Angle Locking of a Levitating Diamond Using Spin Diamagnetism

Nanodiamonds with embedded nitrogen-vacancy (NV) centers have emerged as promising magnetic field sensors, as hyperpolarizing agents in biological environments, as well as efficient tools for spin mechanics with levitating particles. These applications currently suffer from random environmental interactions with the diamond which implies poor control of the N-V direction. Here, we predict and report on a strong diamagnetism of a pure spin origin mediated by a population inversion close to a level crossing in the NV center electronic ground state. We show control of the sign of the magnetic susceptibility as well as angle locking of the crystalline axis of a microdiamond along an external magnetic field, with bright perspectives for these applications.

Figure 1

(a) Trace (i) and trace (ii), show the expected NV susceptibility coefficients ${\chi }_{\perp }$ and ${\chi }_d$ as a function of ${\gamma }_e{B}_0$. Trace (iii) (in dashed lines) displays ${\chi }_{\perp }$ obtained from Eq. (1). The states $|m_s=0^{\prime }⟩$ and $|m_s=-1^{\prime }⟩$ are eigenstates of the Hamiltonian away from the level crossing. (b) and (c) Mechanically detected-magnetic resonances measured in the paramagnetic and diamagnetic regime where $B=23$ and 180 mT, respectively. The inset of (c) is an enlargement on the first spin resonance at 2.2 GHz. The dashed line is a sketch of an MDMR in the weak microwave drive limit (arbitrary scale of the $y$ axis).

Figure 2

Angle of one of the diamond [111] axes versus magnetic field amplitude.

Figure 3

Angle $\theta$ of the diamond [111] axis versus magnetic field angle ${\theta }_B$ (blue circles). See sketch in the inset on the top right. The plain blue line is the response that would be obtained without NV induced magnetism. The inset on the top left is a mechanically detected magnetic-resonance scan taken at ${\theta }_B\approx 14°$.

Figure 4

a) NV center’s electronic spin eigenstates in the ${}^3{A}_2$ state. Green arrows depicts the effective optical pumping to the $|m_s=0⟩$ state that results from the intersystem crossing in the optically excited ${}^{3}E$ state (not shown). Black arrows depict depolarizing mechanisms at rates $1/T_1$. b) Angle of one of the NV axes with respect to the magnetic field direction (as shown in the inset) as a function of the green laser power. c) Trace i) and trace ii), show the power spectral density of the librational modes without/with the green laser respectively. d) Librational frequency of the first mode as a function of laser power.