Wigner Function Reconstruction in Levitated Optomechanics

We demonstrate the reconstruction of the Wigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the effect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics.Comment: 9 pages, 3 figure

Precession Motion in Levitated Optomechanics

We investigate experimentally the dynamics of a non-spherical levitated nanoparticle in vacuum. In addition to translation and rotation motion, we observe the light torque-induced precession and nutation of the trapped particle. We provide a theoretical model, which we numerically simulate and from which we derive approximate expressions for the motional frequencies. Both, the simulation and approximate expressions, we find in good agreement with experiments. We measure a torque of $1.9 \pm 0.5 \times 10^{-23}$ Nm at $1 \times 10^{-1}$ mbar, with an estimated torque sensitivity of $3.6 \pm 1.1 \times 10^{-31}$ Nm/$\sqrt{\text{Hz}}$ at $1 \times 10^{-7}$ mbar.Comment: 10 pages, 4 figure

Wigner Function Reconstruction in Levitated Optomechanics

We demonstrate the reconstruction of theWigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the efect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics

Detection of anisotropic particles in levitated optomechanics

We discuss the detection of an anisotropic particle trapped by an elliptically polarized focused Gaussian laser beam. We obtain the full rotational and translational dynamics, as well as the measured photocurrent in a general-dyne detection. As an example, we discuss a toy model of homodyne detection, which captures the main features typically found in experimental setups

Data used in article: Precession Motion in Levitated Optomechanics

Data associated and used in the following article: Ulbricht, H., Toros, M., Rashid, M., &amp; Setter, A. J. (2018). Precession motion in levitated optomechanics. Physical Review Letters, 121(25), [253601]. DOI: 10.1103/PhysRevLett.121.253601</span

Precession motion in levitated optomechanics

We investigate experimentally the dynamics of a non-spherical levitated nanoparticle in vacuum. In addition to translation and rotation motion, we observe the light torque-induced precession and nutation of the trapped particle. We provide a theoretical model, which we numerically simulate and from which we derive approximate expressions for the motional frequencies. Both, the simulation and approximate expressions, we find in good agreement with experiments. We measure a torque of 1.9±0.5�10�23 Nm at 1�10�1 mbar, with an estimated torque sensitivity of 3.6±1.1�10�31 Nm/�Hz at 1�10�7 mbar

Static force characterization with Fano anti-resonance in levitated optomechanics

We demonstrate a classical analogy to the Fano anti-resonance in levitated optomechanics by applying a DC electric field. Specifically, we experimentally tune the Fano parameter by applying a DC voltage from 0 kV to 10 kV on a nearby charged needle tip. We find consistent results across negative and positive needle voltages, with the Fano line-shape feature able to exist at both higher and lower frequencies than the fundamental oscillator frequency. We can use the Fano parameter to characterize our system to be sensitive to static interactions which are ever-present. Currently, we can distinguish a static Coulomb force of 2.7 ± 0.5 × 10−15 N with the Fano parameter, which is measured with 1 s of integration time. Furthermore, we are able to extract the charge to mass ratio of the trapped nanoparticle

Direct measurement of the electrostatic image force of a levitated charged nanoparticle close to a surface

We report on optical levitation experiments to probe the interaction of a nanoparticle with a surface in vacuum. The observed interaction-induced effect is a controllable anharmonicity of the particle trapping potential. We reconstruct the Coulomb image charge interaction potential to be in perfect agreement with the experimental data for a particle carrying Q=-(11±1)e elementary charges and compare the measured electrostatic interaction with the weaker dispersive forces from theory. Our experimental results may open the route for a new surface sensitive scanning probe technique based on the high mechanical sensitivity of levitated nanoparticles.</p