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arXiv:0707.3857 · Physical Review A

Transfer matrix solution of a model of qubit decoherence due to telegraph noise

Bin Cheng, Qiang-Hua Wang, Robert Joynt

Published Aug 7, 2008• 37 citations
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Abstract

We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be applied to a qubit subject to an arbitrary combination of dephasing and relaxational telegraph noise, in contrast to existing nonperturbative methods that treat only one or the other of these limits. Hence we are able to investigate the crossover from pure dephasing noise to pure relaxational noise in detail. New results at strong coupling include the full qubit dynamics on time scales short compared with the environmental correlation times, which reveals unexpected oscillations and induced magnetization components and strong violations of the widely used relation $1∕{T}_{2}=1∕2{T}_{1}+1∕{T}_{\ensuremath{\phi}},$ which is a result of perturbation theory. We also discuss the effects of bang-bang and spin-echo controls of the qubit dynamics in general settings of the telegraph noises. Finally, we discuss the extension of the method to the cases of many telegraph noise sources and multiple qubits. The method still works when white noise is also present.

DOI
10.1103/physreva.78.022313

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We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be applied to a qubit subject to an arbitrary combination of dephasing and relaxational telegraph noise, in contrast to existing nonperturbative methods that treat only one or the other of these limits. Hence we are able to investigate the crossover from pure dephasing noise to pure relaxational noise in detail. New results at strong coupling include the full qubit dynamics on time scales short compared with the environmental correlation times, which reveals unexpected oscillations and induced magnetization components and strong violations of the widely used relation 1∕T2=1∕2T1+1∕T\ensuremathϕ,1∕{T}_{2}=1∕2{T}_{1}+1∕{T}_{\ensuremath{\phi}},1∕T2​=1∕2T1​+1∕T\ensuremathϕ​, which is a result of perturbation theory. We also discuss the effects of bang-bang and spin-echo controls of the qubit dynamics in general settings of the telegraph noises. Finally, we discuss the extension of the method to the cases of many telegraph noise sources and multiple qubits. The method still works when white noise is also present.
We study the dissipative dynamics of a qubit that is afflicted by classical random telegraph noise and is subject to dynamical decoupling. We derive exact formulas for the qubit dynamics at arbitrary working points in the limit of infinitely strong control pulses (bang-bang control), and we investigate in great detail the efficiency of the dynamical decoupling techniques for both Gaussian and non-Gaussian (slow) noise at qubit pure dephasing and at optimal point. We demonstrate that control sequences can be successfully implemented as diagnostic tools to infer spectral properties of a few fluctuators interacting with the qubit. The analysis is extended in order to include the effect of noise in the pulses, and we give upper bounds on the noise levels that can be tolerated in the pulses while still achieving an efficient dynamical decoupling performance.
We present a method for the solution of the behavior of an ensemble of qubits in a random time-dependent external field. The forward evolution in time is governed by a transfer matrix. The elements of this matrix determine the various decoherence times. The method provides an exact solution in cases where the noise is piecewise constant in time. We show that it applies, for example, to a realistic model of decoherence of electron spins in semiconductors. Results are obtained for the nonperturbative regimes of the models, and we see a transition from weak relaxation to overdamped behavior as a function of noise anisotropy.
We investigate the time evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time evolution of the coherence that are strikingly different from the usual case of a harmonic-oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the density matrix of the qubit.
We investigate the time-evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time-evolution of the coherence that are strikingly different from the usual case of a harmonic oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time-evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the density matrix of the qubit.
We present a general formalism for the dissipative dynamics of an arbitrary quantum system in the presence of a classical stochastic process. It is applicable to a wide range of physical situations, and in particular it can be used for qubit arrays in the presence of classical two-level systems (TLS). In this formalism, all decoherence rates appear as eigenvalues of an evolution matrix. Thus the method is linear, and the close analogy to Hamiltonian systems opens up a toolbox of well-developed methods such as perturbation theory and mean-field theory. We apply the method to the problem of a single qubit in the presence of TLS that give rise to pure dephasing 1/f noise and solve this problem exactly.
Abstract Random telegraph noise (RTN) has been widely used to describe the environmental effects on open quantum systems. In most cases, it is assumed that the environmental noise described by RTN has symmetric properties. However, in some important physical processes, the asymmetric characteristics of environmental noise play a crucial role in the dynamical evolution of the quantum systems. We theoretically study the dephasing dynamics of a two-level quantum system induced by RTN with asymmetric properties. Within the framework of the stochastic Liouville equation, we derive the exact expression of the decoherence function quantifying the coherence evolution of the quantum system. It is shown that, in contrast to the case of the symmetric RTN, the asymmetric RTN can induce a frequency shift and may lead to non-Markovian behavior in the decoherence dynamics of the quantum system. Furthermore, by adjusting the average transition rate, the transition rate difference, and the transition amplitude difference of the environmental noise, the decoherence dynamics of the quantum system can be effectively modulated.