This folder contains the codes to analyze the data obtained from the experiments with optical tweezers in vacuum.
Run overdamped_to_uderdamped_Fig35.m We plot the measured PSD for the z-axis motion, normalized to the damping rate γ_0/(2π), at three different pressures for a levitated particle (radius a = 68 nm, laser power P≋150mW) that is overdamped (blue line), critically damped (orange line), and underdamped (green line). The dashed black lines are least-square fits to equation (164) (1000 mbar) or equation (163) (60 and 2.5 mbar). The colored vertical solid lines indicate the roll-off frequencies Ω_c/2π. For the time traces at 60 and 2.5 mbar, the spectra contain leakage signals from the other oscillation axes above 100 kHz. Data from E. Hebestreit, “Thermal properties of levitated nanoparticles,” Ph.D. thesis, ETH Zurich (2017).
Run composition_gas_Fig39.m Gas composition in a vacuum chamber. Gas composition in the vacuum chamber at pressures below 10^3 mbar plotted over time. The solid lines show the partial pressures of different gas species measured with a residual gas analyzer (RGA). The sum of all the partial pressures yields the total pressure at the RGA (dashed line). Due to the configuration of the vacuum system and the reduced pumping speed at the RGA, the pressure at the RGA deviates from the pressure in the main vacuum chamber (dash-dot line). The initial rise in partial pressures after turning on the RGA is attributed to the warm-up process and desorption of gases from the filament of the RGA. Reproduced from Ref. [467].
Run particle_loading_Fig40.m Particle loading with a nebulizer. The particle is loaded by spraying a solution of nanoparticles through a nozzle which is placed above the focus. (a) Positioning of the nozzle in the vacuum chamber. (b) Nozzle to funnel the falling particles towards the focus of the trapping laser. (c) Histogram of brightness observed with a camera from the side. The inset shows the brightness over a wider range. Reproduced from J. Gieseler, “Dynamics of optically levitated nanoparticles in high vacuum,” Ph.D. thesis, Universitat Politècnica de Catalunya (2014). (a,b) and adapted from F. Ricci, “Levitodynamics toward force nano-sensors in vacuum,” Ph.D. thesis, Universitat Politècnica de Catalunya (2019).
Run detector_calibration_Fig42.m) to obtain S(a) Calibrated z-detector signal
at 10 ± 1 mbar with electric driving response. The area under that peak corresponds to the
thermal temperature kBT. (b) Uncalibrated feedback-cooled oscillator signal with electric
drive for recalibration of the signal. Jan: Add explicit references to each of the panels in this
figure in the text.
Run sideband_thermometry_Fig43.m (a-b) Motional sideband asymmetry measured with heterodyne measurement. The frequency difference Δf is measured relative to the (absolute) local oscillator shift of 1MHz. The grey solid lines show the measurement noise floor, limited by technical laser noise. The vertical dashed lines indicate the integration bandwidth (see equation 188). (c) Mean occupation number as a function of feedback gain. The red diamonds are obtained by integrating the red sideband of the heterodyne spectrum. The black circles show the mean occupation number extracted according to equation (189). The black solid line corresponds to a parameter-free model (see also section 5.7.1). Figures adapted from F. Tebbenjohanns, M. Frimmer, V. Jain, D.Windey, and L. Novotny, “Motional Sideband Asymmetry of a Nanoparticle Optically Levitated in Free Space, Phys. Rev. Lett. 124, 013603 (2020).
Run charge_calibration_Fig44.m to obtain (a) Power spectral density of the motion along the optical axis of a charge-carrying particle at a pressure of 1:9 mbar in the presence of a drive tone fd = w_d/2π applied to the capacitor. The solid line is a Lorentzian function fit to the data. (b) Quadrature component of particle oscillation in response to a driving voltage, demodulated in a bandwidth of 7 Hz. The high-voltage discharge is turned on at t = 0. The oscillation amplitude changes in discrete steps while the high voltage is on. (c) Preparation of charge state. The high voltage is turned off at t = 0, while the particle carries a net charge of 1e. The charge stays constant over the remainder of the measurement. Figure adapted from M. Frimmer, K. Luszcz, S. Ferreiro, V. Jain, E. Hebestreit, and L. Novotny, “Controlling the net charge on a nanoparticle optically levitated in vacuum,” Phys. Rev. A 95, 061801 (2017).
