Fast Arbitrary Qutrit Gates for NV Centers in the Low-Field Regime

Abstract

The ground state of the negatively charged NV center forms a spin-1 manifold providing a versatile platform for sensing and information processing. Here we present a scheme for implementing fast arbitrary qutrit gates in the low-field regime using monochromatic microwave pulses of constant intensity tuned to the zero-field transition. By concatenating pulses with appropriate phases and durations, the NV-ERC scheme is extended from SU(2) operations in the double-quantum subspace to the full three-level structure. We show that arbitrary SU(3) operations can be decomposed into rotations in the double-quantum subspace together with effective implementations of the generators related to $\hatλ_5$ and $\hatλ_8$. We illustrate this decomposition with a use case: performing quantum state tomography of the complete three-level density matrix.

Figures (3)

• Figure 1: Evolution generated by $U(t,\alpha)$ on the double-quantum Bloch sphere. The equatorial path connects $\ket{+}=\ket{\xi(0)}$ to $\ket{\phi}=\ket{\xi( T')}$, passing through $\ket{\xi(0<t<\bar{T}')}$. The curved arrows show the transition from $\ket{0}$ to the corresponding equatorial states. The inset shows the effective Raman coupling in the three-level scheme, with couplings $\mu B$ and $\Omega/2$.
• Figure 2: Evolution of the angle $\xi(t)$ for three driving amplitudes, $\Omega=2\mu B$, $\Omega=3\mu B$, and $\Omega=5\mu B$. Time is expressed in units of $\bar{T}'$, and the angle is shown in units of $\pi$.
• Figure 3: (a) Evolution of the effective rotation angle $\theta_{5}(t)$ for $\Omega=2\mu B$, $\Omega=3\mu B$, and $\Omega=5\mu B$, with time given in units of $\bar{T}'$. (b) Parametric relation between $\xi(t)$ and $\theta_{5}(t)$ for the same driving amplitudes. Angles are shown in units of $\pi$.