(ng1–n1)(ng2–n2) Ec1,2= 4e²CΣ2,1/2(CΣ1,2CΣ2,1 – Cm²)  4e²CΣ2,1/2CΣ1,2CΣ2,1 ng1,2= (Cg1,2Vg1,2 + CpVp)/2e Em= 4e²Cm/(CΣ1CΣ2 – Cm2)

  8. Oscillations at the double degeneracy E00 = E11 E10 = E01 0,0 I2 I1 1,0 0,1 dｃ gate1 dｃgate2 1,1 pulse gate ng1 (= ng2) ng2 time 1,1 1 0,1 0.5 X superposition of four charge states! 0 1,0 0,0 ng1 1 0.5 0

  9. Quantum beatings p1 p2 time, ps 0 1000  -   -   +   +  2 2 operation point ng1 (= ng2) 0.5 0.45 2f

  10. Quantum beatings: experiment   2.5 ns   0.6 ns EJ1 ng2 1,1 1 0,1 X EJ2 0.5 L R 0 1,0 0,0 ng1 1 0.5  -  0  +  theoretically expected EJ1 = 13.4 GHz EJ2 = 9.1 GHz Em = 15.7 GHz

  11. Single-shot readout EJ EJ trap+SET readout conventional readout qp = 0 qp ~ 1/10 ns     trap kept unbiased during coherent evolution no qp relaxation! 2( + Ec) reservoir reservoir probe permanently biased! box box

  12. Trap + SET readout box + trap galvanically isolated from the leads! no qp relaxation! no effect of the leads!

  13. derivative of SET signal control+readout SET signal Time trace

  14. Single-shot readout: coherent oscillations dead zones degeneracy

  15. Relaxation of coherent oscillations no increase in T2

  16. T1 measurement E • create 1 state by NA -pulse • move slowly along the upper band • stay for time  • move slowly back • repeat for different  ng -pulse  with probability exp(-/T1) time

  17. T1 measurement: experiment

  18. Superconducting charge qubits readout group control substrate T1 T2 dc probe NEC pulse pulse probe SiNx 5 ns 5 ns trap+SET switching current 1.8 s 0.5 s SiO2 -waves Saclay 1 s SiNx 100 ns pulse SiO2 Chalmers RF-SET 5 ns 5 ns

  19. What next? 1. Qubit readout: dc probe  pulsed probe trap + SET 2. Qubit control: NA pulses  -waves 3. Materials: qubit Al  Nb? substrate SiNx SiO2 4. Dependence of T1 and T2 on (1-3)

  20. Nb SET Nb lead Nb island AlOx Barrier

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