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We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading order nonlinearities manifest as shifts in the characteristic frequency of the system. The results are compared to numerical simulations. The present calculations enable a direct experimental method to access the nonlinear optical trap parameters by analyzing position data, similarly to standard harmonic tweezers.
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We propose to use optical tweezers to probe the Casimir interaction between microspheres inside a liquid medium for geometric aspect ratios far beyond the validity of the widely employed proximity force approximation. This setup has the potential for revealing unprecedented features associated to the non-trivial role of the spherical curvatures. For a proof of concept, we measure femtonewton double layer forces between polystyrene microspheres at distances above $400$ nm by employing very soft optical tweezers, with stiffness of the order of fractions of a fN/nm. As a future application, we propose to tune the Casimir interaction between a metallic and a polystyrene microsphere in saline solution from attraction to repulsion by varying the salt concentration. With those materials, the screened Casimir interaction may have a larger magnitude than the unscreened one. This line of investigation has the potential for bringing together different fields including classical and quantum optics, statistical physics and colloid science, while paving the way for novel quantitative applications of optical tweezers in cell and molecular biology.
We introduce a new optimization procedure for Euclidean path integrals which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed. Equivalently this is interpreted as a position-dependent UV cutoff. For two-dimensional CFT vacua, we find the optimized metric is given by that of a hyperbolic space and we interpret this as a continuous limit of the conjectured relation between tensor networks and Anti--de Sitter (AdS)/conformal field theory (CFT) correspondence. We confirm our procedure for excited states, the thermofield double state, the Sachdev-Ye-Kitaev model and discuss its extension to higher-dimensional CFTs. We also show that when applied to reduced density matrices, it reproduces entanglement wedges and holographic entanglement entropy. We suggest that our optimization prescription is analogous to the estimation of computational complexity.
We demonstrate a lock-in particle tracking scheme in optical tweezers based on stroboscopic modulation of an illuminating optical field. This scheme is found to evade low frequency noise sources while otherwise producing an equivalent position measurement to continuous measurement. This was demonstrated, and found to yield on average 20dB of noise suppression in the frequency range 10-5000 Hz, where low frequency laser noise and electronic noise was significant, and 35 dB of noise suppression in the range 550-710 kHz where laser relaxation oscillations introduced laser noise. The setup is simple, and compatible with any trapping optics.
Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this Tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely to study single-molecule and single-cell mechanics, microrheology, colloidal interactions, statistical physics, and transport phenomena. Finally, we consider optical tweezers in vacuum, where the absence of a viscous medium offers vastly different dynamics and presents new challenges. We conclude with some perspectives for the field and the future application of optical tweezers. This Tutorial provides both a step-by-step guide ideal for non-specialists entering the field and a comprehensive manual of advanced techniques useful for expert practitioners. All the examples are complemented by the sample data and software necessary to reproduce them.
We show that the optical force field in optical tweezers with elliptically polarized beams has the opposite handedness for a wide range of particle sizes and for the most common configurations. Our method is based on the direct observation of the particle equilibrium position under the effect of a transverse Stokes drag force, and its rotation around the optical axis by the mechanical effect of the optical torque. We find overall agreement with theory, with no fitting, provided that astigmatism, which is characterized separately, is included in the theoretical description. Our work opens the way for characterization of the trapping parameters, such as the microsphere complex refractive index and the astigmatism of the optical system, from measurements of the microsphere rotation angle.
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