Rotating fluorescent nanodiamond assemblies with focused Laguerre-Gaussian beams

TL;DR

This work addresses vector magnetometry with nanodiamond NV centers where the crystal orientation is dynamic. It uses Laguerre-Gaussian beams to transfer orbital angular momentum to self-assembled nanodiamond structures, producing controlled 2D rotation up to 5 Hz. ODMR spectra are collected at multiple points along the orbit, and the angular stability of about Δθ ≈ ±13° under an external field of ~1.3 mT is incorporated into the analysis; the NV Hamiltonian in a field is $H = D S_z^2 + 2E(S_x^2 - S_y^2) + \\gamma_e \\vec{B} \\cdot \\vec{S}$, and a small orientation change yields $ΔE / |B| = Δθ γ_e sin θ$ with θ ≈ π/4. These results demonstrate that 2D rotation provides a route to vector field reconstruction and enhanced sensing with trapped nanodiamonds.

Abstract

Optical tweezers which utilize structured light fields enable the rotation of trapped nanoparticles through the transfer of orbital angular momentum (OAM) from holographically generated Laguerre-Gaussian (LG) modes. In this research we use OAM transfer to demonstrate controlled rotation of bright fluorescent nanodiamond clusters assembled in a focused higher-order LG beam. We find that the assemblies can be effectively rotated in a two-dimensional optical trap with orbital frequencies of up to 5 Hz. We use video tracking to explore the Brownian dynamics of such a trapping arrangement and look at the impact of orientation stability on measurements of optically detected magnetic resonance (ODMR) with an applied weak external magnetic field. By collecting ODMR spectra at multiple points along the orbit, we show that the constrained two-dimensional motion can provide additional insights for vector magnetic field reconstruction.

Figures (5)

• Figure 1: (a) Experimental apparatus: an infrared (1064 nm) laser reflected from a spatial light modulator (SLM) displaying an appropriate phase-mask is used to create a Laguerre-Gaussian mode at the focus of a high magnification objective (OBJ). Diascopic bright field illumination is used with a CCD camera to observe the motion of the nanodiamond (ND) assemblies. A co-linearly aligned green (532 nm) laser is used to excite fluorescence from the NV- defect centres, which is collected with a single photon avalanche diode (SPAD) via a flipper (FLIP) mirror. A 2-4 GHz RF signal applied to the sample via a small loop antenna is used to drive the NV- electronic spin states which creates optical contrast in the fluorescence intensity. (b) In a typical experiment, freely dispersed NDs are pushed to the top cover-slip where they accumulated into aggregates in the high intensity ring. The ND assemblies begin to orbit with controlled rotation due to the transfer of optical angular momentum. The orientation of the assemblies changes with respect to an external magnetic field. (c) Example scanning electron microscope (SEM) images of ND assemblies formed inside the optical tweezers apparatus, which influences the optically detected magnetic resonance (ODMR). (d) ODMR contrast is produced between the $m_s = 0$ and $m_s = \pm 1$ by a preferential relaxation from triplet excited (3E) to ground state (3A) via the non-radiative singlet state. The application of a magnetic field will create a Zeeman splitting of the $m_s = \pm 1$ states.
• Figure 2: (a) CCD camera frames with the tracked particle boundary (green), center of mass position (red) and elliptical fit (white). (b) The particles position over time as it orbits around the center of the beam. (c) The position density function of the contour fit over the measurement. The black line is the elliptical fit and the cross marks the center. (d) A simulated Laguerre-Gaussian beam profile of the optical tweezers, with azimuthal mode $l = +7$ and radial mode $m = 0$ (TEM$_{07}$), 5 $\mu$m displacement in +z from focus. (e) A histogram of the angular difference between the orientation of the rotating particle and the tangent of the nearest position on the elliptical axis, for all the frames in the dataset. The fit (red) to the data (blue) has mean value $|\mu|$ = 1.4 $\deg$ and standard deviation $\sigma$ = 6.3 $\deg$. (f) A graphic of the angular separation and the particle orientation.
• Figure 3: (a) The nanodiamond assemblies orbit around the beam axis (dotted line) and are excited with a Gaussian mode solid-state green laser. The excitation beam is positioned at a point on the orbital path and stimulates emission of the nitrogen-vacancy (NV-) centers (b) The NV- center fluorescence is collected with an avalanche photodiode detector (APD). The time-trace shows periodic peaks which occur when the nanodiamonds coincide with the excitation beam. The dotted region is zoomed to show the shape of individual peaks. (c) The optically detected magnetic resonance (ODMR) spectrum in ambient magnetic field condition. The fit (black line) has a spectral doublet Lorentzian line-shape with center frequency 2870 MHz, separation of 11.0 $\pm$ 0.6 MHz, and linewidth of 14.4 $\pm$ 1.4 MHz. The panel underneath the spectrum contains the cumulative average, which illustrates the convergence of repeated ODMR sweeps over the measurement. The cumulative average is calculated by sequentially averaging spectra collected during rotation. (d) The ODMR spectrum (and cumulative average panel below) when a rare-earth magnet is positioned to create an external magnetic field $\approx$ 1.3 mT. The fit has a 8-peak characteristic Lorentzian shape, where the linewidth is 11.2 $\pm$ 0.9 MHz.
• Figure 4: (a).i-.iii. Optically Detected Magnetic Resonance (ODMR) spectra of rotating nanodiamond assemblies measured under increasing external magnetic field strengths in a Laguerre-Gaussian TEM$_{07}$ beam. (b).i-.iii ODMR measurements collected with the excitation focused at orbital positions corresponding to a relative yaw angle of $0^{\circ}$, $90^{\circ}$ and $180^{\circ}$. The inset image in the top right depicts the orbital position where the ODMR spectra were collected. (c).i-.ii. Simulated ODMR spectra for orbital rotations around the beam center in an external magnetic field which is matched to our system. The locations highlighted are separated by $90^{\circ}$ and matched to the observed spectra in (b).i-.iii.
• Figure : Self-assembled fluorescent nanodiamond clusters are optically trapped and driven into controlled two-dimensional rotation with Laguerre–Gaussian beams. With localized optical excitation, optically detected magnetic resonance spectra are collected at defined points along the orbit in a uniform external magnetic field. This approach reveals orientation stability during rotation and establishes a route toward vector magnetic field reconstruction.