Optical Trapping of High-Aspect-Ratio NaYF Hexagonal Prisms for kHz-MHz Gravitational Wave Detectors

We present experimental results on optical trapping of Yb-doped $\beta$-NaYF subwavelength-thickness high-aspect-ratio hexagonal prisms with a micron-scale radius. The prisms are trapped in vacuum using an optical standing wave, with the normal vector to their face oriented along the beam propagation direction, yielding much higher trapping frequencies than those typically achieved with microspheres of similar mass. This platelike geometry simultaneously enables trapping with low photon-recoil-heating, high mass, and high trap frequency, potentially leading to advances in high frequency gravitational wave searches in the Levitated Sensor Detector, currently under construction. The material used here has previously been shown to exhibit internal cooling via laser refrigeration when optically trapped and illuminated with light of suitable wavelength. Employing such laser refrigeration methods in the context of our work may enable higher trapping intensity and thus higher trap frequencies for gravitational wave searches approaching the several hundred kilohertz range.

Figure 1

(a) Setup. The hexagonal prism is trapped at the conjoined foci of two 1550 nm counterpropagating linearly polarized beams. Fiber-based detection is achieved through homodynelike interference of light coupled back into the polarization-maintaining fiber and the reference light out of the $95/5$ coupler through a fiber photodetector (bandwidth of 1.6 GHz). Scattered light is also detected through a series of three biased photodiodes (PDs) and two quadrant photodetectors (QPDs) viewing the prism from the side, bottom, and top diagonal directions, as indicated. (b) Scanning electron beam micrograph of a cluster of NaYF hexagonal prisms from the $B2$ sample. (c) Optical micrograph of NaYF prism, adapted from Ref. [34]. (d) Spectral density of the motional signal at 2.2 mbar recorded by one of the QPD detectors for two different size hexagonal prisms, batch $B1$ (top $P=475\mathrm{mW}$) and $B2$ (bottom $P=250\mathrm{mW}$), respectively, with dimensions as described in the text. Motion corresponding to five principal degrees of freedom $(x,y,z,{\theta }_x,{\theta }_y)$ of the hexagon is visible, due to the nonperfectly orthogonal viewing angle of the detector. Vertical lines indicate calculated frequencies from a finite-element simulation for similar prisms, showing qualitative agreement.

Figure 2

Experimentally obtained power spectral densities for two sizes of hexagonal prisms, $B1$ (top) and $B2$ (bottom) from multiple detectors oriented to the side (i), bottom (ii), top diagonal (iii), and along the trap axis (iv). Detector types include quadrant photodetectors (blue, orange, and red), biased photodiodes (green), and a fiber-coupled homodynelike interferometric detector (purple). Observed peak maxima corresponding to $x$, $y$, ${\theta }_x$, ${\theta }_y$, and $z$ motion are denoted by vertical dashed lines. The $x$ and $y$ modes are degenerate for this $B1$ prism. The vertical scale corresponds to the displacement in the direction used for detector calibration, as indicated also by the bold label (see Supplemental Material [36]). In some cases, higher harmonics of the labeled peaks are visible in the spectra, indicating the presence of nonlinearities.

Figure 3

(a) Calculated far-field scattered electric field profile $|E|\widehat{k}$ for a hexagonal prism of thickness 200 nm and diameter $4\mu \mathrm{m}$ (within the size range of the $B2$ samples), for beam incident along $x$ with a normalized electric field of $1\mathrm{V}/\mathrm{m}$. The color bar shows the magnitude of the field and the surface plot shows the directional dependence of scattering. (b) (left) Figure of merit ${\eta }_{\text{thermal}}={\omega }_0^2\sqrt{M\rho l}$ (in units of ${\mathrm{Hz}}^2\mathrm{kg}/\mathrm{m}$) in the thermal-noise dominated limit, for spheres and plates of mass $M$ and radius $r=l$ or thickness $t=l$, respectively, for recent experimentally realized trapping configurations. At equal masses, high aspect ratio levitated plates (blue hexagons, $5\mu \mathrm{m}$ diameter prism from sample $B2$) significantly outperform levitated spheres (black circles, as reported in Refs. [1, 9, 10, 42, 43], in order of decreasing frequency) for gravitational wave experiments due to their correspondingly higher trapping frequencies. Projected sensitivity for the same size plate held at higher trapping frequency is shown (open blue hexagon), as may be possible by using a higher intensity trap. (right) Figure of merit ${\eta }_{\text{recoil}}={\omega }_0^{3/2}\sqrt{M/{\gamma }_{\mathrm{sc}}}$ (in units of $\mathrm{Hz}{\mathrm{kg}}^{1/2}$) in the photon-recoil-heating dominated limit. Data for nanospheres from Refs. [1, 42]. Projections shown for a prism of the size trapped in this work, for currently realized beam parameters with an estimated ${\mathcal{F}}_{\mathrm{disc}}$ of $1.1\times {10}^3$ (solid hexagon) and for two trapping frequencies with a suitably apodized edge and beam waist profile, with an estimated ${\mathcal{F}}_{\mathrm{disc}}$ of ${10}^5$ (open hexagons).