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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Entanglement Quantification in Atomic Ensembles.

Matteo Fadel1, Ayaka Usui2, Marcus Huber3,4

  • 1Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland.

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|July 16, 2021
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Summary
This summary is machine-generated.

Quantifying quantum entanglement is challenging with limited data. This study introduces a practical method using variance-based criteria to bound entanglement measures, applicable to realistic experiments with minimal measurements.

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Area of Science:

  • Quantum Information Science
  • Atomic Physics
  • Quantum Optics

Background:

  • Quantifying quantum entanglement is crucial for understanding nonclassical correlations.
  • Calculating entanglement measures is often computationally intensive, especially with incomplete state information.
  • Existing methods face challenges in realistic experimental scenarios with limited measurement data.

Purpose of the Study:

  • To develop a practical and experimentally feasible method for quantifying entanglement.
  • To derive analytical lower bounds for entanglement measures using variance-based criteria.
  • To apply this method to quantify entanglement in complex quantum systems like Bose-Einstein condensates.

Main Methods:

  • Considered broad families of entanglement criteria based on operator variances.
  • Analytically derived lower bounds for the best separable approximation and generalized robustness.
  • Applied the method to spin-squeezed Bose-Einstein condensates with approximately 500 atoms.

Main Results:

  • Established a practical approach for quantifying entanglement from limited experimental data.
  • Successfully lower bounded entanglement measures using only first and second moments of the collective spin operator.
  • Demonstrated the method's efficacy in quantifying both bipartite and multipartite entanglement in Bose-Einstein condensates.

Conclusions:

  • The developed method offers a robust way to quantify entanglement in realistic experimental settings.
  • Variance-based entanglement criteria provide accessible lower bounds for entanglement measures.
  • This work facilitates the characterization of entanglement in large quantum systems like Bose-Einstein condensates.