Levitated optomechanics with cylindrically polarized vortex beams

TL;DR

This work demonstrates that cylindrically polarized vector vortex beams (AVB and RVB) can markedly mitigate photon-recoil and bulk heating in levitated optomechanics, enabling robust 3D trapping of larger particles beyond the Rayleigh regime. Using Mie theory and Richard–Wolf focusing, the authors compute trap depths, frequencies, and heating rates for AVB/RVB versus conventional Gaussian traps across low- and high-NA geometries, revealing recoil-heating reductions up to about an order of magnitude in many configurations. RVB traps benefit from tighter axial focusing and reduced scattering in several regimes, while AVB traps offer tunable transverse potentials and potential non-linear or repulsive traps via wavelength control. The findings indicate practical routes to longer coherence times and access to non-classical motional states for massive nanoparticles, with bulk heating also favorably affected in many high-index configurations, though resonances can drive internal temperatures higher for certain materials.

Abstract

Optically levitated and cooled nanoparticles are a new quantum system whose application to the creation of non-classical states of motion and quantum limited sensing is fundamentally limited by recoil and bulk heating. We study the creation of stable 3D optical traps using optical cylindrically polarized vortex beams with radial and azimuthal polarization and show that a significant reduction in recoil heating by up to an order of magnitude can be achieved when compared with conventional single Gaussian beam tweezers. Additionally these beams allow trapping of larger particles outside the Rayleigh regime using both bright and dark tweezer trapping with reduced recoil heating. By changing the wavelength of the trapping laser, or the size of the particles, non-linear and repulsive potentials of interest for the creation of non-classical states of motion can also be created.

Figures (11)

• Figure 1: a) Trap depth, $\Delta U$, for a Si spherical nanoparticle in a linear polarized GB. The potential oscillates between attractive and repulsive trapping in the Mie Regime for a size parameter $kR |n-1| \approx 1$. b) A reduced size parameter interval shows asymmetry between the $x$ and $y$ potential in the transient phase between Rayleigh and Mie Regime. Black and brown dashed lines represent TM and TE modes respectively.
• Figure 2: Optical intensity and polarization pattern a-c) associated with Gaussian beam (GB), radial (RVB) and azimuthal beam (AVB), respectively, in the paraxial approximation. d-f) Optical intensity for high-focused beams ($\text{NA}=0.8$).
• Figure 3: a) Calculated trap depths, $\Delta U$, for a NA = 0.4 counter propagating AVB. The axial force becomes attractive for the entire range, reaching a maximum amplitude at the TM modes. Black and brown dashed lines represent TM and TE modes, respectively. b) Illustration of the counterpropagating AVB beams and the location of the trapped particle represented by a grey circle of size $R=222nm$ drawn at the equilibrium point. c) The optical potential for a $kR=0.9 (R=222nm)$.
• Figure 4: a) Calculated trap depth, $\Delta U$, for the single beam AVB focused using a 0.8 NA lens. The axial repulsive force becomes dominant near the TM modes. Three-dimensional trapping is found for size parameter regions given by $kR=[1.30, 1.36]$ and $[1.54,1.59]$. Black and brown dashed lines represent TM and TE modes, respectively. b) Illustration of the AVB single beam trap with a circle of size R representing the trapped particle at $z=z_{\text{eq}}$ where the particle finds an equilibrium point. c) The optical potential for $kR=1.56$ ($R=385nm$) at $z_{\text{eq}}=-1.3µ m$.
• Figure 5: Transverse potential profile as a function of wavelength in a AVB trap. Curves are shown for a particle radius $R=385nm$. Red shifting the trapping wavelength flattens the potential and can even lead to a repulsive potential as proposed in quantum interference protocols.