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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Optimized coherence selection.

Vesselin Z Miloushev1, Arthur G Palmer2

  • 1Department of Radiology, Memorial Sloan Kettering Cancer Center, 1275 York Ave, New York, NY 10065, United States.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|November 5, 2018
PubMed
Summary
This summary is machine-generated.

A new theoretical framework optimizes coherence order selection for cogwheel phase cycling in Nuclear Magnetic Resonance (NMR) spectroscopy. This framework provides a general formula for valid phase cycles, improving spectrometer software.

Keywords:
Cogwheel phase cyclingCoherence order selectionLattice reductionLinear diophantine equationsMixed radix positional encoding

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Quantum Information Science

Background:

  • Cogwheel phase cycling is crucial for selecting coherence orders in NMR.
  • Existing methods for phase cycle generation can be complex and empirical.

Purpose of the Study:

  • To develop a theoretical framework for optimized coherence order selection in NMR.
  • To derive a general formula for constructing valid cogwheel phase cycles.

Main Methods:

  • Analysis of solutions to homogeneous linear Diophantine equations.
  • Derivation of the Hughes-Carravetta-Levitt conjectures.
  • Construction and proof of optimality for a general phase cycle formula.

Main Results:

  • A theoretical framework for optimized coherence order selection is established.
  • A general formula guaranteeing valid phase cycles is constructed.
  • Optimality is proven for specific conditions, with methods for non-ideal cases.

Conclusions:

  • The developed formula provides a systematic and optimal approach to cogwheel phase cycling.
  • This framework can be integrated into NMR spectrometer software for automated phase cycle generation.
  • Enhances efficiency and accuracy in NMR experiments.