Optical trapping of (sub)micron-sized particles is broadly employed in nanoscience and engineering. The materials commonly employed for these particles, however, have physical properties that limit the transfer of linear or angular momentum (or both). This reduces the magnitude of forces and torques, and the spatiotemporal resolution, achievable in linear and angular traps. Here, we overcome these limitations through the use of single-crystal rutile TiO ₂ , which has an exceptionally large optical birefringence, a high index of refraction, good chemical stability, and is amenable to geometric control at the nanoscale. We show that rutile TiO ₂ nanocylinders form powerful joint force and torque transducers in aqueous environments by using only moderate laser powers to apply nN·nm torques at kHz rotational frequencies to tightly trapped particles. In doing so, we demonstrate how rutile TiO ₂ nanocylinders outperform other materials and offer unprecedented opportunities to expand the control of optical force and torque at the nanoscale.

Single-molecule manipulation techniques have provided unprecedented insights into the structure, function, interactions, and mechanical properties of biological macromolecules. Recently, the single-molecule toolbox has been expanded by techniques that enable measurements of rotation and torque, such as the optical torque wrench (OTW) and several different implementations of magnetic (torque) tweezers. Although systematic analyses of the position and force precision of single-molecule techniques have attracted considerable attention, their angle and torque precision have been treated in much less detail. Here, we propose Allan deviation as a tool to systematically quantitate angle and torque precision in single-molecule measurements. We apply the Allan variance method to experimental data from our implementations of (electro)magnetic torque tweezers and an OTW and find that both approaches can achieve a torque precision better than 1 pN · nm. The OTW, capable of measuring torque on (sub)millisecond timescales, provides the best torque precision for measurement times ≲10 s, after which drift becomes a limiting factor. For longer measurement times, magnetic torque tweezers with their superior stability provide the best torque precision. Use of the Allan deviation enables critical assessments of the torque precision as a function of measurement time across different measurement modalities and provides a tool to optimize measurement protocols for a given instrument and application.

The bacterial flagellar motor of Escherichia coli is a nanoscale rotary engine essential for bacterial propulsion. Studies on the power output of single motors rely on the measurement of motor torque and rotation under external load. Here, we investigate the use of magnetic tweezers, which in principle allow the application and active control of a calibrated load torque, to study single flagellar motors in Escherichia coli. We manipulate the external load on the motor by adjusting the magnetic field experienced by a magnetic bead linked to the motor, and we probe the motor's response. A simple model describes the average motor speed over the entire range of applied fields. We extract the motor torque at stall and find it to be similar to the motor torque at drag-limited speed. In addition, use of the magnetic tweezers allows us to force motor rotation in both forward and backward directions. We monitor the motor's performance before and after periods of forced rotation and observe no destructive effects on the motor. Our experiments show how magnetic tweezers can provide active and fast control of the external load while also exposing remaining challenges in calibration. Through their non-invasive character and straightforward parallelization, magnetic tweezers provide an attractive platform to study nanoscale rotary motors at the single-motor level.