Can quantum Rabi model with \({\varvec{A}}^\textbf{2}\)-term avoid no-go theorem and make quantum simulation of mass-enhancement in SUSY breaking?

We study the model of a mass enhancement in the supersymmetric quantum mechanics. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. It is evolved from a prototype based on the quantum Rabi model. Here, our quantum simulation means the realization of the target quantum phenomenon as a physical entity with some quantum-information devices. The original prototype is given as a mathematical model, and has the transition from the \({\mathcal {N}}=2\) $\mathcal{N}=2$   SUSY to its spontaneous breaking, though it has no mass enhancement. It is recently reported that the transition is observed for this prototype in a trapped-ion experiment with devising a method experimentally to realize the transition. The model proposed in this paper describes how the mass enhancement takes place in the fermionic states by the excitation of the 1-mode light boson in the SUSY breaking. In this model, the bosonic and fermionic states are graded by qubits. Although our model’s interaction does not have the Higgs potential, the mass enhancement in the fermionic states is caused by the radiative enhancement with the help of the X-gate’s swap between the fermionic and bosonic states.