Modelling and Structure-Preserving Discretization of the Schrödinger as a Port-Hamiltonian System, and Simulation of a Controlled Quantum Box

Authors

Gabriel Verrier, Ghislain Haine, Denis Matignon

Abstract

The modelling of the Schrödinger Equation as a port-Hamil-tonian system is addressed. We suggest two Hamiltonians for the model, one based on the probability of presence and the other on the energy of the quantum system in a time-independent potential. In order to simulate the evolution of the quantum system, we adapt the model to a bounded domain. The model is discretized thanks to the structure-preserving Partitioned Finite Element Method (PFEM). Simulations of Rabi oscillations to control the state of a system inside a quantum box are performed. Our numerical experiments include the transition between two levels of energy and the generation of Schrödinger cat states.

Keywords

port-Hamiltonian systems; open quantum systems

Citation

ISBN: 9783031382987
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-38299-4_41
Note: International Conference on Geometric Science of Information

BibTeX

@inbook{Verrier_2023,
  title={{Modelling and Structure-Preserving Discretization of the Schrödinger as a Port-Hamiltonian System, and Simulation of a Controlled Quantum Box}},
  ISBN={9783031382994},
  ISSN={1611-3349},
  DOI={10.1007/978-3-031-38299-4_41},
  booktitle={{Geometric Science of Information}},
  publisher={Springer Nature Switzerland},
  author={Verrier, Gabriel and Haine, Ghislain and Matignon, Denis},
  year={2023},
  pages={392--401}
}

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References

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Verrier, G., Haine, G. & Matignon, D. Modelling and Structure-Preserving Discretization of the Schrödinger as a Port-Hamiltonian System, and Simulation of a Controlled Quantum Box. Lecture Notes in Computer Science 392–401 (2023) doi:10.1007/978-3-031-38299-4_41 – 10.1007/978-3-031-38299-4_41