# Fast magnetic field manipulations and nonadiabatic geometric phases of nitrogen-vacancy center spin in diamond

## TL;DR

This paper develops exact solutions for fast control of nitrogen-vacancy center spins in diamond, exploring nonadiabatic geometric phases, which could enhance quantum information processing and experimental measurements.

## Contribution

It provides a precise evolution operator for NV spin systems under magnetic fields and investigates nonadiabatic geometric phases, advancing fast quantum control methods.

## Key findings

- Exact evolution operator constructed for NV spin under magnetic fields
- Analysis of cyclic and non-cyclic nonadiabatic geometric phases
- Potential for experimental measurement of geometric phases in fast manipulations

## Abstract

Fast quantum spin manipulation is needed to design spin-based quantum logic gates and other quantum applications. Here, we construct exact evolution operator of the nitrogen-vacancy-center (NV) spin in diamond under external magnetic fields and investigate the nonadiabatic geometric phases, both cyclic and non-cyclic, in these fast-manipulated NV spin systems. It is believed that the nonadiabatic geometric phases can be measured in future experiments and these fast quantum manipulations can be useful in designing spin-based quantum applications.