Characterizing the 1s:E state in the ²⁸Si :⁷⁷Se⁺ spin-photon system by the equation-of-motion variational quantum eigensolver method

Silicon based spin-photon interfaces are attractive candidates for quantum memory nodes in quantum networks. Silicon is the dominant host due to the vast silicon microelectronics industry and photonic integrated circuit infrastructure. One prominent spin-photon interface in the Si-platform is ²⁸Si :⁷⁷Se⁺ as it boasts a singlet-triplet T₁ time of 4.6 hours at temperatures below 2 K and a T₂ time of 2 seconds [1, 2]. However, the radiative efficiency of this spin-photon interface is only 0.8%, which is very low and makes spin-dependent luminescence readout schemes challenging, requiring additional steps such as Purcell enhancement or absorption spectroscopy [3-5]. It has been predicted that the energy of the 1s:E state in ²⁸Si :⁷⁷Se⁺ lies above the 1s:T₂ state [6]. However, this has never been observed and it is entirely feasible that the 1s:E state lies below the 1s:T₂ state, leading to the low radiative efficiency of the 1s:A-1s:T₂:Γ₇ transition. Traditionally, variational quantum eigensolvers only find the ground state of a Hamiltonian. Newer methods extend the algorithm to find the excited states of a Hamiltonian [7, 8]. This work utilizes the equation-of-motion variational quantum eigensolver method to find the energy level of the 1s:E state in the ²⁸Si :⁷⁷Se⁺ spin-photon system and examine the causes of low radiative efficiency to identify avenues for improvement.