Shot-noise-limited monitoring and phase locking of the motion of a single trapped ion

Measuring Ion Oscillations at the Quantum Level with Fluorescence Light

We demonstrate an optical method for detecting the mechanical oscillations of an atom with single-phonon sensitivity. The measurement signal results from the interference between the light scattered by a trapped atomic ion and that of its mirror image. We detect the oscillations of the atom in the Doppler cooling limit and reconstruct average trajectories in phase space. We demonstrate single-phonon sensitivity near the ground state of motion after electronically induced transparency cooling. These results could be applied for motion detection of other light scatterers of fundamental interest, such as trapped nanoparticles.

Real-time optimal quantum control of mechanical motion at room temperature

The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering¹. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems^2,3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback⁴. Successful implementations thus far include experiments on the level of optical and atomic systems^5-7. Here we demonstrate real-time optimal control of the quantum trajectory⁸ of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.

Calibration and energy measurement of optically levitated nanoparticle sensors

Optically levitated nanoparticles offer enormous potential for precision sensing. However, as for any other metrology device, the absolute measurement performance of a levitated-particle sensor is limited by the accuracy of the calibration relating the measured signal to an absolute displacement of the particle. Here, we suggest and demonstrate calibration protocols for levitated-nanoparticle sensors. Our calibration procedures include the treatment of anharmonicities in the trapping potential, as well as a protocol using a harmonic driving force, which is applicable if the sensor is coupled to a heat bath of unknown temperature. Finally, using the calibration, we determine the center-of-mass temperature of an optically levitated particle in thermal equilibrium from its motion and discuss the optimal measurement time required to determine the said temperature.

Cavity-Assisted Measurement and Coherent Control of Collective Atomic Spin Oscillators

We demonstrate continuous measurement and coherent control of the collective spin of an atomic ensemble undergoing Larmor precession in a high-finesse optical cavity. The coupling of the precessing spin to the cavity field yields phenomena similar to those observed in cavity optomechanics, including cavity amplification, damping, and optical spring shifts. These effects arise from autonomous optical feedback onto the atomic spin dynamics, conditioned by the cavity spectrum. We use this feedback to stabilize the spin in either its high- or low-energy state, where, in equilibrium with measurement backaction heating, it achieves a steady-state temperature, indicated by an asymmetry between the Stokes and the anti-Stokes scattering rates. For sufficiently large Larmor frequency, such feedback stabilizes the spin ensemble in a nearly pure quantum state, in spite of continuous measurement by the cavity field.

A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields

The miniaturization of force probes into nanomechanical oscillators enables ultrasensitive investigations of forces on dimensions smaller than their characteristic length scales. It also unravels the vectorial character of the force field and how its topology impacts the measurement. Here we present an ultrasensitive method for imaging two-dimensional vectorial force fields by optomechanically following the bidimensional Brownian motion of a singly clamped nanowire. This approach relies on angular and spectral tomography of its quasi-frequency-degenerated transverse mechanical polarizations: immersing the nanoresonator in a vectorial force field not only shifts its eigenfrequencies but also rotates the orientation of the eigenmodes, as a nanocompass. This universal method is employed to map a tunable electrostatic force field whose spatial gradients can even dominate the intrinsic nanowire properties. Enabling vectorial force field imaging with demonstrated sensitivities of attonewton variations over the nanoprobe Brownian trajectory will have a strong impact on scientific exploration at the nanoscale.

Suppression of ion transport due to long-lived subwavelength localization by an optical lattice

We report the localization of an ion by a one-dimensional optical lattice in the presence of an applied external force. The ion is confined radially by a radio frequency trap and axially by a combined electrostatic and optical-lattice potential. Using a resolved Raman sideband technique, one or several ions are cooled to a mean vibrational number <n>=(0.1±0.1) along the optical lattice. We measure the average position of a periodically driven ion with a resolution down to λ/40, and demonstrate localization to a single lattice site for up to 10 ms. This opens new possibilities for studying many-body systems with long-range interactions in periodic potentials, as well as fundamental models of friction.