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

TL;DR

This paper combines matrix product states and numerical mode decomposition to analyze gauge-invariant multimode cavity QED systems, resolving gauge ambiguities and enabling efficient simulation of complex quantum interactions.

Contribution

It introduces a combined numerical approach using MPS and NMD for multimode cavity QED, addressing gauge ambiguities and transforming Hamiltonians for efficient simulation.

Findings

Successfully verified gauge invariance for multimode models

Demonstrated efficient simulation of 1D cavity QED systems

Extracted electromagnetic modes using NMD in complex environments

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 single quantized electromagnetic mode. In this work, 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 1D cavity QED systems in various settings.