Introduction

Haeberlen, Ulrich

doi:10.1016/b978-0-12-025561-0.50007-1

Cited by 174 publications

(249 citation statements)

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“…Once τ s and v(t) are known, the coefficients η 21 , η 22 , and η 23 can be easily computed according to (8). Thereby, we have an analytical prediction for the leading order of d as function of J including the prefactor.…”

Section: The Spin Chain As Decoherence Bathmentioning

confidence: 99%

“…π pulses: vanishing linear order We consider symmetric and asymmetric pulses with angle θ = π which satisfy η 11 = η 12 = 0 as defined in (8). For comparison, also the standard pulse with constant amplitude and finite η (1) is computed.…”

Section: The Numerical Analysismentioning

confidence: 99%

“…Experimentally, the spin echo and the CPMG sequence are standard in NMR [8]. To our knowledge, other sequences have not yet been tested.…”

Section: Introductionmentioning

confidence: 99%

“…For instance a π pulses rotates the spin by 180 • . These pulses find a wide range of applications in dynamical decoupling [1,2,3,4,5,6,7] and in NMR [8,9] where also π/2 pulses are crucial. In quantum information processing the π/2 pulse in combination with a π pulse realizes the important Hadamard gate.…”

Section: Introductionmentioning

confidence: 99%

“…From a theoretical point of view the topic has been widely studied and many different sequences of pulses have been proposed. Among these we recall the series of periodic equidistant π pulses, called bang-bang control (BB) [1,2], the periodically iterated 2-pulse sequence according to Carr/Purcell and Meiboom/Gill (CPMG) [8,11,12], the concatenated sequence (CDD) proposed by Khodjasteh and Lidar [13,14] as well as the fully optimized sequence (UDD) derived by one of the authors [7,15].…”

Section: Introductionmentioning

confidence: 99%

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Numerical analysis of optimized coherent control pulses

2008

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Numerically we simulate the effect of optimized coherent control pulses with a finite duration on a qubit in a bath of spins. The pulses of finite duration are compared with ideal instantaneous pulses. In particular, we show that properly designed short pulses can approximate ideal instantaneous pulses up to a certain order in the shortness of the pulse. We provide examples of such pulses, quantify the discrepancy from the ideal case and compare their effect for various ranges of the coupling constants.

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Section: The Spin Chain As Decoherence Bathmentioning

confidence: 99%

Section: The Numerical Analysismentioning

confidence: 99%

“…Experimentally, the spin echo and the CPMG sequence are standard in NMR [8]. To our knowledge, other sequences have not yet been tested.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical analysis of optimized coherent control pulses

2008

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The Hamiltonians of NMR. part I

Smith

Palke

Gerig

1992

Concepts Magn. Reson.

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Nuclear magnetic resonance spectroscopy has evolved in complexity to the extent that it is often useful to carry out computer simulations of experiments as a way to refine experimental conditions, to maximize usable information, or to interpret results reliably. The starting point for such simulations is an appropriate quantum mechanical formulation. This article presents many of the physical ideas that are important in high-resolution NMR spectroscopy and then develops expressions for the contribution of each of these to the Hamiltonian for the system under consideration. The Hamiltonians for the Zeeman interaction, scalar coupling, and the chemical shielding effect are discussed with the aim of explaining the quantum mechanics of NMR in a manner understandable to a nontheoretician. Consequently, much of the discussion is explicit and includes points skimmed over in other presentations in the literature. FOREWORDIn this article and in Part 11, we will discuss the Hamiltonians needed to describe highresolution NMR experiments, including those interactions that lead to relaxation. The mathematical expressions for the interactions and their corresponding Hamiltonians become more complicated in the progression from the simple Zeeman term, to dipolar interactions, to chemical shift anisotropy, and so forth. We express all of the interactions in as similar a form as possible, even though doing so involves making some of the simple terms look more complicated than usual. Nevertheless, we believe that using consistent notation simplifies the study of all of the interactions, and thus the reader is not confronted with completely new expressions with the introduction of each new feature of the spin interactions. We encourage readers to persevere through the initial discussion of the format for writing the Hamiltonians, with the expectation that the benefit of consistent notation will outweigh the toil of introducing and becoming familiar with it.We have inserted notes in shaded boxes at numerous places in the discussion; these are not required for understanding the logical flow of the text. The notes either explain relationships to other topics or elaborate on side issues.

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The Hamiltonians of NMR. Part II

Smith

Palke

Gerig

1992

Concepts Magn. Reson.

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Building on our previous discussions of the Hamiltonian operators that are important in the description of high-resolution NMR experiments, we use here the same symbolism and approach to develop formulations for time-dependent operators. These considerations lead to discussions of free precession and the influence of applied radio-frequency fields. As with the previous articles, the presentations are explicit, the mathematical operations are explained in detail, and all assumptions made are indicated.

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Introduction

Cited by 174 publications

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Numerical analysis of optimized coherent control pulses

Numerical analysis of optimized coherent control pulses

The Hamiltonians of NMR. part I

The Hamiltonians of NMR. Part II

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