1. P. Bertet Quantum Transport Group, Kavli Institute for Nanoscience, TU Delft, Lorentzweg 1, 2628CJ Delft, The Netherlands A. ter Haar A. Lupascu J. Plantenberg F. Paauw J. Eroms C.J.P.M. Harmans J.E. Mooij I. Chiorescu Y. Nakamura Photon-noise induced dephasing in a flux-qubit G. Burkard D. DiVicenzo +

2. Introduction Dephasing ? (weak coupling) Very slow and strongly coupled fluctuators Underdamped modes strongly coupled to qubit E. Paladino et al., Phys. Rev. Lett. 88, 228304 (2002) M. Thorwart et al., Chem. Phys. 296, 333 (2004)

3. Qubit dephased by photon noise Temperature T Dispersive regime : Shift of oscillator frequency Shift of qubit frequency Coupling Quality factor Q

4. Qubit dephased by photon noise Photon fluctuations Qubit frequency Dephasing factor Phase shift with around A. Blais et al., PRA 69, 062320 (2004) Dephasing time T 

5. 2) Thermal fluctuations in the non-driven oscillator Thermal field : D. Schuster et al., PRL 94, 123602 (2005) Cf also M. Brune et al., PRL 76, 1800 (1996) Qubit dephased by photon noise 1) Oscillator driven by a coherent field Measurement induced dephasing Photon shot noise

6. Flux-qubit coupled to SQUID plasma mode Our circuit : Flux-qubit DC-SQUID plasma mode Optimal points (with respect to photon noise) whenever Our measurements : qubit coherence limited by thermal fluctuations in plasma mode 1) Quantitative agreement with formula 2) Thanks to our circuit geometry, coupling constants

7. The flux-qubit QQ Josephson junctions 1 control parameter Al/AlOx/Al junctions by shadow evaporation + e-beam lithography

8. 0.480.500.52 0 40 80 Frequency(GHz) |0> |1> |2> |3>  Q /2  qubit Qubit energy levels E J =225GHz E C =7.2GHz  =0.76

9. Persistent-current Property of states |0> and |1> : Useful to measure the qubit state -0.020.000.02 -300 0 300 I(nA) I0I0 I1I1  Q -  -I p +I p |0> |1> |0>

10. Frequency (GHz) 0.5 0 5 10 01  Q /2   Two-level approximation Flux-noise optimal point In thebasis, (cf Saclay)

11. Control of the qubit state Arbitrary state Rotation axis : (  ) Angle :   x  x +  x cos(2  t+  ) Microwave pulse  t

12. Our detector : a hysteretic DC-SQUID as on-chip comparator 01 0 4 Ic (  A )  Sq /  0 Persistent-current and detection of the qubit state

13. Qubit inductively coupled to SQUID I C depends on qubit state (i) Persistent-current and detection of the qubit state P(1)  P sw 5.45.6 0 50 100 Pswitch (%) Current I b (  A ) |0> Theoretical |1> relaxation P(1)=P sw

14. Persistent-current and detection of the qubit state SQUID shunted by a capacitor PLASMA MODE

15. Coupling of the qubit and the plasma mode Complex : qubit Circ current J Plasma mode current M dJ/dI b (I b ) 2 different effects : a) Effective inductive coupling with tunable mutual inductance b) Flux dependent SQUID Josephson inductance

16. SQUID circulating current dJ/dI b =0 dJ/dI b (Ib) Ideal symmetric SQUID : dJ/dIb(0)=0 Including asymmetries : Decoupling current

17. Coupling of the qubit and the plasma mode 1) Measurement shift -0.020.000.02 Energy (GHz) 2 1 Current (  A) (e/I p )  2) Coupling hamiltonian NON RESONANT inductiveFlux-dependent Josephson inductance

18. The sample IbIb V Microwave antenna C sh G. Burkard et al., cond-mat/0405273

19. 1k 3k3k The setup

20. Qubit spectroscopy time trigger Ib pulse read-out tt Microwave pulse at frequency f Parameters :  =5.85GHz, I q =270nA B -0.010.000.01 0 5 10 15 20 25 Larmor frequency (GHz) (  x -  0 /2)/  0

