Measurement of the motional heating of a levitated nanoparticle by thermal light

We report on measurements of the photon-induced heating of silica nanospheres levitated in a vacuum by a thermal light source formed by a superluminescent diode. Heating of the nanospheres motion along the three trap axes was measured as a function of gas pressure for two particle sizes and recoil heating was shown to dominate other heating mechanisms due to relative intensity noise and beam pointing fluctuations. Heating rates were also compared with the much lower reheating of the same sphere when levitated by a laser.

Figure 1

(a) A schematic of our experimental setup in which a particle can be levitated and parametrically cooled using a laser beam or the light from a superluminescent diode. Different components are as follows: D is balanced photodiode, M represnets the mirror, BS the beam splitter, L the lens, PBS is the polarizing beam splitter, and $\lambda /2$ the half wave plate. (b) Normalized spectral intensity profiles of the superluminescent diode, a single longitudinal mode laser, and an ideal blackbody source at $T=295\mathrm{K}$. The spectral profile of the SLD is fitted with a Gaussian (black solid line). (c) Relative intensity noise (RIN) of the SLD and the laser that we use in our experiment.

Figure 2

Position power spectral densities (PSDs) of a $55\pm 16\mathrm{nm}$ radius silica nanosphere levitated using a SLD. The trapping power at the focus was $130\mathrm{mW}$. The top graphs show PSDs at $5\mathrm{mbar}$ while the bottoms graphs are the PSDs at $5\times {10}^{-8}\mathrm{mbar}$ when the particle is parametrically feedback cooled.

Figure 3

(a) The evolution of the center-of-mass temperature of a $r=55\pm 12\mathrm{nm}$ radius silica nanoparticle at $4\times {10}^{-7}\mathrm{mbar}$ after parametric feedback is switched off at time zero. This particle was levitated using the SLD. Each data point is the average of 600 time traces. The $x$ axis represents the direction parallel to the light field polarization direction while the $y$ axis is orthogonal to the light field polarization direction. The $z$ axis is the propagation direction of the trapping light beam. Solid lines represent lines of the form $a_0+a_1^{q}t$, where $t$ denotes time, $a_0$ is the offset, and $a_1^q$ is the reheating rate. (b) Reheating rates as functions of gas pressure. Solid lines represent $a_{\text{ph}}^q+a_2{P}_g$, where $a_{\text{ph}}^q$ is the heating rate due to the recoil of photons along the axis $q$, $P_g$ is the gas pressure inside the vacuum chamber, and $a_2$ is a proportionality constant.

Figure 4

Reheating rates of a $r=70\pm 20\mathrm{nm}$ radius silica nanoparticle. This particle was initially trapped using the SLD beam and data on the reheating rates (top three data sets) at different gas pressures were collected. Subsequently, the particle was transferred to the laser beam and the reheating rates (bottom three data sets) at different gas pressure were recorded. The trapping laser power at the focus was $105\mathrm{mW}$. Solid black lines represent fits of the form $a_{\text{ph}}^q+a_2{P}_g$.

Figure 5

Power spectral density associated with the SLD beam pointing instability along the $x$ axis.