Laser-induced rotation and cooling of a trapped microgyroscope in vacuum

Abstract

Quantum state preparation of mesoscopic objects is a powerful playground for the elucidation of many physical principles. The field of cavity optomechanics aims to create these states through laser cooling and by minimizing state decoherence. Here we demonstrate simultaneous optical trapping and rotation of a birefringent microparticle in vacuum using a circularly polarized trapping laser beam--a microgyroscope. We show stable rotation rates up to 5 MHz. Coupling between the rotational and translational degrees of freedom of the trapped microgyroscope leads to the observation of positional stabilization in effect cooling the particle to 40 K. We attribute this cooling to the interaction between the gyroscopic directional stabilization and the optical trapping field.

Figure 1. PSD signals of the scattered light from a trapped particle.

(a) Optical trapping by an LP light field (that is, no induced rotation) at 1 kPa. (b) Optical trapping by CP light at 1 kPa showing an optical beating frequency at 2f_rot together with f_rot. (c) PSD at 15.1 Pa showing translational (f_xy, f_z) and rotational (f_rot) frequencies of a trapped particle.

Figure 2. Rotation rate of a trapped particle at different gas pressures.

The model fits to the experimental data for 0≤K_n≤880. Inset shows the PSD at a rotation rate of 2.45 MHz at a pressure of 1 Pa.

Figure 3. Coupling of the rotational and translational motion of a trapped particle.

(a) Major peaks of the PSD signal around the resonance frequency at f_rot≈f_xy. In red are frequency peaks associated with rotation and in blue the ones associated with translational oscillations. (b) Resonances found at f_xy and 2f_xy when f_rot scans across these frequencies. (c) Photodiode signal in time domain showing mixed frequency components at 13.6 Pa. Inset shows the expanded view of the selected region. (d) Fourier transform of the time-domain signal (Fig. 3c) showing the rotation frequency of f_rot with sidebands separated by f_xy. (e) Simulated PSD signal at a high rotation frequency showing the appearance of sidebands and their harmonics due to the modulation of the trapping frequency. (f) Simulated PSD signal for two different gas viscosities corresponding to the resonant (blue) and non-resonant (red) cases.

Figure 4. Effective cooling of the microgyroscope as a function of the rotation rate.

(a) Simulated distribution of the angular velocity, ν_x around a transversal axis and (b) around the longitudinal axis, ν_z for different average rotation rates. The bimodal distribution is owing to particle precession at low rotation rates. (c) Position distributions of a trapped particle at different rotation rates. (d) Particle effective temperature, T_eff at different pressures determined by the equipartition method. (e) PSD signals of the scattered light from a trapped particle with and without rotation. (f) Effective temperatures, T_eff determined for both a rotating and a non-rotating particle using the PSD signals.

Figure 5. Schematic of the experimental set-up used for the trapping and rotation of a birefringent microparticle in vacuum.

Labels denote the continuous wave (CW), half-wave plate (λ/2), polarizing beam splitter (PBS), lenses (L), mirror (M), dichroic filters (DF), quarter-wave plate (λ/4), microscope objective (MO), circularly polarized trapping laser beam (CP), condenser (CD), 50/50 beam splitter cube (BS), photodiodes (PD_i), nanosecond laser (NS), fast imaging device (CMOS), digital storage oscilloscope (DSO), computer (PC), vacuum chamber (VC), piezo electric transducer (PZT), vacuum gauge (VG), vacuum pump (VP), rotational frequency of a trapped particle (f_rot) and translational oscillation frequencies (f_xy, f_z) of a trapped particle in lateral and axial directions.

Figure 6. SEM images of vaterite crystals.

(a) A selection of monodisperse particles. (b) A closer look at Fig. 6a. (c) A single vaterite crystal with a near-perfect sphericity. (d) A closer look at Fig. 6c showing the surface roughness of the particle. Scale bars, 10 μm in (a), 5 μm in (b), 2 μm in (c) and 500 nm in (d).