Subkelvin Parametric Feedback Cooling of a Laser-Trapped Nanoparticle

We optically trap a single nanoparticle in high vacuum and cool its three spatial degrees of freedom by means of active parametric feedback. Using a single laser beam for both trapping and cooling we demonstrate a temperature compression ratio of four orders of magnitude. The absence of a clamping mechanism provides robust decoupling from the heat bath and eliminates the requirement of cryogenic precooling. The small size and mass of the nanoparticle yield high resonance frequencies and high quality factors along with low recoil heating, which are essential conditions for ground state cooling and for low decoherence. The trapping and cooling scheme presented here opens new routes for testing quantum mechanics with mesoscopic objects and for ultrasensitive metrology and sensing.

Figure 1

Trapping of a nanoparticle. (a) Photograph of light scattered from a trapped silica nanoparticle (arrow). The object to the right is the outline of the objective that focuses the trapping laser. (b) Time trace of the particle’s $x$ coordinate (transverse to the optical axis) at 2 mbar pressure.

Figure 2

Principle of parametric feedback cooling. The center-of-mass motion of a laser-trapped nanoparticle in ultrahigh vacuum is measured interferometrically with three detectors, labeled $x$, $y$, and $z$. Each detector signal is frequency doubled and phase shifted. The sum of these signals is used to modulate the intensity of the trapping beam.

Figure 3

Trap stiffness and spectral densities. (a) Normalized trap stiffness in the $x$, $y$, and $z$ directions as a function of normalized laser power. Dots are experimental data and the solid line is a linear fit. (b) Spectral densities of the $x$, $y$, and $z$ motions. The trapped particle has a radius of $R=69\mathrm{nm}$ and the pressure is $P_{\mathrm{gas}}=6.3\mathrm{mbar}$. The resonance frequencies are $f_0=37\mathrm{kHz}$, 120 kHz, and 134 kHz, respectively. The dashed curves are fits according Eq. (4) and the data on the bottom correspond to the noise floor.

Figure 4

Damping rate as a function of gas pressure. The damping rate ${\Gamma }_0$ decreases linearly with pressure $P_{\mathrm{gas}}$. The dashed line is a fit according to Eq. (3).

Figure 5

Parametric feedback cooling. (a) Dependence of the center-of-mass temperature$T_{\mathrm{c}.\mathrm{m}.}$ on pressure. The cooling rate (the slope of the dashed lines) is similar for the different directions $x$, $y$, and $z$. The feedback gain has been increased at a pressure of $\sim 0.3\mu \mathrm{Bar}$ causing a kink in the curves. (b) Spectra of the $z$ motion evaluated for different pressures and temperatures $T_{\mathrm{c}.\mathrm{m}.}$. The area under the curves is proportional to $T_{\mathrm{c}.\mathrm{m}.}$. The numbers in the figure indicate the pressure in mbar.