Poor man's Majorana bound states in quantum dot based Kitaev chain coupled to a photonic cavity

TL;DR

This paper explores how quantum light in a photonic cavity can be used to engineer and control poor man's Majorana bound states in a quantum dot-based Kitaev chain, even under realistic microscopic conditions.

Contribution

It demonstrates that cavity photon states can effectively tune interactions and hopping in a quantum dot Kitaev chain, enabling the realization of poor man's MBSs without perfect fine-tuning.

Findings

Photon coupling modifies the pairing term in the effective Hamiltonian.

Cavity photon states can cancel particle interactions at the sweet spot.

Large photon numbers suppress hopping amplitudes, leading to a degenerate spectrum.

Abstract

Quantum dot based platforms offer a promising route towards realizing the Kitaev chain Hamiltonian hosting Majorana bound states (MBSs). Poor man's MBSs arise in a two-site Kitaev chain when the parameters of the system are fine-tuned to the sweet spot. Based on our previous work [Phys. Rev. B 111, 155410 (2025)], we consider a microscopic model for the Kitaev chain based on quantum dots with proximity effect embedded in a photonic cavity. We find that the photon coupling in the microscopic model yields an effective Hamiltonian where the cavity affects the pairing term. However, we demonstrate that even in this case, it is possible to screen particle interactions and reach the sweet spot condition for the emergence of the poor man's MBSs. In particular, we find that attractive particle interactions can be canceled for the cavity prepared in the zero-photon state, while repulsive ones can be screened with a cavity prepared in the one-photon state. Furthermore, in case of a large number of photons in the cavity, we find that the hopping amplitudes are suppressed resulting in a degenerate spectrum. This motivates the use of quantum light for engineering poor man's MBSs with cavity embedding.