Experimental realization of a thermal squeezed state of levitated optomechanics

We experimentally squeeze the thermal motional state of an optically levitated nanosphere by fast switching between two trapping frequencies. The measured phase-space distribution of the center of mass of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7 dB of squeezing along one motional direction. In these experiments the average thermal occupancy is high and, even after squeezing, the motional state remains in the remit of classical statistical mechanics. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing in the quantum regime if preceded by cooling of the levitated mechanical oscillator. Additionally, a higher degree of squeezing could, in principle, be achieved by repeating the frequency-switching protocol multiple times

Dynamical model selection near the quantum-classical boundary

We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in post-selection as well as for real-time analysis, and offers an alternative to statistical tests based on state-reconstruction methods. We examine the conditions that optimize quantum hypothesis testing, maximizing one's ability to discriminate between classical and quantum models. We set upper limits on the temperature and lower limits on the measurement efficiencies required to explore these differences, using a novel experiment in levitated optomechanical systems as an example.Comment: 9 pages, 1 figure. Accepted for publication in Physical Review A (Rapid Communication

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

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

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

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 one second of integration time. Furthermore, we are able to extract the charge to mass ratio of the trapped nanoparticle

Force sensing with an optically levitated charged nanoparticle

Levitated optomechanics is showing potential for precise force measurements. Here, we report a case study to show experimentally the capacity of such a force sensor, using an electric field as a tool to detect a Coulomb force applied onto a levitated nanosphere. We experimentally observe the spatial displacement of up to 6.6 nm of the levitated nanosphere by imposing a DC field. We further apply an AC field and demonstrate resonant enhancement of force sensing when a driving frequency, ωAC, and the frequency of the levitated mechanical oscillator, ω0, converge. We directly measure a force of 3.0 ± 1.5 × 10–20 N with 10 s integration time, at a centre of mass temperature of 3 K and at a pressure of 1.6 × 10–5 mbar