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Journal of Physics B Atomic Molecular and Optical Physics

Theory of decoherence control in a fluctuating environment

Sachiko Kitajima, Masashi Ban, Fumiaki Shibata

Published Jun 23, 2010• 8 citations
Publisher

Abstract

Detailed studies are carried out for the problem of decoherence control by a successive application of ?-pulses when a relevant spin-1/2 (qubit) system is surrounded by a stochastically fluctuating environment. Specifically, considerations are given to two representative stochastic processes: a two-state-jump Markov process and a Gauss?Markov process. Exact analytical solutions are obtained for the decoherence control by the ?-pulse application even for non-stationary stochastic processes as well as for stationary processes. In view of recent advances in dynamical decoupling experiments with artificial (engineered) stochastic noise, the results are useful in analysing qubit systems under the influence of a fluctuating environment.

DOI
10.1088/0953-4075/43/13/135504

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Detailed studies are carried out for the problem of decoherence control by a successive application of ?-pulses when a relevant spin-1/2 (qubit) system is surrounded by a stochastically fluctuating environment. Specifically, considerations are given to two representative stochastic processes: a two-state-jump Markov process and a Gauss?Markov process. Exact analytical solutions are obtained for the decoherence control by the ?-pulse application even for non-stationary stochastic processes as well as for stationary processes. In view of recent advances in dynamical decoupling experiments with artificial (engineered) stochastic noise, the results are useful in analysing qubit systems under the influence of a fluctuating environment.
Decoherence of qubits under the influence of random phase fluctuations is studied by means of the stochastic Liouville equation, where the phase fluctuations are characterized by means of the Gauss-Markov process and the two-state-jump Markov process. We investigate how an observation of a stochastic variable during the time evolution influences the decoherence of the qubit system. We examine the decays of distinguishability and entanglement of qubit states. It is shown that the decoherence of qubits can be suppressed by the observation of the stochastic variable. It is also found that the suppression of the decoherence does not depend on the observed value.
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
We reexamine the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. 94, 060502 (2005)]. A systematic comparison with standard cyclic decoupling is effected for a variety of dynamical regimes, including the case of both semiclassical and fully quantum decoherence models. In particular, exact analytical expressions are derived for randomized control of decoherence from a bosonic environment. We investigate quantitatively control protocols based on purely deterministic, purely random, as well as hybrid design, and identify their relative merits and weaknesses at improving system performance. We find that for time-independent systems, hybrid protocols tend to perform better than pure random and may improve over standard asymmetric schemes, whereas random protocols can be considerably more stable against fluctuations in the system parameters. Beside shedding light on the physical requirements underlying randomized control, our analysis further demonstrates the potential for explicit control settings where the latter may significantly improve over conventional schemes.
In this work, two experimentally feasible methods of decoherence engineering-one based on the application of stochastic classical kicks and the other based on temporally randomized pulse sequences are combined. A different coupling interaction is proposed, which leads to amplitude damping as compared to existing methods which model phase damping, utilizing the zzzzzz coupling interaction. The decoherence process on combining the stochastic kick method and the randomized pulse sequence method and the effectiveness of dynamical decoupling under these coupling interactions are analyzed. Finally, a counter-intuitive result where decoherence is suppressed in the presence of two noise sources under certain resonant conditions is presented.
Abstract. The efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the qubits. Recently a substantial progress was achieved in enhancing the time, which a solid-state qubit demonstrates a coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions the material-inherent sources of noise start to play a crucial role. In most cases the noise that quantum device demonstrate has 1/f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review we discuss the current state of the theory of the decoherence due to the qubit interaction with the fluctuators. We describe the effect of such an environment on different protocols of the qubit manipulations- free induction and echo signal. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function only.
Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic Liouville equation is shown to be derived from the quantum master equation of the Lindblad under certain conditions. Relaxation processes of single and bipartite quantum systems which are initially correlated with a stochastic environment are investigated. It is shown the possibility that the stochastic fluctuation can create coherence and entanglement of a quantum system with the assistance of the initial correlation. The results are examined in the pure dephasing processes of qubits, which are caused by the nonstationary Gauss-Markov process and two-state jump Markov process.