Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle's motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle's motion with a sensitivity of 1.7×10^{-12} m/sqrt[Hz], corresponding to a detection efficiency of 2.1%, with a numerical aperture of 0.18. As an application of this method, we cool the particle, via feedback, to temperatures below those achieved in the same setup using a standard position measurement.
Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle's motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle's motion with a sensitivity of 1.7×10^{-12} m/sqrt[Hz], corresponding to a detection efficiency of 2.1%, with a numerical aperture of 0.18. As an application of this method, we cool the particle, via feedback, to temperatures below those achieved in the same setup using a standard position measurement.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scat tered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥tot , 𝜂𝑦tot , 𝜂𝑧tot ) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scattered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥 tot , 𝜂𝑦 tot , 𝜂𝑧 tot) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scattered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥 tot , 𝜂𝑦 tot , 𝜂𝑧 tot) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
Cooling the center-of-mass motion of levitated nanoparticles provides a route to quantum experiments at mesoscopic scales. Here we demonstrate three-dimensional sympathetic cooling and detection of the center-of-mass motion of a levitated silica nanoparticle. The nanoparticle is electrostatically coupled to a feedback-cooled particle while both particles are trapped in the same Paul trap. We identify two regimes, based on the strength of the cooling: in the first regime, the sympathetically cooled particle thermalizes with the directly cooled one, while in the second regime, the sympathetically cooled particle reaches a minimum temperature. This result provides a route to efficiently cool and detect particles that cannot be illuminated with strong laser light, such as absorptive particles, and paves the way for controlling the motion of arrays of several trapped nanoparticles.
Levitated nanoparticles in vacuum are prime candidates for generating macroscopic quantum superposition states of massive objects. Most protocols for preparing these states necessitate coherent expansion beyond the scale of the zero-point motion to produce sufficiently delocalized and pure phase-space distributions. Here, we spatially expand and subsequently recontract the thermal state of a levitated nanoparticle by modifying the stiffness of the trap holding the particle. We achieve state-expansion factors of 25 in standard deviation for a particle initially feedback-cooled to a center-of-mass thermal state of \SI{155}{\milli\kelvin}. Our method relies on a hybrid scheme combining an optical trap, for cooling and measuring the particle's motion, with a Paul trap for expanding its state. Consequently, state expansion occurs devoid of measurement backaction from photon recoil, making this approach suitable for coherent wavefunction expansion in future experiments.