21. Plasma mode spectroscopy time Microwave pulse at frequency f IbIb Switching probability enhancement if f= p : resonant activation Resonant activation peak : Typical width : 20-50MHz C sh =12pF, L=170pH (design) P. Bertet et al., Phys. Rev. B 70, 100501 (2004)

22. Evaluating the coupling constants Measure (I b ) Spectroscopy Ib*Ib* -0.0010.0000.001 5.5 6.0 6.5 Frequency (GHz) (  x -  0 /2)/  0 I b =0  A I b =0.6  A

23. Evaluating the coupling constants Measure (I b ) Spectroscopy Ib*Ib* g1g1 g2g2 Ib*Ib* 0.00.30.6 -0.2 0.0 Coupling (GHz) I b (  A)

24. Frequency shift ac-Zeeman shift. Always >0 Frequency shift  0 due to g 1 -20MHz +26MHz 0MHz Frequency shift  0 due to g 2 Shift has same sign as epsilon  =0

25. Frequency shift  0 =0 Quantitative prediction : optimal point for photon noise Optimal point for flux/current noise Optimal point For flux-noise Optimal point for photon noise

26. Characterizing decoherence (1) : spectroscopy 5 types of experiments : Low-power spectroscopy Rabi oscillations T 1 measurements Spin-echo measurements At decoupled optimal point (I b =I b *,  =0) 5.525.565.60 68 78 Pswitch (%) Freq F(GHz) f 1,w 1 f 2,w 2 Strongly coupled 2-level fluctuator Ramsey fringes Thermal photon noise : « high frequency »

27. Pswitch (%) 012 100 200 Pulse duration Dt (  s) Non-exponential because low-frequency noise Characterizing decoherence (2) : Rabi oscillations At decoupled optimal point (I b =I b *,  =0) Dt MW = Q 0.000.06 60 80 Pulse length(  s)

28. Characterizing decoherence (3) : T 1 measurements Dt  01020 60 80 Pswitch (%) Delay Dt (  s ) - Exponential decay At decoupled optimal point (I b =I b *,  =0)

29. Characterizing decoherence (4) : Ramsey fringes 0.00.10.20.30.4 60 80 100 120 140 160 Pswitch (%) Delay between pulses (microseconds) T  /2  /2 T  /2 MW - Q Difficult to extract dephasing time … At decoupled optimal point (I b =I b *,  =0)

30. T  /2 =2.2  s Bertet et al., cond-mat/0412485 Characterizing decoherence (5) : spin-echo sequence tt  /2  T  /2 T  /2 /2

31. T 1 dependence on I b Ib*Ib* Away from I b *, T 1 limited by coupling to measuring circuit

32. Spin-echo and t2 dependence on I b and  I b =I b * g 1 =0 T echo t 2 =2/  (w 1 +w 2 ) Best coherence :  =0 (optimal point) I b =0  A g 1 =80MHz Best coherence :  =  m <0 NOT LIMITED by flux-noise

33. Decoherence due to qubit-plasma mode coupling mm  0 =0 Dephasing minimum for spin-echo and Ramsey when  0 =0 Quantum coherence limited by photon noise

34. I b =I b * g 1 =0 T=70mK, Q=150 I b =0  A g 1 =80MHz Spin-echo and t 2 dependence Quantitative agreement

35. Conclusion Long spin-echo time (4  s) at optimal bias point Dephasing due to thermal fluctuations of the photon number in an underdamped resonator coupled to the qubit : very general situation Case of a flux-qubit coupled to the plasma mode of its SQUID detector By tuning coupling constants, could decouple qubit from photon noise Quantitative agreement with simple model for spin-echo time 2 questions : - mechanism for low-freq noise ? (charge or critical current noise ?) - effect of dispersive shifts in usual spin-boson model ?