Optical $\Lambda$ transitions and quantum computing in the $^{15}$N-V$^{-}$ Center in Diamond

TL;DR

This paper analyzes the energy levels and $ ext{Lambda}$ transitions in the $^{15}$N-V$^{-}$ center in diamond, demonstrating its potential for room-temperature quantum computing through hyperfine-mediated two-photon processes.

Contribution

It provides a detailed derivation of excited state energy levels and identifies a spin non-conserving $ ext{Lambda}$ transition enabling quantum information processing.

Findings

$ ext{Lambda}$ transition rate of ~10 MHz at room temperature

Approximately $10^4$ quantum logic operations possible within coherence time

Hyperfine interaction mediates spin non-conserving two-photon transitions

Abstract

We present a thorough derivation of the excited state energy levels of the negatively charged $^{15}$N-V$^{-}$ center in diamond for the strong applied electric field case. We show that in the $^{15}$N-V$^{-}$ center a spin non-conserving two-photon $\Lambda$ transition exists that is mediated by the hyperfine interaction, which provides the possibility to write quantum information. Using second order perturbation theory we obtain a $\Lambda$ transition rate of the order of 10 MHz at room temperature, which allows for approximately $10^4$ quantum logic operations within the spin coherence time $\tau_d(T=300 K)\approx 1m$s of the $^{15}$N-V$^{-}$ center.