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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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EPR pairing dynamics in Hubbard model with resonant U.

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We study fermion collisions in the Hubbard model, finding their scattering matrix separates into spatial and spin parts. This enables creating entangled pairs without precise timing or measurement.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics

Background:

  • The Hubbard model describes interacting electrons in materials.
  • Understanding multi-particle collisions is crucial for quantum simulations.

Purpose of the Study:

  • To analyze the collision dynamics of two fermions in the Hubbard model.
  • To explore the potential for generating entangled quantum states.

Main Methods:

  • Exact solution of the two-fermion collision problem.
  • Analysis of the scattering matrix (S-matrix).

Main Results:

  • The scattering matrix is separable into spatial and spin components.
  • The spin S-matrix mimics a Heisenberg-type pulsed interaction.
  • Entangled (EPR) pairs can be created for specific collision parameters (|vr/U| = 1).

Conclusions:

  • Fermion collisions offer a novel method for generating distant entangled pairs.
  • The process bypasses the need for temporal control and measurement.
  • The findings extend to multi-particle collision scenarios.