Feedback Cooling and Thermometry of a Single Trapped Ion Using a Knife Edge

Abstract

We report on the first feedback cooling of a single trapped ion below the Doppler limit of $\hbarΓ/2 k_\mathrm{B}$. The motion of a single ion is monitored in real-time and cooled up to 9-times below the Doppler cooling temperature by applying electronic feedback. Real-time motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. The method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence.

Figures (5)

• Figure 1: Schematic of the experimental setup. Fluorescence photons emitted by the single $\mathrm{^{174}Yb^+}$ ion at 369.5 nm are collected by the parabolic mirror, passed through a pinhole to suppress stray light, and subsequently focused onto a partially coated glass plate, which acts as a knife edge, before reaching two photomultiplier tubes (PMT). The ion motion creates an intensity modulation in the PMT signals. PMT 1 is used to measure the out-loop spectrum for thermometry, while PMT 2 is connected to the feedback circuit(s) to generate feedback signals. Each signal is applied to a different compensation electrode to independently feedback cool ion motion along either of the two radial trap axes. L: lens, BS: 95:5 (R:T) beam splitter, DM: dichroic mirror, PH: pinhole.
• Figure 2: Temperature of the ion motion measured for different feedback gain settings and knife edge orientations. (a) Orientation A provides best feedback cooling performance for ion motion along one particular trap axis. The lowest temperature achieved was $T_{\mathrm{min},\,\omega_2} = 432 \pm 56\,\mu$K. (b) Orientation B allows ion motion along multiple trap axes to be feedback cooled simultaneously at the cost of some cooling performance. The lowest temperature achieved was $T_{\mathrm{min},\,\omega_1} = 751 \pm 73\,\mu$K and $T_{\mathrm{min},\,\omega_2} = 484 \pm 52\,\mu$K for the respective radial trap axes. The lines between data points are there to guide the eye.
• Figure 3: Temperature of the ion motion along the radial trap axis with frequency $\omega_2$ vs. different count rates of detected photons with a wavelength of 297 nm scattered by the ion. At each count rate, a measurement similar to the one shown in Fig. \ref{['fig:fb_cooling_temperatures']}(a) was taken. The solid green line shows a fit of Eq. \ref{['eq:ion_temp_count_rate']} to the data without feedback cooling. The gray dashed lines indicate the count rates corresponding to different saturation parameters, parametrized by saturation measurements.
• Figure 4: Images of the ion recorded with an EMCCD camera for different setups of the external drive to determine the orientation of the radial trap axes. (a) Ion without external drive applied. (b) and (c) Ion with external drive applied to resonantly drive the ion along the radial trap axis with frequency $\omega_1$ and $\omega_2$ respectively. The turquoise lines indicate the radial trap axis along which the ion is driven by the external drive, while the black lines indicate the other remaining radial trap axis. The length of the lines corresponds to the width of the Gaussian intensity profile of the ion image along the given axis. The intensities in the image are given in units of the camera's analog-to-digital converter.
• Figure 5: (a) Normalized count rate of 369.5 nm photons measured at different positions of the ion trap along the trap axis with frequency $\omega_2$. The count rates are normalized to the value measured when the ion is positioned in the focus of the parabolic mirror, i.e. $d = 0$. (b) Normalized correlation between detected 369.5 nm photon counts and an external sinusoidal drive with a frequency of 458 kHz applied to the ion. The drive frequency was chosen such that the frequency is close to, but still several linewidths away from the secular motion. (c) Calibrated power spectral density of the signal from the out-loop PMT showing ion motion along one radial trap axis at a center frequency of $\omega_2 = 2\pi \cdot 455$ kHz, as well as the external drive used to calibrate the spectrum.