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Matrix product states and numerical mode decomposition for the analysis of gauge-invariant cavity quantum electrodynamics

Christopher J. Ryu1, Dong-Yeop Na2, and Weng C. Chew1,3,*

  • 1Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
  • 2Department of Electrical Engineering, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
  • 3Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA

  • *wcchew@purdue.edu
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Phys. Rev. A 107, 063707 – Published 20 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.063707

Abstract

There has been a problem of gauge ambiguities with the Rabi Hamiltonian due to the fact that it can be derived from two formally different but physically equivalent fundamental Hamiltonians. This problem has recently been resolved for models with a single quantized electromagnetic mode. In this paper, we mathematically and numerically verify this for multimode models. With this established, we combine the numerical methods, matrix product states (MPS) and numerical mode decomposition (NMD), for analyzing cavity QED systems. The MPS method is used to efficiently represent and time evolve a quantum state. However, since the coupling structure of the Rabi Hamiltonian is incompatible with MPS, it is numerically transformed into an equivalent Hamiltonian that has a chain coupling structure, which allows efficient application of MPS. The technique of NMD is used to extract the numerical electromagnetic modes of an arbitrary environment. As a proof of concept, this combined approach is demonstrated by analyzing one-dimensional cavity QED systems in various settings.

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Phys. Rev. A 107, 063707– Published 20 June, 2023
  • Received 9 December 2022
  • Accepted 19 May 2023
Article part of CHORUS
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