Quantifying the limits of controllability for the nitrogen-vacancy electron spin defect

TL;DR

This paper investigates the fundamental limits of controlling nitrogen-vacancy center electron spins in diamond, revealing how control complexity and duration affect fidelity and highlighting a feasible nanosecond control regime for quantum applications.

Contribution

The study provides a quantitative analysis of population inversion limits in NV centers, incorporating high-accuracy simulations and quantum optimal control to identify practical control regimes.

Findings

Exponential increase in amplitude and bandwidth with shorter control durations.

Non-Markovian effects emerge in multipulse sequences at sub-nanosecond scales.

A feasible nanosecond control regime for high-fidelity quantum operations.

Abstract

Solid-state electron spin qubits, like the nitrogen-vacancy center in diamond, rely on control sequences of population inversion to enhance sensitivity and improve device coherence. But even for this paradigmatic system, the fundamental limits of population inversion and potential impacts on applications like quantum sensing have not been assessed quantitatively. Here, we perform high accuracy simulations beyond the rotating wave approximation, including explicit unitary simulation of neighboring nuclear spins. Using quantum optimal control, we identify analytical pulses for the control of a qubit subspace within the spin-1 ground state and quantify the relationship between pulse complexity, control duration, and fidelity. We find exponentially increasing amplitude and bandwidth requirements with reduced control duration and further quantify the emergence of non-Markovian effects for multipulse sequences using sub-nanosecond population inversion. From this, we determine that the reduced fidelity and non-Markovianity is due to coherent interactions of the electron spin with the nuclear spin environment. Ultimately, we identify a potentially realizable regime of nanosecond control duration for high-fidelity multipulse sequences. These results provide key insights into the fundamental limits of quantum information processing using electron spin defects in diamond.