1. Two Level Systems and Kondo-like traps as possible sources of decoherence in superconducting qubits Lara Faoro and Lev Ioffe Rutgers University (USA)

2. Outline Decoherence in superconducting qubit [ experimental state of the art ]: low frequency noise (1/f noise) high frequency noise (f noise) We discuss two possible microscopic mechanisms for the fluctuators weakly interacting quantum Two Level Systems (TLSs) environment made by Kondo-like traps TLSs model: significant source of noise detailed characteristics of the noise power spectrum are in a qualitative and quantitative disagreement with the data Kondo-like traps model: significant source of noise agreement with most features observed in the experiments

3. What are the sources of noise? There are several experiments in different frequency regimes but the dominant source of noise is yet to be identified! Electromagnetic fluctuations of the circuit (gaussian) Discrete noise due to fluctuating background charges (BC) trapped in the substrate or in the junction

4. ? Experimental picture of the noise power spectrum Zimmerli et al. 1992 Visscher et al. 1995 Zorin et al. 1996 Kenyon et al. 2000 Nakamura et al. 2001 Astafiev et al. 2004 Wellstood et al. 2004 T Origin of both types of noise are the same ?

5. Low frequency noise ( 1/f ) 1/f spectrum up to frequency ~ 100-1000 Hz. [ where is the upper cut-off ??? ] The intensity is in the range of at f=10Hz some samples clearly produce a telegraph noise but 1/f spectrum points to numerous charges participating in generating the noise. This noise dominates and it is greatly reduced by echo technique. - Temperature dependence of the noise high frequency noise ( f )

6. Theoretical analysis Upper level: use a proper model to study decoherence. “fluctuators model” and not spin boson model Paladino, Faoro, Falci and Fazio (2002) Galperin, Altshuler, Shantsev (2003) Lower level: understanding which is the microscopic mechanism of decoherence that originate the fluctuators Faoro, Bergli, Altshuler and Galperin (2004) Faoro and Ioffe (2005)

7. Quantum TLSs model with The effective strength of the interactions is controlled by and it is always very weak. Many TLSs interacts via dipole-dipole interactions: interaction with low energy phonons T>100 mk Relaxations for TLSs

8. Dipole and qubit interaction Each dipole induces a change in the island potential or in the gate charge i.e. barrier substrate Charge Noise Power Spectrum: Rotated basis: ++++++ ------

9. Dephasing rates for the dipoles pure dephasing: The weak interaction causes a width in each TLS at low frequency some of the TLSs become classical Effective electric field N.B: density of thermally activated TLSs enough (Continuum)

10. Relaxation rates for the dipoles Fermi Golden Rule But in presence of large disorder, some of TLSs: These dipoles become classical and will be responsible for 1/f noise

11. at high frequency white!

12. In the barrier... The density of TLSs ~ too low! Astafiev et al. 2004 Strongly coupled TLS

13. In the substrate... Comparison with experiments : Astafiev et al. 2004

14. at low frequency it has a 1/f dependence for it has only linear dependence on Temperature it has intensity in agreement with experimental data

15. What did we learn from the dipole picture? dependence Search for fluctuators of different nature... Number of thermally activated TLSs dependence

16. Andreev fluctuators model qubit correlations are short range amplitude of oscillations increases with increasing  Faoro, Bergli, Altshuler and Galperin (2004) dependence

17. Kondo-like traps model Kondo Temperature

18. Properties of the ground state and the localized excited state Weak coupling Strong coupling

19. “Physics” of the Kondo-like traps Slow processes Fast processes barrier superconductor Superconductor coherence lenght Density of states close to the Fermi energy bare density weight of the Kondo resonance Transition amplitude:

20. at high frequency This noise is dominated by fast tunneling processes between traps effectively the motion of electrons between trap acts as resistor R From the conductance G we calculate the resistance R The noise power spectrum raises linearly with the frequency! NB: Andreev fluctuators have the same but … and

21. at low frequency in the barrier : experimental value: estimates :

22. We have discussed a novel microscopic mechanism (Kondo-like traps) that might be the dominant source of noise for dephasing But the “physics” of the device is complex : Kondo-like + TLSs TLSs are “killed” by the T-dependence! Our analysis cannot be done in greater details, due to the lack of an analytical theory of kondo-like impurites with superconductor Try to measure 1/f noise after suppressing the superconductivity. We expect reduction of 1/f noise Reasonable level of noise even only in the barrier. Different substrates no changes in the intensity of the noise (NEC) relevant for phase qubit. Conclusions