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Dirac Equation in (1+1)-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model.

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We found a quantum simulation for Dirac particles in curved spacetime using a quantum Rabi model. Gravity causes Zitterbewegung and wave function squeezing, even near black holes.

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Area of Science:

  • Quantum physics
  • General relativity
  • Quantum optics

Background:

  • The Dirac equation describes relativistic quantum particles.
  • Curved spacetime, like near black holes, affects particle behavior.
  • Quantum simulations offer new ways to study complex physical systems.

Purpose of the Study:

  • To establish an exact mapping between the Dirac equation in curved spacetime and a multiphoton quantum Rabi model.
  • To propose a trapped-ion quantum simulation for Dirac particles in curved spacetime.
  • To investigate the effects of gravity on Dirac particle dynamics, including Zitterbewegung.

Main Methods:

  • Developed an exact mathematical mapping between the Dirac equation in (1+1)-dimensional curved spacetime and a multiphoton quantum Rabi model.
  • Utilized a trapped-ion system to implement the quantum Rabi model with one- and two-photon terms.
  • Performed numerical analysis of a Dirac particle's free fall into a (1+1)-dimensional black hole.

Main Results:

  • The quantum Rabi model with specific terms simulates Dirac particles in curved spacetime.
  • The Zitterbewegung effect, an oscillatory motion, persists for Dirac particles in gravitational fields.
  • Gravity induces squeezing of the Dirac particle's wave function through metric coupling.

Conclusions:

  • A quantum simulation approach can effectively model Dirac particles in curved spacetime.
  • Gravity's influence on quantum phenomena like Zitterbewegung is significant and observable.
  • The duality reveals how gravity generates quantum squeezing effects.