Lara Faoro and Lev Ioffe

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

4. Experimental picture ofthe noise power spectrum ? T Origin of both types of noise are the same ? 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

5. Low frequency noise ( 1/f ) • - Temperature dependence of the noise • 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. 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 Relaxations for TLSs • interaction with low energy phonons T>100 mk • Many TLSs interacts via dipole-dipole interactions: The effective strength of the interactions is controlled by and it is always very weak.

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 • The weak interaction • causes a width in each TLS • at low frequency some of the TLSs become classical Effective electric field pure dephasing: 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! Strongly coupled TLS Astafiev et al. 2004

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

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 Number of thermally activated TLSs dependence Search for fluctuators of different nature ...

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

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 Density of states close to the Fermi energy bare density weight of the Kondo resonance barrier Transition amplitude: Fast processes superconductor Slow processes Superconductor coherence lenght

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 : estimates : experimental value:

22. Conclusions • 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.