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arXiv:cond-mat/0501301 · Physical Review B

Dephasing by a nonstationary classical intermittent noise

Josef Schriefl, Maxime Clusel, David Carpentier, Pascal Degiovanni

Published Jul 14, 2005• 16 citations
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Abstract

We consider a phenomenological model for a $1∕{f}^{\ensuremath{\mu}}$ classical intermittent noise and study its effects on the dephasing of a two-level system. Within this model, the evolution of the relative phase between the $\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}⟩$ states is described as a continuous time random walk (CTRW). Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the nonstationarity and pronounced non-Gaussian features of this noise, including some anomalous and aging dephasing scenarios.

DOI
10.1103/physrevb.72.035328

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We consider a phenomenological model for a 1∕f\ensuremathμ1∕{f}^{\ensuremath{\mu}}1∕f\ensuremathμ classical intermittent noise and study its effects on the dephasing of a two-level system. Within this model, the evolution of the relative phase between the \ensuremath∣\ifmmode±\else\textpm\fi⟩\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}⟩\ensuremath∣\ifmmode±\else\textpm\fi⟩ states is described as a continuous time random walk (CTRW). Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the nonstationarity and pronounced non-Gaussian features of this noise, including some anomalous and aging dephasing scenarios.
We investigate the influence of nonstationary 1/ f μ noise, produced by interacting defects, on a quantum two-level system. Adopting a simple phenomenological model for this noise we describe exactly the corresponding dephasing in various regimes. The nonstationarity and pronounced non-Gaussian features of this noise induce new anomalous dephasing scenarii. Beyond a history-dependent critical coupling strength, the dephasing time exhibits a strong dependence on the age of the noise and the decay of coherence is not exponential.
Motivated by recent experiments with Josephson qubits we propose a new phenomenological model for 1/f noise due to collective excitations of interacting defects in the qubit's environment. At very low temperatures the effective dynamics of these collective modes are very slow leading to pronounced non-Gaussian features and nonstationarity of the noise. We analyze the influence of this noise on the dynamics of a qubit in various regimes and at different operation points. Remarkable predictions are absolute time dependences of a critical coupling and of dephasing in the strong coupling regime.
We theoretically study the dynamical dephasing of a quantum two level system interacting with an environment which exhibits non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss the quantum dephasing dynamics of the system and the non-Markovian character exhibiting in the dynamical dephasing induced by non-Markovian random telegraph noise. We show that the dynamical dephasing of the quantum system does not always exhibit non-Markovian character which results from that the non-Markovian character in the dephasing dynamics depends both on the environmental non-Markovian character and the interaction between the system and environment. In addition, the dynamical dephasing of the quantum system can be modulated by the external modulation frequency of the environment. This result is significant to quantum information processing and helpful for further understanding non-Markovian dynamics of open quantum systems.
This thesis deals with different aspects of statistical physics of correlated systems. The first part is related to the fluctuations of global quantities in correlated systems. Various studies clam that such fluctuations are well described by the BHP distribution. We use the 2D Ising model to test and quantify this proposition. Using observations from Monte Carlo simulations, we build a theoretical analysis, showing that the apparent universality of the BHP distribution is related to the Gaussian model obtained from perturbation expansion. Deviations from BHP, due to a non-linear term are expected. In the second part we consider a new model for a 1/f classical intermittent noise and study its effects on the dephasing of a two-level system.Within this model, the evolution of the relative phase between the two states is described as a continuous time random walk. Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, including some new anomalous and aging dephasing scenarios. In the last part we present an alternative method to obtain some exact results for the 2D Ising model with a boundary magnetic field, for a finite size system. This method is a generalisation of ideas from Plechko presented for the 2D Ising model in zero field, based on the representation of the Ising model using a Grassmann algebra. A Gaussian 1D action is obtained for a general configuration of the boundary magnetic field. When the magnetic field is homogeneous, our results are in agreement with McCoy and Wu's previous work. This 1D action is used to compute in an efficient way the free energy in a special case of inhomogeneous boundary magnetic field. This allows us to compute the phase diagram of a wetting transition induced by a boundary defect.
We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites, and attention is focused on non-Gaussian telegraph noise, going beyond the usual assumption of fast Gaussian noise. We observe the emergence of two different dynamical behaviors for the walker, corresponding to two opposite noise regimes: slow noise (i.e., strong coupling with the environment) confines the walker into few lattice nodes, while fast noise (weak coupling) induces a transition between quantum and classical diffusion over the lattice. A phase transition between the two dynamical regimes may be observed by tuning the ratio between the autocorrelation time of the noise and the coupling between the walker and the external environment generating the noise. We also address the non-Markovianity of the quantum map by assessing its memory effects, as well as evaluating the information backflow to the system. Our results suggest that the non-Markovian character of the evolution is linked to the dynamical behavior in the slow noise regime, and that fast noise induces a Markovian dynamics for the walker.
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions such as (exp(i ∫(0)(t) Q(s)ds)), where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous-time random walk describes an environment that undergoes slow steplike changes in time. It also has a well-defined Gaussian limit and so allows for non-Gaussian and Gaussian stochastic dynamics to be studied within a single framework. We apply the results to extract qubit-lattice interaction parameters from dephasing data of P-doped Si semiconductors (data collected elsewhere) and to calculate the two-dimensional spectrum of a three-level harmonic oscillator undergoing random frequency modulations.