1. DC-squid for measurements on a Josephson persistent-current qubit Applied Physics Quantum Transport Group Alexander ter Haar May 2000 Supervisors: Ir. C.H. van der Wal Prof. dr. ir. J.E. Mooij

2. Introduction 3  m

3. Introduction Superconductor   Superconductor    Insulator 1  m

4. Introduction Quantum mechanics State of the system: Left OR Right Classical mechanics: Quantum mechanics: State of the system: Left AND Right

5. |  |  |  |  |0  |1> |0  |1  Introduction Two level system: Two level systems Two currents in opposite direction creating an opposite magnetic flux: E1E1 E0E0 3  m

6. Counts Introduction I sw (nA)‏ Flux (  0 )‏ The squid as a magnetometer 2000 100 120 140 160 180 I sw (nA)‏ 0 I bias (nA)‏ V (  V)‏ Switching point

7. Motivation Study dynamical behavior of a quantum mechanical 2-level system using a dc-squid. Use dynamics of this quantum 2-level system for quantum computing.

8. Introduction Factorize large numbers into integers.

9. Goal of this research Understand the dc-squid as a device for measuring the small magnetic flux signal of a quantum system.

10. Outline Introduction to Josephson junction structures Analysis of the dc-squid Measurements on a single junction Measurements on the dc-squid Application of the dc-squid The qubit system Measurements on the qubit system

11. Josephson junction structures E   I bias = 0 0<I bias < I c I bias = I c I bias Introduction m C x  I bias (nA)‏ V (  V)‏ Switching point C

12. Josephson junction structures Statistical escape mechanisms from the zero voltage state: Hopping over the barrier Quantum tunneling through the barrier Escape mechanisms I sw (nA)‏ 100 120 140 160 180 2000 Counts 0 E 

13. Josephson junction structures Tunneling from higher levels within the potential well. Escape mechanisms E 

14. Measurements on the single junction T=30mK T=40mK T=60mK T=80mK T=120mK 40 60 I sw (nA)‏ Counts We can use the histograms to calculate the escape rates from the zero voltage state.

15. Measurements on the single junction I sw (nA)‏ Counts  (1/s)‏

16. Measurements on the single junction  (1/s)‏ I sw (nA)‏ 50 60 70 T=30mK T=40mK T=60mK T=80mK T=120mK 10 6 10 4 10 6 10 4 10 6 10 4 10 6 10 4 10 6 10 4

17. The dc-squid f I bias introduction     bias = 0.5 (       cir = 0.5 (      f C I cir 100  m

18. The dc-squid The internal degree of freedom E  cir  bias

19. The dc-squid Quantum fluctuations Quantum fluctuations in the flux through the squid loop: Qubit signal:  prod  0.001  0 <  

20. Measurements on the dc-squid Comparing (nA)‏  (nA)‏ T (mK)‏ Interpolated data for the squid. Single Junction.

21. Counts T = 20 mK T = 40 mK T = 80 mK T = 160 mK T = 640 mK T = 320 mK I switch (nA)‏ Measurements on the dc-squid Histograms of the small test squid versus temperature The test squid

22. Measurements on the dc-squid The dc-squid C= 2pF C= 0.2pF C=0.02pF 100 150 200 10 6 10 5 10 4 10 3 10 2 3000 2000 1000 T=30 mK  (1/s)‏ I switch (nA)‏

23. Measurements on the dc-squid Comparing Conclusions: Quantum fluctuations in the internal degree of freedom play an important role in widening the histograms. Quantum fluctuations in the internal degree of freedom are much larger than the qubit signal.

24. The qubit system I cir (I c )‏ f qubit (    E (E J )‏ f 3  m

25. Measurements on the qubit system I sw (nA)‏ f squid (nA)‏ f qubit

26. - linear trend (nA)‏ Measurements on the qubit system f qubit

27. Measurements on the qubit system - linear trend (nA)‏ f qubit

28. Measurements on the qubit system - linear trend (0.4 nA/division)‏ 9.711 GHz 8.650 GHz 6.985 GHz 5.895 GHz 4.344 GHz 3.208 GHz 2.013 GHz 1.437 GHz 1.120 GHz 0.850 GHz 0.498 0.5 0.502 f qubit

29. Measurements on the qubit system ff Frequency (Ghz)‏ f qubit (    E (E J )‏

30. Conclusions Quantum fluctuations in the internal degree of freedom of the dc-squid play an important role in widening the histograms of the dc-squid. Spectroscopy measurements show the existence of an energy gap at a frustration of half a flux quantum indicating the two energy levels repel at that point. dc-squid measurements

31. Questions ?

32. Outline