Super-resolution imaging of a low frequency levitated oscillator

We describe the measurement of the secular motion of a levitated nanoparticle in a Paul trap with a CMOS camera. This simple method enables us to reach signal-to-noise ratios as good as 10$^{6}$ with a displacement sensitivity better than 10$^{-16}\,m^{2}$/Hz. This method can be used to extract trap parameters as well as the properties of the levitated particles. We demonstrate continuous monitoring of the particle dynamics on timescales of the order of weeks. We show that by using the improvement given by super-resolution imaging, a significant reduction in the noise floor can be attained, with an increase in the bandwidth of the force sensitivity. This approach represents a competitive alternative to standard optical detection for a range of low frequency oscillators where low optical powers are require

Optomechanics with an electrodynamically levitated oscillator

In this work I report on a hybrid trap platform for sensitive optomechanics experiments with applications in quantum physics, thermodynamics and material science. We characterise a miniature linear Paul trap which can be used in combination with an optical cavity. The low-frequency harmonic motion of a nanoparticle levitated in a Paul trap can be detected with competitive sensitivities using a super-resolution imaging technique. This same method can be applied to characterise trap stability and nanosphere parameters such as mass with a 3% uncertainty. Using this same method at room temperature and at pressure of 3×10⁻⁷ mbar, we were able to measure an ultra-narrow mechanical linewidth of ∼80 µHz with a novel phase sensitive scheme which removes slow drifts in the mechanical frequency. We used this measurement to place new bounds on dissipative versions of wavefunction collapse models. Using two optical cavity modes with different frequencies interacting with a nanoparticle levitated within a Paul trap realises a versatile optomechanical system, which can be operated in regimes dominated by either linear or quadratic optomechanical coupling. We demonstrated cooling of the centre-of-mass motion of the nano-oscillator exclusively provided by the quadratic coupling. This nonlinear interaction gives rise to a highly non-thermal state of motion which matches well with theoretical predictions. In the linear regime, we report cooling down to Teff=21±4 mK limited by Paul trap noise, demonstrating stable trapping in the cavity standing-wave down to pressures ∼10⁻⁶ mbar. Using the same technique, we show that in theory, near ground state cooling could be achieved with better electronics used in conjunction with the filtering cavity developed as part of this work

Quadratic optomechanical cooling of a cavity-levitated nanosphere

We report on cooling the center-of-mass motion of a nanoparticle due to a purely quadratic coupling between its motion and the optical field of a high finesse cavity. The resulting interaction gives rise to a Van der Pol nonlinear damping, which is analogous to conventional parametric feedback where the cavity provides passive feedback without measurement. We show experimentally that like feedback cooling the resulting energy distribution is strongly nonthermal and can be controlled by the nonlinear damping of the cavity. As quadratic coupling has a prominent role in proposed protocols to generate deeply nonclassical states, our work represents a first step for producing such states in a levitated system

Characterisation of a charged particle levitated nano-oscillator

We describe the construction and characterisation of a nano-oscillator formed by a Paul trap. The frequency and temperature stability of the nano-oscillator was measured over several days allowing us to identify the major sources of trap and environmental fluctuations. We measure an overall frequency stability of 2 ppm/hr and a temperature stability of more than 5 hours via the Allan deviation. Importantly, we find that the charge on the nanoscillator is stable over a timescale of at least two weeks and that the mass of the oscillator, can be measured with a 3 % uncertainty. This allows us to distinguish between the trapping of a single nanosphere and a nano-dumbbell formed by a cluster of two nanospheres

An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapse

Levitated nano-oscillators are seen as promising platforms for testing fundamental physics and testing quantum mechanics in a new high mass regime. Levitation allows extreme isolation from the environment, reducing the decoherence processes that are crucial for these sensitive experiments. A fundamental property of any oscillator is its line width and mechanical quality factor, Q. Narrow line widths in the microHertz regime and mechanical Q's as high as $10^{12}$ have been predicted for levitated systems, but to date, the poor stability of these oscillators over long periods have prevented direct measurement in high vacuum. Here we report on the measurement of an ultra-narrow line width levitated nano-oscillator, whose line width of $81\pm\,23\,\mu$Hz is only limited by residual gas pressure at high vacuum. This narrow line width allows us to put new experimental bounds on dissipative models of wavefunction collapse including continuous spontaneous localisation and Di\'{o}si-Penrose and illustrates its utility for future precision experiments that aim to test the macroscopic limits of quantum mechanics

Millikelvin cooling of the center-of-mass motion of a levitated nanoparticle

Cavity optomechanics has been used to cool the center-of-mass motion of levitated nanospheres to millikelvin temperatures. Trapping the particle in the cavity field enables high mechanical frequencies bringing the system close to the resolved-sideband regime. Here we describe a Paul trap constructed from a printed circuit board that is small enough to fit inside the optical cavity and which should enable an accurate positioning of the particle inside the cavity field. This will increase the optical damping and therefore reduce the final temperature by at least one order of magnitude. Simulations of the potential inside the trap enable us to estimate the charge- to-mass ratio of trapped particles by measuring the secular frequencies as a function of the trap parameters. Lastly, we show the importance of reducing laser noise to reach lower temperatures and higher sensitivity in the phase-sensitive readout

Role of lateral and feedback connections in primary visual cortex in the processing of spatiotemporal regularity: a TMS study

Our human visual system exploits spatiotemporal regularity to interpret incoming visual signals. With a dynamic stimulus sequence of four collinear bars (predictors) appearing consecutively toward the fovea, followed by a target bar with varying contrasts, we have previously found that this predictable spatiotemporal stimulus structure enhances target detection performance and its underlying neural process starts in the primary visual cortex (area V1). However, the relative contribution of V1 lateral and feedback connections in the processing of spatiotemporal regularity remains unclear. In this study we measured human contrast detection of a briefly presented foveal target that was embedded in a dynamic collinear predictor-target sequence. Transcranial magnetic stimulation (TMS) was used to selectively disrupt V1 horizontal and feedback connections in the processing of predictors. The coil was positioned over a cortical location corresponding to the location of the last predictor prior to target onset. Single-pulse TMS at an intensity of 10% below phosphene threshold was delivered at 20 or 90ms after the predictor onset. Our analysis revealed that the delivery of TMS at both time windows equally reduced, but did not abolish, the facilitation effect of the predictors on target detection. Furthermore, if the predictors’ ordination was randomized to suppress V1 lateral connections, the TMS disruption was significantly more evident at 20ms than at 90ms time window. We suggest that both lateral and feedback connections contribute to the encoding of spatiotemporal regularity in V1. These findings develop understanding of how our visual system exploits spatiotemporal regularity to facilitate the efficiency of visual perception