Motional Sideband Asymmetry of a Nanoparticle Optically Levitated in Free Space

The hallmark of quantum physics is Planck’s constant $h$, whose finite value entails the quantization that gave the theory its name. The finite value of $h$ gives rise to inevitable zero-point fluctuations even at vanishing temperature. The zero-point fluctuation of mechanical motion becomes smaller with growing mass of an object, making it challenging to observe at macroscopic scales. Here, we transition a dielectric particle with a diameter of 136 nm from the classical realm to the regime where its zero-point motion emerges as a sizable contribution to its energy. To this end, we optically trap the particle at ambient temperature in ultrahigh vacuum and apply active feedback cooling to its center-of-mass motion. We measure an asymmetry between the Stokes and anti-Stokes sidebands of photons scattered by the levitated particle, which is a signature of the particle’s quantum ground state of motion.

Figure 1

Experimental setup. A silica nanoparticle carrying a finite net charge $q$ is optically trapped in vacuum using a laser beam focused by an objective. To measure the $z$ motion of the particle, the backscattered light is rerouted by a free-space circulator and mixed with two local oscillators (LO) for simultaneous homodyne (homo) and heterodyne (hetero) detection. The time derivative of the homodyne signal is applied to a capacitor enclosing the particle for cold damping. The heterodyne signal is recorded for sideband thermometry.

Figure 2

(a) Motional sideband asymmetry. The figure shows single-sided power spectral densities ${\tilde{S}}_{zz}^{\mathrm{het}}(f)$ obtained by the heterodyne out-of-loop measurement. The frequency difference $\mathrm{\Delta }f$ is measured relative to the (absolute) local-oscillator frequency shift of 1 MHz. Spectra are taken simultaneously under linear feedback cooling with ${\gamma }_{\mathrm{fb}}=2\pi \times 4\mathrm{kHz}$. We observe an asymmetry in the power contained in the two sidebands. The gray solid lines indicate the noise floor (limited by technical laser noise). The vertical dashed lines indicate the integration range. The calibration of the signal to absolute units follows the procedure outlined in Ref. [34]. (b) Mean occupation number as a function of feedback gain. The red diamonds are obtained by integrating the left sideband of the heterodyne spectrum according to Eq. (3). The black circles show the mean occupation number extracted from the sideband asymmetry according to Eq. (2). The black solid line corresponds to a parameter-free model according to Ref. [31]. Error bars (one standard deviation) are smaller than the symbol size.