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arXiv:1202.5056 · Physical Review A

Nonperturbative quantum dynamical decoupling

Jun Jing, Lian-Ao Wu, J. Q. You, Ting Yu

Published Aug 27, 2013• 27 citations
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Abstract

Current dynamical control based on the bang-bang control mechanism involving various types of pulse sequences is essentially a perturbative theory. This paper presents a nonperturbative dynamical control approach based on the exact stochastic Schr\"odinger equation. We report our findings on the pulse parameter regions in which the effective dynamical control can be exercised. The onset of the effective control zones reflects the nonperturbative feature of our approach. The nonperturbative methods offer possible new implementations when several different parameter regions are available.

DOI
10.1103/physreva.88.022333

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Current dynamical control based on the bang-bang control mechanism involving various types of pulse sequences is essentially a perturbative theory. This paper presents a nonperturbative dynamical control approach based on the exact stochastic Schr"odinger equation. We report our findings on the pulse parameter regions in which the effective dynamical control can be exercised. The onset of the effective control zones reflects the nonperturbative feature of our approach. The nonperturbative methods offer possible new implementations when several different parameter regions are available.
Parametric fluctuations or stochastic signals are introduced into the rectangular pulse sequence to investigate the feasibility of random dynamical decoupling. In a large parameter region, we find that the out-of-order control pulses work as well as the regular pulses for dynamical decoupling and dissipation suppression. Calculations and analysis are enabled by and based on a nonperturbative dynamical decoupling approach allowed by an exact quantum-state-diffusion equation. When the average frequency and duration of the pulse sequence take proper values, the random control sequence is robust, fault-tolerant, and insensitive to pulse strength deviations and interpulse temporal separation in the quasi-periodic sequence. This relaxes the operational requirements placed on quantum control devices to a great deal.
This paper considers a spin-chain model by numerically solving the exact model to explore the nonperturbative dynamical decoupling regime, where an important issue recently arose. Our study has revealed a few universal features of nonperturbative dynamical control irrespective of the types of environments and system-environment couplings. We have shown that, for the spin-chain model, there is a threshold and a large pulse parameter region where the effective dynamical control can be implemented, in contrast to the perturbative decoupling schemes where the permissible parameters are represented by a point or converge to a very small subset in the large parameter region admitted by our nonperturbative approach. An important implication of the nonperturbative approach is its flexibility in implementing the dynamical control scheme in an experimental setup. Our findings have exhibited several interesting features of the nonperturbative regimes such as the chain-size independence, pulse strength upper bound, noncontinuous valid parameter regions, etc. Furthermore, we find that our nonperturbative scheme is robust against randomness in model fabrication and time-dependent random noise.
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.
A general coherent control scenario to suppress or accelerate tunneling of quantum states decaying into a continuum is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling protocols and to sequences of pulses that collapse the coherent evolution and induce quantum Zeno (QZE) or quantum anti-Zeno effects (AZE). The analysis reveals a subtle interplay between coherent and incoherent phenomena and demonstrates that dynamics analogous to the evolution due to QZE or AZE can be generated from stochastic sequences of unitary pulses when averaged over all possible realizations.
In this work we develop a numerical framework to investigate the renormalization of the non-Markovian dynamics of an open quantum system to which dynamical decoupling is applied. We utilize a non-Markovian master equation of the spin-boson model. The effects of the decoupling pulses are then incorporated. A wide class of decoupling pulses can be described equally within this approach. We have performed a comprehensive investigation on the renormalized dynamics within various noise models, including the Ornstein-Uhlenbeck noise and the spin-boson model. The renormalized dynamics under bang-bang control and continuous dynamical decoupling are simulated. The condition for efficient decoupling is assessed for each scenario. Our results indicate that the renormalization of the non-Markovian dynamics critically depends on the spectral density of the environment and the envelope of the decoupling pulses. Consequently, it is difficult to have a simple universal condition that ensures the efficiency. The framework developed in this work provides a unified approach to investigate the efficiency of realistic decoupling pulses. It also opens an avenue to further optimize the decoupling via pulse shaping.
A general coherent control scenario to suppress, or accelerate, tunneling of quantum states decaying into a continuum, is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling (DD) protocols and sequences of pulses that collapse the coherent evolution and induce quantum Zeno (QZE) or quantum anti-Zeno effects (AZE). The analysis reveals a subtle interplay between coherent and incoherent phenomena and demonstrating that dynamics analogous to evolution due to QZE or AZE can be generated from stochastic sequences of unitary pulses when averaged over all possible realizations.