Imaging-based feedback cooling of a levitated nanoparticle.

Imaging-based detection of the motion of levitated nanoparticles complements a widely used interferometric detection method, providing a precise and robust way to estimate the position of the particle. Here, we demonstrate a camera-based feedback cooling scheme for a charged nanoparticle levitated in a linear Paul trap. The nanoparticle levitated in vacuum was imaged using a complementary metal-oxide semiconductor (CMOS) camera system. The images were processed in real-time with a microcontroller integrated with a CMOS image sensor. The phase-delayed position signal was fed back to one of the trap electrodes, resulting in cooling by velocity damping. Our study provides a simple and versatile approach applicable for the control of low-frequency mechanical oscillators.

Realizing Einstein's Mirror: Optomechanical Damping with a Thermal Photon Gas.

Einstein described the damping and thermalization of the center-of-mass motion of a mirror placed inside a blackbody cavity by collisions with thermal photons. While the time for damping even a microscale or nanoscale object is so long that it is not experimentally viable, we show that this damping is feasible using the high-intensity light from an amplified thermal light source with a well-defined chemical potential. We predict this damping of the center-of-mass motion will occur on timescales of tens of seconds for small optomechanical systems.

Quantum Spectrometry for Arbitrary Noise.

We present a technique for recovering the spectrum of a non-Markovian bosonic bath and/or non-Markovian noises coupled to a harmonic oscillator. The treatment is valid under the conditions that the environment is large and hot compared to the oscillator, and that its temporal autocorrelation functions are symmetric with respect to time translation and reflection-criteria which we consider fairly minimal. We model a demonstration of the technique as deployed in the experimental scenario of a nanosphere levitated in a Paul trap, and show that it would effectively probe the spectrum of an electric field noise source from 10^{2} to 10^{6} Hz with a resolution inversely proportional to the measurement time. This technique may be deployed in quantum sensing, metrology, computing, and in experimental probes of foundational questions.

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 106 with a displacement sensitivity better than 10-16 m2/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 time scales 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 required.

Field Evaluation of a Portable Whispering Gallery Mode Accelerometer.

An accelerometer utilising the optomechanical coupling between an optical whispering gallery mode (WGM) resonance and the motion of the WGM cavity itself was prototyped and field-tested on a vehicle. We describe the assembly of this portable, battery operated sensor and the field-programmable gate array automation. Pre-trial testing using an electrodynamic shaker demonstrated linear scale-factors with <0.3% standard deviation ( ± 6 g range where g = 9.81 ms - 2 ), and a strong normalised cross-correlation coefficient (NCCC) of r ICP / WGM = 0.997 when compared with an integrated circuit piezoelectric (ICP) accelerometer. A noise density of 40 µ g Hz - 1 / 2 was obtained for frequencies of 2⁻7 kHz, increasing to 130 µ g Hz - 1 / 2 at 200 Hz, and 250 µ g Hz - 1 / 2 at 100 Hz. A reduction in the cross-correlation was found during the trial, r ICP / WGM = 0.36, which we attribute to thermal fluctuations, mounting differences, and the noisy vehicle environment. The deployment of this hand-fabricated sensor, shown to operate and survive during ±60 g shocks, demonstrates important steps towards the development of a chip-scale device.

Gravimetry through non-linear optomechanics.

Precision gravimetry is key to a number of scientific and industrial applications, including climate change research, space exploration, geological surveys and fundamental investigations into the nature of gravity.  A variety of quantum systems, such as atom interferometry and on-chip-Bose-Einstein condensates have thus far been investigated to this aim. Here, we propose a new method which involves using a quantum optomechanical system for measurements of gravitational acceleration. As a proof-of-concept, we investigate the fundamental sensitivity for gravitational accelerometry of a cavity optomechanical system with a trilinear radiation pressure light-matter interaction. The phase of the optical output encodes the gravitational acceleration g and is the only component which needs to be measured. We prove analytically that homodyne detection is the optimal readout method and we predict an ideal fundamental sensitivity of Δg = 10-15 ms-2 for state-of-the-art parameters of optomechanical systems, showing that they could, in principle, surpass the best atomic interferometers even for low optical intensities. Further, we show that the scheme is strikingly robust to the initial thermal state of the oscillator.

An analytical model for the detection of levitated nanoparticles in optomechanics.

Interferometric position detection of levitated particles is crucial for the centre-of-mass (CM) motion cooling and manipulation of levitated particles. In combination with balanced detection and feedback cooling, this system has provided picometer scale position sensitivity, zeptonewton force detection, and sub-millikelvin CM temperatures. In this article, we develop an analytical model of this detection system and compare its performance with experimental results allowing us to explain the presence of spurious frequencies in the spectra.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions.

We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9} amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.

Burning and graphitization of optically levitated nanodiamonds in vacuum.

A nitrogen-vacancy (NV(-)) centre in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic centre-of-mass superpositions and for testing quantum gravity. Here, we study the behaviour of optically levitated nanodiamonds containing NV(-) centres at sub-atmospheric pressures and show that while they burn in air, this can be prevented by replacing the air with nitrogen. However, in nitrogen the nanodiamonds graphitize below ≈10 mB. Exploiting the Brownian motion of a levitated nanodiamond, we extract its internal temperature (T(i)) and find that it would be detrimental to the NV(-) centre's spin coherence time. These values of T(i) make it clear that the diamond is not melting, contradicting a recent suggestion. Additionally, using the measured damping rate of a levitated nanoparticle at a given pressure, we propose a new way of determining its size.

Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances.

We demonstrate simultaneous center-of-mass cooling of two coupled oscillators, consisting of a microsphere-cantilever and a tapered optical fiber. Excitation of a whispering gallery mode (WGM) of the microsphere, via the evanescent field of the taper, provides a transduction signal that continuously monitors the relative motion between these two microgram objects with a sensitivity of 3 pm. The cavity enhanced optical dipole force is used to provide feedback damping on the motion of the micron-diameter taper, whereas a piezo stack is used to damp the motion of the much larger (up to 180 µm in diameter), heavier (up to 1.5 × 10(-7) kg) and stiffer microsphere-cantilever. In each feedback scheme multiple mechanical modes of each oscillator can be cooled, and mode temperatures below 10 K are reached for the dominant mode, consistent with limits determined by the measurement noise of our system. This represents stabilization on the picometer level and is the first demonstration of using WGM resonances to cool the mechanical modes of both the WGM resonator and its coupling waveguide.

Cavity cooling a single charged levitated nanosphere.

Optomechanical cavity cooling of levitated objects offers the possibility for laboratory investigation of the macroscopic quantum behavior of systems that are largely decoupled from their environment. However, experimental progress has been hindered by particle loss mechanisms, which have prevented levitation and cavity cooling in a vacuum. We overcome this problem with a new type of hybrid electro-optical trap formed from a Paul trap within a single-mode optical cavity. We demonstrate a factor of 100 cavity cooling of 400 nm diameter silica spheres trapped in vacuum. This paves the way for ground-state cooling in a smaller, higher finesse cavity, as we show that a novel feature of the hybrid trap is that the optomechanical cooling becomes actively driven by the Paul trap, even for singly charged nanospheres.

Trapping cold ground state argon atoms.

We trap cold, ground state argon atoms in a deep optical dipole trap produced by a buildup cavity. The atoms, which are a general source for the sympathetic cooling of molecules, are loaded in the trap by quenching them from a cloud of laser-cooled metastable argon atoms. Although the ground state atoms cannot be directly probed, we detect them by observing the collisional loss of cotrapped metastable argon atoms and determine an elastic cross section. Using a type of parametric loss spectroscopy we also determine the polarizability of the metastable 4s[3/2](2) state to be (7.3±1.1)×10(-39) C m(2)/V. Finally, Penning and associative losses of metastable atoms in the absence of light assisted collisions, are determined to be (3.3±0.8)×10(-10) cm(3) s(-1).

Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin.

We show how the interference between spatially separated states of the center of mass (c.m.) of a mesoscopic harmonic oscillator can be evidenced by coupling it to a spin and performing solely spin manipulations and measurements (Ramsey interferometry). We propose to use an optically levitated diamond bead containing a nitrogen-vacancy center spin. The nanoscale size of the bead makes the motional decoherence due to levitation negligible. The form of the spin-motion coupling ensures that the scheme works for thermal states so that moderate feedback cooling suffices. No separate control or observation of the c.m. state is required and thereby one dispenses with cavities, spatially resolved detection, and low-mass-dispersion ensembles. The controllable relative phase in the Ramsey interferometry stems from a gravitational potential difference so that it uniquely evidences coherence between states which involve the whole nanocrystal being in spatially distinct locations.

Single-shot coherent Rayleigh-Brillouin scattering using a chirped optical lattice.

We present a method for obtaining coherent Rayleigh-Brillouin scattering (CRBS) spectra on timescales of hundreds of nanoseconds using rapidly chirped, pulsed, optical lattices. This enables us to transfer the spectral profile to a temporal profile which can be easily recorded on a single shot of an oscilloscope. These spectra are demonstrated to have sufficient signal-to-noise ratio to study CRBS models over a wide range of gas densities.

A deep optical cavity trap for atoms and molecules with rapid frequency and intensity modulation.

We describe a deep far-off resonance trap for metastable argon atoms utilizing a medium finesse cavity and a high input power (30 W) to produce trap depths of up to 11 mK. The depth can be rapidly modulated allowing efficient loading of the trap, characterization of trapped atom temperature, and reduction of intensity noise. We measure the change in radius of curvature of the mirrors due to heating by the high circulating intensity and show that trapping is not adversely effected by this for all input powers.

Frequency stabilization of an external-cavity diode laser to metastable argon atoms in a discharge.

A laser stabilization scheme using magnetic dichroism in a RF plasma discharge is presented. This method has been used to provide a frequency stable external-cavity diode laser that is locked to the 4s[3/2](2) → 4p[5/2](3) argon laser cooling transition at 811.53 nm. Using saturated absorption spectroscopy, we lock the laser to a Doppler free peak which gave a locking range of 20 MHz when the slope of the error signal was maximized. The stability of the laser was characterized by determining the square root Allan variance of laser frequency fluctuations when the laser was locked. A stability of 129 kHz was measured at 1 s averaging time for data acquired over 6000 s.

Coherent Brillouin scattering.

We measure the spectrum of coherent Brillouin scattering (CBS) in a gas as a function of time and observe for the first time additional spectral sidebands and line shape narrowing of the Brillouin peak. We find that both effects result from the interference of the density modulation induced by the moving dipole force of the pump beams with the acoustic waves induced by their fast thermalization and are predicted by a hydrodynamic-light scattering model. These line shapes differ from both spontaneous and stimulated Brillouin scattering spectra and also from previous coherent Rayleigh-Brillouin measurements.