Markovian theory of dynamical decoupling by periodic control

Szczygielski, Krzysztof; Alicki, Robert

doi:10.1103/physreva.92.022349

Cited by 16 publications

(21 citation statements)

References 25 publications

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“…For a review of the development and state-of-the-art see the recent review article by Lidar [11]. For recent discussions on the Markovianity versus non-Markovianity see [12] and [13] Our interest will be in the question of whether the approach works for open systems. In particular, suppose we are given a fixed quantum dynamical semigroup (or equivalently, a master equation) can we say whether a prescribed DD scheme will be effective.…”

Section: Introductionmentioning

confidence: 99%

Can quantum Markov evolutions ever be dynamically decoupled?

Gough

Nurdin

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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We consider the class of quantum stochastic evolutions (SLH-models) leading to a quantum dynamical semigroup over a fixed quantum mechanical system (taken to be finite-dimensional). We show that if the semigroup is dissipative, that is, the coupling operators are non-zero, then a dynamical decoupling scheme based on unitary rotations on the system space cannot suppress decoherence even in the limit where the period between pulses vanishes. We emphasize the role of the Fock space dilation used here to construct a quantum stochastic model, as there are often dilations of the same semigroup using an environmental noise model of lower level of chaoticity for which dynamical decoupling is effective. We show that the Chebotarev-Gregoratti Hamiltonian behind a quantum stochastic evolution is an example of a Hamiltonian dynamics on a joint system-environment that cannot be dynamically decoupled in this way. * J. E. Gough is with the

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Section: Introductionmentioning

confidence: 99%

Can quantum Markov evolutions ever be dynamically decoupled?

Gough

Nurdin

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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“…To obtain the Floquet-Markovian master equation for the periodic system, we need to expandˆ( ) S t in the quasistationary state space [59]. From Floquet theorem, we know that if the system is initially prepared in one…”

Section: Discussionmentioning

confidence: 99%

“…We concentrate here on the influence from the dissipation effects of the environments on NVCs, which affect the quantum dynamics and result in the deviation from the desired target states. Considering each NVC weakly coupled to a zero-temperature environment, the Floquet-Markovian master equation reads [48]   å å r r r r g w w r w w r r w…”

Section: Effect Of Decoherencementioning

confidence: 99%

Floquet engineering to entanglement protection of distant nitrogen vacancy centers

Yang

Song

et al. 2019

New J. Phys.

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It remains challenging to preserve entanglement between distant solid-state qubits with high-fidelity, such as nitrogen vacancy centers (NVCs). We propose a Floquet engineering strategy to protect the maximal entanglement between two weakly interacting NVCs separated in long spatial distance by locally applying periodic strong driving on the NVCs. It is found that entanglement of the Floquet states of the NVCs resonantly reaches its maximum during the whole driving period at certain values of the driving parameters. Our analysis reveals that it is the occurrence of the avoided level crossing in the Floquet quasienergy spectrum which results in such entanglement resonance. The dissipation effect on the generated entanglement has also been analyzed. Our results may be of both theoretical and experimental interests in exploring the long-lasting entanglement between weakly interacting spins to long distances in realistic environments.

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“…This condition means that the dynamics induced by any time-dependent control is slow compared to the frequencies of the system's transitions (to be defined below). Master equations can be derived for certain classes of time-dependent systems in which the above condition is broken, but we will not deal with these here [21][22][23][24][25].…”

Section: The Thermal Master Equation For Weakly Damped Systemsmentioning

confidence: 99%

Fermi’s golden rule, the origin and breakdown of Markovian master equations, and the relationship between oscillator baths and the random matrix model

Santra

Cruikshank

Balu

et al. 2017

J. Phys. A: Math. Theor.

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Fermi's golden rule applies to a situation in which a single quantum state |ψ is coupled to a near-continuum. This "quasi-continuum coupling" structure results in a rate equation for the population of |ψ . Here we show that the coupling of a quantum system to the standard model of a thermal environment, a bath of harmonic oscillators, can be decomposed into a "cascade" made up of the quasi-continuum coupling structures of Fermi's golden rule. This clarifies the connection between the physics of the golden rule and that of a thermal bath, and provides a non-rigorous but physically intuitive derivation of the Markovian master equation directly from the former. The exact solution to the Hamiltonian of the golden rule, known as the Bixon-Jortner model, generalized for an asymmetric spectrum, provides a window on how the evolution induced by the bath deviates from the master equation as one moves outside the Markovian regime. Our analysis also reveals the relationship between the oscillator bath and the "random matrix model" (RMT) of a thermal bath. We show that the cascade structure is the one essential difference between the two models, and the lack of it prevents the RMT from generating transition rates that are independent of the initial state of the system. We suggest that the cascade structure is one of the generic elements of thermalizing many-body systems.

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Markovian theory of dynamical decoupling by periodic control

Cited by 16 publications

References 25 publications

Can quantum Markov evolutions ever be dynamically decoupled?

Can quantum Markov evolutions ever be dynamically decoupled?

Floquet engineering to entanglement protection of distant nitrogen vacancy centers

Fermi’s golden rule, the origin and breakdown of Markovian master equations, and the relationship between oscillator baths and the random matrix model

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