Decoherence in superconducting nanocircuits: Classical vs Quantum noise sources

Elisabetta Paladino

DMFCI Universita' di Catania, MATIS CNR-INFM & DMFCI, Catania, Spain

The main limitation toward the relization of controllable and reliable quantum circuits as those allowing quantum computation, is decoherence due to material (and device) dependent noise sources. In superconducting nanocircuits a particularly detrimental role is played by fluctuating impurities located in the insulating material surrounding the qubit and responsible for charge noise and flux/E_J noise. Backgorund charges are known to be responsible for low-frequency 1/f noise, moreover experiments with Josepshon devices suggested that spurious two-level systems may also affect high-frequency noise [1]. Connection between low and high-frequency noise features have been suggested in the recent experiment Ref [2]. Different microscopic mechanisms [3] and effective models [4] have been proposed to explain the observed spectral features. The possibility that both low- and high-frequency noises may be produced by an ensemble of coherent two-level systems characterised by a broad distribution of parameters and coupling strengths has been explored [4].

In this perspective some questions naturally arise. First of all a characterisation of the effects on the qubit dynamics played by coherent quantum impurities is needed. Furthermore the interplay with incoherent impurities responsible for random telegraph noise has to be analysed and the question of the observability of the different effects in the decay of the coherences in present day experiments has to be addressed. To this end one has to also keep in mind that, either because of limited control on protocols (responsible for instance of inhomogeneous broadening ) or because protocols effectively decouple part of noise sources (f.i. echo protocol), nanodevices often operate in regimes of limited sensitivity to details of the nature of the noise sources.

We propose [5] the following classification of the noise sources according to the effects on the controlled dynamics rather than on their specific nature: "quantum noise" whose effect is to trigger spontaneous decay; "adiabatic noise" whose main effect is analogous to inhomogeneous broadening in NMR and "strongly coupled noise", producing the analogue of uncontrollable chemical shifts. Each class has its specific approximation scheme which does not work (or it is impractical) for other classes of noise.

The time evolution of a superconducting qubit in the simultaneous presence of low frequency non-Markovian and non-Gaussian noise, and of high frequency quantum noise is analyzed. We present different techniques ranging from analytical treatments based on generalized master equation and on path-integrals to numerical approaches based on stochastic Schroedinger simulations and exact diagonalization methods. The developped a theory is flexible enough to work for different coupling conditions, i.e. from weak coupling to strong coupling, and from classical to quantum regime [6]. By exploiting these different techniques we are able to deal with the various typical scenarios for decoherence in the solid state.

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[5] G. Falci, A. D'Arrigo, A. Mastellone, E. Paladino, Phys. Rev. Lett., 94, 167002,(2005).
[6] E. Paladino, M. Sassetti, G. Falci, J. Stockburger, U. Weiss in prep. 06