Pure dephasing due to damped bistable quantum impurities E. Paladino a,b, * , M. Sassetti c , G. Falci a,b , U. Weiss d a MATIS-Istituto Nazionale per la Fisica della Materia, Catania, Italy b Dipartimento di Metodologie Fisiche e Chimiche (DMFCI), Universita ` di Catania, Viale Andrea Doria 6, 95125 Catania, Italy c Dipartimento di Fisica, INFM-Lamia, Universita ` di Genova, Via Dodecaneso 33, 16146 Genova, Italy d II Institute fu ¨ r Theoretische Physik, Universita ¨ t Stuttgart, Pfaffenwaldring 57, Germany Received 1 June 2005; accepted 12 August 2005 Available online 15 November 2005 Abstract We study the dynamics of a spin (qubit) coupled to a bistable quantum impurity interacting with a Gaussian bath modeled by a ohmic spin boson model. For white noise the complete dynamics in the four-dimensional Hilbert space is analyzed within a Lindblad formalism. For ohmic damping at finite temperatures we resort to a functional integral approach. We show how different dynamical regimes and crossover of the nonlinear spin boson system are probed by the qubit dynamics. Ó 2005 Elsevier B.V. All rights reserved. PACS: 03.65.Yz; 03.67.Lx Keywords: Decoherence; Quantum statistical methods; Quantum computation 1. Introduction The quantum dynamics of dissipative two state systems has been the subject of intense research in the last thirty years [1,2]. This topic has recently received a great deal of interest in connection with quantum information pro- cessing. The extraordinary progress in nanofabrication techniques has in fact paved the way to the observation of coherent effects at the nanoscale [3,4]. Due to the many kinds of low energy excitations typical of the solid state these devices are extremely sensitive to decoherence and dissipation. Much of the efforts in the analysis of decoherence in quantum logic devices has so far mainly focused on para- digmatic models, like harmonic baths [5,6] or nonlinear spin-baths [7]. In many situations the effect of nonlinear baths, despite of their non-Gaussian nature, can be cap- tured by lowest order correlators of the bath variables, i.e., spectral densities or power spectra [2], this description being exact for harmonic baths. However, a more detailed information on the statistical properties of the environment is needed when the bath has memory on the typical scales of the system dynamics [8,9]. Experiments with solid state qubits [3] have revealed the sensitivity of these nanostructures to decoherence mecha- nisms which are strictly material, device and protocol dependent. Often these features may be attributed to the interaction with nonlinear and non-Markovian baths. In superconducting qubits background charge fluctuators rep- resent the dominant decoherence source and are presently considered responsible of a variety of effects, ranging from 1/f [10] to random telegraph noise. From recent spectro- scopic data, the existence of coherent interaction of a superconducting phase-qubit with a single bistable resona- tor has been inferred [11]. The analysis of these effects requires the introduction of nonlinear bath models and methodologies which go beyond standard weak coupling approaches [8]. In [9], background charges in superconducting qubits have been modeled as an ensemble of Fano impurities [12] whose incoherent switching produces a bistable fluctuation of 0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.08.065 * Corresponding author. Tel.: +390957382803; fax: +39095333231. E-mail address: epaladino@dmfci.unict.it (E. Paladino). www.elsevier.com/locate/chemphys Chemical Physics 322 (2006) 98–107