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Area of Science:

  • Quantum physics
  • Many-body systems
  • Bose-Hubbard model

Background:

  • Standard adiabatic processes are insufficient for systems with mixed phase-space (chaotic and quasi-regular regions).
  • The Bose-Hubbard Hamiltonian describes many-body systems of atoms on bosonic sites.
  • Quasi-static protocols are crucial for understanding system dynamics under slow parameter variations.

Purpose of the Study:

  • To investigate quasi-static protocols for Bose-Hubbard systems exhibiting mixed phase-space characteristics.
  • To analyze the effects of a sweep process involving slow variation of rotation frequency (time-dependent Sagnac phase).
  • To determine the compatibility of such protocols with linear response theory given parametric phase-space topology variations.

Main Methods:

  • Focus on a many-body system of atoms governed by the Bose-Hubbard Hamiltonian.
  • Implementation of a sweep process involving the slow variation of the device's rotation frequency.
  • Analysis of the time-dependent Sagnac phase and its impact on phase-space topology.

Main Results:

  • The parametric variation of phase-space topology renders the quasi-static limit incompatible with linear response theory.
  • Standard adiabatic process paradigms are insufficient for these complex systems.
  • Detailed analysis is required to predict the outcome and efficiency of the transfer protocol.

Conclusions:

  • Quasi-static protocols in mixed phase-space systems necessitate advanced analytical approaches beyond linear response theory.
  • The sweep process highlights the limitations of traditional adiabatic assumptions.
  • Understanding these dynamics is crucial for controlling and optimizing quantum system protocols.