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Quantum Phase Transition and Universal Dynamics in the Rabi Model.

Myung-Joong Hwang1, Ricardo Puebla1, Martin B Plenio1

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This study proves quantum phase transitions (QPT) in the Rabi model. Universal dynamics under quantum quenches are demonstrated, with critical exponents accurately predicting residual energy via the Kibble-Zurek mechanism.

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Area of Science:

  • Quantum Optics
  • Condensed Matter Physics
  • Quantum Phase Transitions

Background:

  • The Rabi Hamiltonian describes light-matter interaction, a fundamental system in quantum mechanics.
  • Investigating quantum phase transitions (QPT) in simplified models provides insights into complex quantum phenomena.

Purpose of the Study:

  • To rigorously prove the existence of a QPT in the Rabi model.
  • To analyze the universal dynamics and residual energy scaling during quantum quenches near the critical point.

Main Methods:

  • Derivation of an exact solution in the limit of infinite atomic transition frequency.
  • Analytical calculation of finite-frequency scaling exponents.
  • Numerically exact diagonalization of the Hamiltonian.
  • Application of the Kibble-Zurek mechanism for quench dynamics analysis.

Main Results:

  • Exact proof of QPT in the Rabi model under specific limits.
  • Demonstration of universal dynamics characterized by critical exponents during slow quenches.
  • Precise prediction of residual energy scaling using the Kibble-Zurek mechanism.
  • Observation of universal dynamics even with finite transition frequencies.

Conclusions:

  • The Rabi model serves as a key system for understanding QPT and universal dynamics.
  • The Kibble-Zurek mechanism is applicable to non-spatial quantum systems for predicting quench dynamics.
  • Finite transition frequencies do not preclude the observation of universal quantum dynamics.