1. Non-linear driving and Entanglement of a quantum bit with a quantum readout Irinel Chiorescu Delft University of Technology

2. Quantum Transport group Flux-qubit team Prof. J.E. Mooij Prof. Kees Harmans technical staff students visitors Yasunobu Nakamura (NEC Japan, 2001-2002) Kouichi Semba (NTT Japan, 2002-2003) postdocs Patrice Bertet Irinel Chiorescu PhD students Alexander ter Haar Adrian Lupascu Jelle Plantenberg collaborations NTT, NEC, MIT, TU Delft (theory), U Munich acknowledgements FOM (NL), IST (EU), ARO (US)

3. Outline basics about the flux-qubit qubit initialization, operation & readout Rabi oscillations, Ramsey fringes present status - extreme stability during qubit operation - strong microwave driving multi-photon induced coherent oscillations experimental demonstration of entanglement quantum bit quantum readout (squid) conclusions

4. 3 Josephson-junctions Quantum Bit superconducting loop, with 3 Josephson junctions 2 are identical and the 3rd is smaller (  Josephson Potential: J.E. Mooij et al, Science, 285, 1036 (1999) U=  E J I u = U/E J u = 2 +  - cos  1 - cos  2 -  cos(  2 -  1 + 2  f)  1 = (  1 -  2 )/2,  2 = (  1 +  2 )/2 u = 2(1 - cos  1 cos  2 ) + 2  sin 2 (  1 -  f)

5. Josephson potential - phase space T in T out  =0.8, f=0.5 2 wells separated by a barrier for f=0.5, symmetric barrier

6. Flux Qubit – two level system C. van der Wal et al, Science, 290, 773 (2000) see also, J. Friedman et al, Nature, 406, 43 (2000) Exact diagonalisation: two levels at the bottom of the spectra Two wells separated by a barrier Persistent currents of opposite direction |  and |  SQUID critical current  qubit persistent current Microwave induced excitation  level structure 0.5

7. Coherent oscillations Rabi oscillations microwave excitation with frequency  and amplitude A coherent rotations with  Rabi  A Bloch sphere |  >=  |  >+  |  > |g>|g> |e>|e>  =  E  Rabi  A MW pulse A Magnetic resonance with a single, macroscopic quasi-spin

8. Qubit operated at the magic point Hamiltonian and eigenstates H = -  /2  z –  /2  x tan2  =  /  |0  = cos  |  + sin  |  |1  = -sin  |  + cos  |  |0  |1  |  |  |0  |1  Initialization,  = 0 |Q  = |0  = (|  +|  )/  2 Operation,  = 0 |Q  =  |0  +  |1  Readout,  > 0 |Q  =  |0  +  |1  |Q  MW pulse ON (rotating frame) MW pulse OFF (lab frame) |Q  = |  | 2 - |  | 2

9. Switching event measurements Device qubit merged with the SQUID strong coupling L Readout bias current to switch the SQUID ramping generates the shift (preserving the qubit information) switching current depends on qubit state (spin up or down) pulse height: I sw0 < I b < I sw1 I pulse ~30ns rise/fall time t

10. Single shot resolution (in an ideal sample)

11. Sample E J /E C = 34.65 E C = 7.36 GHz  = 0.8  = 3.4 GHz I p = 330 nA large junctions I c = 2  A strong coupling L=10 pH shunt capacitance C = 10 pF bias line R b = 150  voltage line R v = 1 k 

12. Cavity, wiring

13. Qubit spectroscopy

14. Rabi: pulse scheme RF line: one microwave pulse with varying length bias line: Ib pulse time trigger MW pulse Ib pulse read-outoperation voltage line: detection of the switching pulse

15. Rabi coherent oscillations F Larmor = 6.6 GHz decay time  150 ns I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, J.E. Mooij, Science, 299, 1869 (2003)

