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arXiv:1701.04477 · Physical Review A

Shot-noise-dominant regime for ellipsoidal nanoparticles in a linearly polarized beam

Changchun Zhong, F. Robicheaux

Published May 26, 2017• 18 citations
arXivHTMLPDF

Abstract

Results on the heating and the parametric feedback cooling of an optically trapped anisotropic nanoparticle in the laser-shot-noise-dominant regime are presented. The related dynamical parameters, such as the oscillating frequency and shot noise heating rate, depend on the shape of the trapped particle. For an ellipsoidal particle, the ratio of the axis lengths and the overall size controls the shot noise heating rate relative to the frequency. For a particle with smaller ellipticity or bigger size, the relative heating rate for rotation tends to be smaller than that for translation indicating a better rotational cooling. For one feedback scheme, we also present results on the lowest occupation number that can be achieved as a function of the heating rate and the amount of classical uncertainty in the position measurement.

DOI
10.1103/physreva.95.053421

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Results on the heating and the parametric feedback cooling of an optically trapped anisotropic nanoparticle in the laser-shot-noise-dominant regime are presented. The related dynamical parameters, such as the oscillating frequency and shot noise heating rate, depend on the shape of the trapped particle. For an ellipsoidal particle, the ratio of the axis lengths and the overall size controls the shot noise heating rate relative to the frequency. For a particle with smaller ellipticity or bigger size, the relative heating rate for rotation tends to be smaller than that for translation indicating a better rotational cooling. For one feedback scheme, we also present results on the lowest occupation number that can be achieved as a function of the heating rate and the amount of classical uncertainty in the position measurement.
We report on direct feedback cooling of single nanoparticles in an optical lattice to near their motional ground state. We find that the laser phase noise triggers severe heating of nanoparticles' motion along the optical lattice. When the laser phase noise is decreased by orders of magnitude, the heating rate is reduced and accordingly the occupation number is lowered to about 3. We establish a model directly connecting the heating rate and the measured laser phase noise and elucidate that the occupation number under the lowest laser phase noise in our system is limited only by photon recoil heating. Our results show that the reduction of the laser phase noise near the oscillation frequency of nanoparticles is crucial for bringing them near the ground state and pave the way to sensitive accelerometers and quantum mechanical experiments with ultracold nanoparticles in an optical lattice.
We optically trap a single nanoparticle in high vacuum and cool its three spatial degrees of freedom by means of active parametric feedback. Using a single laser beam for both trapping and cooling we demonstrate a temperature compression ratio of four orders of magnitude. The absence of a clamping mechanism provides robust decoupling from the heat bath and eliminates the requirement of cryogenic precooling. The small size and mass of the nanoparticle yield high resonance frequencies and high quality factors along with low recoil heating, which are essential conditions for ground state cooling and for low decoherence. The trapping and cooling scheme presented here opens new routes for testing quantum mechanics with mesoscopic objects and for ultrasensitive metrology and sensing.
We propose and demonstrate purely optical feedback cooling of neutral nanoparticles in an optical lattice to an occupation number of 0.85 ± 0.20. The cooling force is derived from the optical gradients of displaced optical lattices produced with two sidebands on the trapping laser. To achieve highly accurate position observations required for cooling near the ground state, we reduce the laser intensity noise to a relative power noise of 6×10−8/Hz in a frequency band of 30 kHz to 600 kHz. We establish a reproducible method for neutralizing nanoparticles at high vacuum via a combination of discharging and irradiating an ultraviolet light. Our results form an important basis for the investigation of quantum mechanical properties of ultracold nanoparticles and are also useful for precision measurements with neutral nanoparticles.
The concept of critical ambient pressure is introduced in this paper. The particle escapes from its trap when the ambient pressure becomes comparable with or smaller than a critical value, even if the particle motion is cooled by one of the feedback cooling (or cavity cooling) schemes realized so far. The critical ambient pressure may be so small that it is not a limiting factor in ground-state cooling, but critical feedback cooling rates, which are also introduced in this paper, are limiting factors. The particle escapes from its trap if any of the feedback cooling rates (corresponding to the components of the particle motion) becomes comparable with or larger than its critical value. The critical feedback cooling rate is different from the well-known manifestation of the measurement noise. The critical feedback cooling rate corresponding to a certain component of the particle motion is usually smaller than the optimum feedback cooling rate at which the standard quantum limit happens, unless that component is cooled by the Coulomb force (instead of the optical gradient force). In addition, given that the measurement noise for the z component of the particle motion is smaller than the measurement noises for the other two components (assuming that the beam illuminating the particle for photodetection propagates parallel to the z axis), the feedback scheme in which the z component of the particle motion is cooled by the Coulomb force has the best performance. This conclusion is in agreement with the experimental results published after writing the first version of this paper. The dependence of the critical ambient pressure, the critical feedback cooling rates, and the minimum achievable mean phonon numbers on the parameters of the system is derived in this paper, and can be verified experimentally. The insights into and the subtle points about the electromagnetic (EM) force (including the gradient force, radiation pressure, and recoil force), the EM force fluctuations, and the measurement noise presented in this paper are all of theoretical and practical importance, and might be useful in many systems besides those examined in this paper.
We demonstrate optical levitation and feedback cooling of a silica nanoparticle (radius = 78~nm) trapped within a radial vector beam (RVB) in high vacuum. Radial vector beams, when focused by a high-NA lens, produce a smaller focal spot than conventional Gaussian beams, yielding tighter optical potentials and potentially reduced photon-recoil heating rates. A vortex wave plate was used to generate the RVB using an aspheric lens (NA = 0.77) to form the trap. Cold-damping feedback was used to cool the center of mass motion in the radial and axial trap directions to temperatures in the mK range. At higher temperatures and pressures, additional trap frequencies arising from the nonlinear RVB optical potential are observed. This demonstration is a step toward exploiting structured light for levitated quantum optomechanics where these traps can be used to suppress bulk and motional heating.
We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force, and we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10−5^{-5}−5mbar and with feedback engaged the pressure is reduced to 10−6^{-6}−6mbar. Modifications to the harmonic motion in the presence of noise and feedback are studied, and an experimental mechanical quality factor >4×107>4\times 10^7>4×107 is estimated.