Run mass_calibration_Fig45.m Power spectral density Sv(w) of a thermally and harmonically driven resonator at P = 50 mbar. The broad peak centered at Ω_0/2π = 125 kHz corresponds to the thermally driven state. We fit it with a Lorentzian function (orange) to extract S^th _vv (ω_d) together with G/(2π) = 31.8 kHz and the corresponding uncertainties. The narrowband peak at ω = 135 kHz, also shown in detail in the inset, depicts the electrical excitation from which we retrieve S^th _vv (ω_d). Gray data points at the bottom of the plot is the measurement which we retrieve Sd noise, which is ∼ 40 dB below the particle’s signal. Figure adapted from F. Ricci, “Levitodynamics toward force nano-sensors in vacuum,” Ph.D. thesis, Universitat Politècnica de Catalunya (2019).
Run particle_heating_fig_46.m(a) Heating rates as a function of pressure extracted from relaxation measurements without additional heating of the internal temperature (blue) and with heating by a CO2 laser intensity of 0.47 μWμm^2 (orange). The dashed lines are linear fits to the data points. Error bars are smaller than the marker size. (b) Heating rates at different intensities of the CO2 laser measured at a pressure of 1 x 10^-5 mbar. The error bars indicate the standard deviation of the measurements. (c) Calculated temperature dependence of oscillation frequency. When the particle is heated with the CO2 laser, its oscillation frequency increases due to changes in the particle’s material properties. This leads to a nearly linear relation between relative frequency change and increase of the internal particle temperature. Adapted from E. Hebestreit, R. Reimann, M. Frimmer, and L. Novotny, “Measuring the internal temperature of a levitated nanoparticle in high vacuum,” Phys. Rev. A 97, 043803 (2018).
Run feedback_cooling_Fig47.m (a) Single-sided power spectral densities S^ol_ yy of the motion of the nanoparticle measured by the out-of-loop detector for different feedback damping rates fb. The solid lines are Lorentzian fits to the data. The black data points denote the measured shotnoise level on the out-of-loop detector. (b) Mode temperature Ty derived from the out-of-loop signal as a function of feedback gain fb. The black circles denote the measured values at a pressure of 1.4 x10^-8 mbar. Photon shot noise is shown as black data points. In contrast to (a), for a large feedback gain the measured signal drops below the noise floor. (c) Power spectral densities measured by the in-loop detector for the same settings as in (a). (d) Steady state under parametric PLL feedback cooling. Mean occupation number along the three principal axes (x; y; z) as a function of gas pressure measured under constant feedback cooling. At low enough pressures, photon recoil becomes the main source of heating and therefore the occupation number remains constant. Adapted from F. Tebbenjohanns, M. Frimmer, A. Militaru, V. Jain, and L. Novotny, “Cold damping of an optically levitated nanoparticle to microkelvin temperatures,” Phys. Rev. Lett. 122, 223601 (2019). (a-b) and from V. Jain, J. Gieseler, C. Moritz, C. Dellago, R. Quidant, and L. Novotny, “Direct measurement of photon recoil from a levitated nanoparticle,” Phys. Rev. Lett. 116, 243601 (2016).
This repository includes the analysis and plot codes for the the article Optical Tweezers: A comprehensive Tutorial from Calibration to Applications by Jan Gieseler, Juan Ruben Gomez-Solano, Alessandro Magazù, Isaac Pérez Castillo, Laura Pérez García, Martha Gironella-Torrent, Xavier Viader-Godoy, Felix Ritort, Giuseppe Pesce, Alejandro V. Arzola, Karen Volke-Sepulveda and Giovanni Volpe.