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Engineering Arbitrary Hamiltonians in Phase Space.

Lingzhen Guo1,2, Vittorio Peano2

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We present a new method to engineer quantum Hamiltonians in Floquet phase space using noncommutative Fourier transforms. This technique enables the creation of novel quantum states and Hamiltonians for quantum computation.

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Area of Science:

  • Quantum physics
  • Quantum optics
  • Condensed matter theory

Background:

  • Periodically driven systems (Floquet systems) are crucial for quantum control.
  • Engineering Hamiltonians in phase space allows for novel quantum phenomena.
  • Current methods have limitations in arbitrary Hamiltonian generation.

Purpose of the Study:

  • To develop a general method for engineering arbitrary Hamiltonians in the Floquet phase space.
  • To establish a direct link between real-space driving potentials and phase-space Hamiltonians.
  • To enable the creation of novel quantum states and computational protocols.

Main Methods:

  • Utilizing the noncommutative Fourier transformation technique.
  • Establishing analytical relationships between target Floquet Hamiltonians and driving potentials.
  • Deriving expressions for real-space potentials to generate desired phase-space Hamiltonians.

Main Results:

  • A general method to engineer arbitrary Hamiltonians in Floquet phase space is introduced.
  • Analytical expressions for driving potentials are derived.
  • Novel Hamiltonians, including rotational lattices and sharp-boundary wells, can be generated.

Conclusions:

  • The proposed protocol offers a versatile approach to quantum Hamiltonian engineering.
  • It is compatible with various experimental platforms.
  • The method facilitates nonclassical state generation and bosonic quantum computation.