Divergence-free multi-mode circuit quantum electrodynamics

  1. Mario F. Gely,
  2. Adrian Parra-Rodriguez,
  3. Daniel Bothner,
  4. Ya. M. Blanter,
  5. Sal J. Bosman,
  6. Enrique Solano,
  7. and Gary A. Steele
Circuit quantum electrodynamics studies the interaction of artificial atoms and electromagnetic modes constructed from superconducting circuitry. While the theory of an atom coupled to one mode of a resonator is well studied, considering multiple modes leads to divergences which are not well understood. Here, we introduce a full quantum model of a multi-mode resonator coupled to a Josephson junction atom. Using circuit quantization, we find a Hamiltonian in which parameters of the atom are naturally renormalized as additional modes are considered. In our model, we circumvent the divergence problem, and its formulation reveals a physical understanding of the mechanisms of convergence in ubiquitous models in circuit quantum electrodynamics.
arxiv pdf

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