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Register a new user5D cooling and nonlinear dynamics of an optically levitated nanodumbbell
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Optically levitated nonspherical particles in vacuum are excellent candidates for torque sensing, rotational quantum mechanics, high-frequency gravitational wave detection, and multiple other applications. Many potential applications, such as detecting the Casimir torque near a birefringent surface, require simultaneous cooling of both the center-of-mass motion and the torsional vibration (or rotation) of a nonspherical nanoparticle. Here we report the first 5D cooling of a levitated nanoparticle. We cool the 3 center-of-mass motion modes and 2 torsional vibration modes of a levitated nanodumbbell in a linearly-polarized laser simultaneously. The only uncooled rigid-body degree of freedom is the rotation of the nanodumbbell around its long axis. This free rotation mode does not couple to the optical tweezers directly. Surprisingly, we observe that it strongly affects the torsional vibrations of the nanodumbbell. This work deepens our understanding of the nonlinear dynamics and rotation coupling of a levitated nanoparticle and paves the way towards full quantum control of its motion.
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According to quantum theory, measurement and backaction are inextricably linked. In optical position measurements, this backaction is known as radiation pressure shot noise. In analogy, a measurement of the orientation of a mechanical rotor must disturb its angular momentum by radiation torque shot noise. In this work, we observe the shot-noise torque fluctuations arising in a measurement of the angular orientation of an optically levitated nanodumbbell. We feedback cool the dumbbells rotational motion and investigate its reheating behavior when released from feedback. In high vacuum, the heating rate due to radiation torque shot noise dominates over the thermal and technical heating rates in the system.
Levitated optomechanics has great potentials in precision measurements, thermodynamics, macroscopic quantum mechanics and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell in vacuum. The linearly-polarized optical tweezer provides a restoring torque to confine the orientation of the nanodumbbell, in analog to the torsion wire which provides restoring torque for suspended lead spheres in the Cavendish torsion balance. Our calculation shows its torque detection sensitivity can exceed that of the current state-of-the-art torsion balance by several orders. The levitated nanodumbbell torsion balance provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity as proposed recently. With a circularly-polarized laser, we drive a 170-nm-diameter nanodumbbell to rotate beyond 1~GHz, which is the fastest nanomechanical rotor realized to date. Our calculations show that smaller silica nanodumbbells can sustain rotation frequency beyond 10 GHz. Such ultrafast rotation may be used to study material properties and probe vacuum friction.
Optomechanical systems explore and exploit the coupling between light and the mechanical motion of matter. A nonlinear coupling offers access to rich new physics, in both the quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising of a nanosphere levitated and cooled in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere to millikelvin temperatures for indefinite periods of time in high vacuum. We observe cooling of the linear and non-linear motion, leading to a $10^5$ fold reduction in phonon number $n_p$, attaining final occupancies of $n_p = 100-1000$. This work puts cavity cooling of a levitated object to the quantum ground-state firmly within reach.
A nitrogen-vacancy (NV$^-$) center in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic center-of-mass superpositions cite{Scala2013, Zhang2013} and for testing quantum gravity cite{Albrecht2014}. Here, we study the behavior of optically levitated nanodiamonds containing NV$^-$ centers 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 $approx 10$ 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$^-$ centers spin coherence time cite{Toyli2012}. These values of $T_i$ make it clear that the diamond is not melting, contradicting a recent suggestion cite{Neukirch2015}. Additionally, using the measured damping rate of a levitated nanoparticle at a given pressure, we propose a new way of determining its size.
Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius $2~mutext{m}$ with index of refraction $n=1.45$ and $n=2.0$ as well as disks of radius 200 nm with $n=1.45$. Calculations of the forces and torques were conducted both analytically and numerically using a discrete-dipole approximation method. Besides harmonic terms, third order ro-translational coupling terms in the potential energy can be significant and a necessary consideration when describing the dynamics of disks outside of the Rayleigh limit. The coupling terms are a result of the finite extension of the disk coupling to both the Gaussian and standing wave geometry of the beam. The resulting dynamics of the degrees of freedom most affected by the coupling terms exhibit several sidebands as evidenced in the power spectral densities. Simulations show that for Gaussian beam waists of $1-4~mutext{m}$ the disk remains stably trapped.
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