Controlling the centre of mass motion of levitated particles using structured wavefronts

TL;DR

This work investigates how the spatial structure of the trapping wavefront affects the center-of-mass motion of optically levitated nanoparticles in vacuum. By combining phase-only wavefront shaping with a Zernike polynomial basis and a GLMT-based theoretical framework, the authors quantify how structured beams modify the trap stiffness and the ratios of the CoM frequencies $\\Omega^{(i)} = \sqrt{k_{trap}^{(i)}/m}$ along different axes, enabling a robust metric based on $\\Omega_x/\\Omega_z$ and related ratios. The study demonstrates that correcting aberrations with a low-order Zernike sequence can restore symmetry and maximize longitudinal or transverse frequencies depending on the experimental objective, with theory and experiment in close agreement via MOFT predictions. The resulting practical recipe for beam shaping reduces optical backaction and decoherence, advancing quantum sensing and fundamental tests with levitated nanoparticles.

Abstract

Optically levitated particles have great potential to form the basis of novel quantum- enhanced sensors. These systems are very well suited for inertial sensing, as the particles are isolated from the environment when they are levitated at low pressures. However, there are many challenges in the experimental realization that may affect the performance of these systems. For example, optical aberrations in the wavefront of the trapping laser which arise from optical elements or misalignment have a great impact on the trapping potential. The detrimental effect of optical aberrations has not been thoroughly studied, and usually they are iteratively corrected, giving some conflicting results depending on the figures of merit that are used. In this work, we present a thorough study of the effects of structuring the wavefront of the trapping beams. We observe that clean beams, i.e. highly focused beams with unaberrated wavefronts, may be used to optimize the longitudinal frequencies, at the cost of the transversal ones. Our work is based in a combination of experimental studies using a complete basis of orthogonal polynomials (Zernike polynomials) to control the wavefront and a set of numerical calculations, which allow us to compare the impact of structured wavefronts on the quality of traps for optically levitated particles in vacuum. This will have direct applications in quantum sensing and fundamental studies of quantum mechanics, as it allows the reduction of optical backaction and thermal decoherence of the particles.

Figures (10)

• Figure 1: The schematic diagram of our experimental setup: Starting from the bottom-right: A 1064 nm laser is collimated and expanded to the approximate diameter of the SLM. The holograms programmed on the are used to diffract the beam and correct its wavefront. Then a 4f system filters and collimate the first diffracted order into the chamber microscope objective OBJ inside the vacuum chamber. An aspheric lens collects the scattered light and send it to the detection system.
• Figure 2: Theoretical simulation of of back aperture filling of the objective lens ($NA=0.9$) in linear (a) and circular (b) polarization with respect to the ratios of the frequencies of the multiple particles by GLMT.
• Figure 3: (a)-(b) represents the Power spectrum density of levitated nanoparticle. PSD in (a) linear and (b) in circular polarization, the dashed lines represent uncorrected and the solid lines are in corrected beam. (c)-(d) is the Frequency ratios of levitated nanoparticle. The solid lines represents the theoretical prediction of back aperture filling of the objective lens in linear (c) and circular (d) polarization with respect to the ratios of the frequencies of the particle. The black circular dots in (c) and (d) represents the CoM motion ratios in uncorrected beam profile. The red star in (c) and (d) represent the CoM motion ratios in the corrected beam profile.
• Figure 4: Sweep of Spherical in circular polarization. The green line in (a) represents the variation of frequency along the longitudinal axis ${\Omega_z}$, (b) shows the change in frequencies along transversal axis ${\Omega_x}$, ${\Omega_y}$. And (c) represents the ratios between transversal and longitudinal directions ${\Omega_x}/{\Omega_z}$ and ${\Omega_y}/{\Omega_z}$, respectively.
• Figure 5: Maps of the CoM frequencies for the (a) z, (b) x and (c) for for a grid sweep of the Spherical and Defocus parameters in linear polarization. The fixed values of Astigmatism X and Astigmatism D were selected to restore the cylindrical symmetry in circular polarization, while the fixed values of Coma X and Coma Y where selected to maximize $\Omega_z$, resulting in an small increase of around $3\ \mathrm{kHz}$.