16. Fast oscillations

17. Ramsey interference Ramsey: two  /2 pulses with varying time in between time trigger Ib pulse read-outoperation  /2 free run  /2

18. Ramsey fringes F L = 5.61 GHz

19. Ramsey interference Ramsey: decoherence time    20 ns F L = 5.7 GHz, dF= 220 MHz, TRamsey: 4.5 ns

20. Relaxation measurements one  pulse and read-out pulse delayed time trigger Ib pulse read-outoperation  delay time

21. Sample (2003) heat sink qp traps quasi-particle traps strong coupling with the MW line heat sinks on the current and voltage lines current injection: high frequency noise  ground via the shunt capacitance IbIb V

22. Spectroscopy level repulsion 5.866 GHz persistent current 272 nA spectroscopy peaks: Q – qubit  –plasma frequency 2.91GHz Q+/-  – sidebands 2-, 3-photon peaks

23. Rabi oscillations at the magic point low coherence time, but extreme stability of the qubit energy levels

24. Ramsey fringes at the magic point coherence time ~15-20 ns  = 5.856 GHz

25. Coherence time at the magic point coherence time ~20 ns (mostly limited by the relaxation time) when optimizing the readout   ~120 ns

26. Spectroscopy spectroscopy peaks: Q – qubit  –plasma frequency 2.91GHz Q+/-  – sidebands 2-, 3-photon peaks

27. Multi-photon processes

28. Rabi frequency:  n =  J n (  mw /F L )  can be renormalized by noise (   <  ) ~ power calibration (check the b fit parameter)

29. Coherent rotations in the non-linear regime several peaks in the Fourier transform of the oscillations Rabi frequencies higher than the Larmor frequency

30.  x =0.1 GHz 00  0 Numerical simulations H/h=  0  z /2+  x  x /2+(  1  x cos  t)/2

31. Qubit entangled with a quantum readout QUBIT, two-level systemSQUID, harmonic oscillator hphp hF L microwave field MI q I circ...... |0 , |1  |0 , |1 ,..., |N  |00  |10  |11  |01  |12  |02 ... FLFL pp

32. Coherent oscillations of the coupled system qubit Larmor frequency 7.16 GHz plasma frequency : 2.91 GHz coupled system at 10.15 GHz |10  |11  |01  |00  blue-side band

33. Blue-side band qubit Larmor frequency 6.43 GHz, plasma frequency : 2.91 GHz coupled system at 9.38 GHz |10  |11  |01  |00  either  pulse or incoherent population with a bright pulse

34. Red-side band qubit Larmor frequency 6.43 GHz plasma frequency : 2.91 GHz coupled system at 3.52 GHz |10  |11  |01  |00  after  after 2  

35. Conclusion entanglement of the qubit with its quantum readout multi-photon induced coherent oscillations very strong (non-linear) qubit driving, F Rabi >F L qubit operated at the “magic point” extreme stability of the qubit operation  rel  1  s,  Rabi  150 ns Ramsey interference: decoherence time  20 ns

36. Switching curves

38. Spin-echo experiments spin-echo: two  /2 pulses and one  pulse in between with varying position time trigger Ib pulse read-outoperation  /2  F L = 5.7 GHz, dF= 220 MHz, TRamsey: 4.5 ns, Tspin-echo: 2.3 ns

39. Signal decay in spin-echo spin-echo: max signal decay time T 2  30 ns

40. Automatic shift of  Q and switching qubit merged with the SQUID big junctions strong coupling L large circulating currents bias current generates a shift in  qubit switching occurs far from degeneracy

41. Linear MW field H/h=  0  z /2+  x  x /2+(  1  x cos  t)/2 for a rotating mw field, the Rabi frequency is  1 (one peak in the FFT of oscillations)

42. H/h=  0  z /2+  x  x /2+(  1  x cos  t)/2 Symmetry point:  0 =5.86 GHz,  x =0 2020 4040 6060 “usual” Rabi ~7.1GHz