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

Testing collapse models with levitated nanoparticles: the detection challenge

We consider a nanoparticle levitated in a Paul trap in ultrahigh cryogenic vacuum, and look for the conditions which allow for a stringent noninterferometric test of spontaneous collapse models. In particular we compare different possible techniques to detect the particle motion. Key conditions which need to be achieved are extremely low residual pressure and the ability to detect the particle at ultralow power. We compare three different detection approaches based respectively on a optical cavity, optical tweezer and a electrical readout, and for each one we assess advantages, drawbacks and technical challenges

Sympathetic cooling and squeezing of two co-levitated nanoparticles

Levitated particles are an ideal tool for measuring weak forces and investigating quantum mechanics in macroscopic objects. Arrays of two or more of these particles have been suggested for improving force sensitivity and entangling macropscopic objects. In this article, two charged, silica nanoparticles, that are coupled through their mutual Coulomb repulsion, are trapped in a Paul trap, and the individual masses and charges of both particles are characterised. We demonstrate sympathetic cooling of one nanoparticle coupled via the Coulomb interaction to the second nanoparticle to which feedback cooling is directly applied. We also implement sympathetic squeezing through a similar process showing non-thermal motional states can be transferred by the Coulomb interaction. This work establishes protocols to cool and manipulate arrays of nanoparticles for sensing and minimising the effect of optical heating in future experiments.Comment: 8 pages, 4 figure

Performance and limits of feedback cooling methods for levitated oscillators: a direct comparison

Cooling the centre-of-mass motion is an important tool for levitated optomechanical systems, but it is often not clear which method can practically reach lower temperatures for a particular experiment. We directly compare the parametric and velocity feedback damping methods, which are used extensively for cooling the motion of single trapped particles in a range of traps. By performing experiments on the same particle, and with the same detection system, we demonstrate that velocity damping cools the oscillator to lower temperatures and is more resilient to imperfect experimental conditions. We show that these results are consistent with analytical limits as well as numerical simulations that include experimental noise.Comment: 11 pages, 5 figure

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

Calibrated quantum thermometry in cavity optomechanics

Cavity optomechanics has achieved the major breakthrough of the preparation and observation of macroscopic mechanical oscillators in peculiarly quantum states. The development of reliable indicators of the oscillator properties in these conditions is important also for applications to quantum technologies. We compare two procedures to infer the oscillator occupation number, minimizing the necessity of system calibrations. The former starts from homodyne spectra, the latter is based on the measurement of the motional sidebands asymmetry in heterodyne spectra. Moreover, we describe and discuss a method to control the cavity detuning, that is a crucial parameter for the accuracy of the latter, intrinsically superior procedure

Dynamical two-mode squeezing of thermal fluctuations in a cavity opto-mechanical system

We report the experimental observation of two-mode squeezing in the oscillation quadratures of a thermal micro-oscillator. This effect is obtained by parametric modulation of the optical spring in a cavity opto-mechanical system. In addition to stationary variance measurements, we describe the dynamic behavior in the regime of pulsed parametric excitation, showing enhanced squeezing effect surpassing the stationary 3dB limit. While the present experiment is in the classical regime, our technique can be exploited to produce entangled, macroscopic quantum opto-mechanical modes

Control of Recoil Losses in Nanomechanical SiN Membrane Resonators

In the context of a recoil damping analysis, we have designed and produced a membrane resonator equipped with a specific on-chip structure working as a "loss shield" for a circular membrane. In this device the vibrations of the membrane, with a quality factor of $10^7$, reach the limit set by the intrinsic dissipation in silicon nitride, for all the modes and regardless of the modal shape, also at low frequency. Guided by our theoretical model of the loss shield, we describe the design rationale of the device, which can be used as effective replacement of commercial membrane resonators in advanced optomechanical setups, also at cryogenic temperatures