Efficient ground-state cooling of an ion in a large room-temperature linear Paul trap with a sub-Hertz heating rate

We demonstrate efficient resolved sideband laser cooling ($99\pm 1\%$ ground-state population) of a single ${}^{40}{\mathrm{Ca}}^{+}$ ion in a large linear Paul trap (electrode spacing of 7 mm) operated at an rf drive frequency of just 3.7 MHz. For ion oscillation frequencies in the range 280–585 kHz, heating rates below or about one motional quantum per second have been measured at room temperature. The results, obtained under these unconventional sideband cooling conditions, pave the way for a range of new types of cold ion experiments, including spectroscopy of molecular ions as well as ultracold chemistry.

Figure 1

(a) Sketch of the macroscopic linear Paul trap including dimensions of and electrical potentials on the electrodes. The electrodes have, in addition to the rf potential, a dc potential for axial confinement. The orientation of the applied magnetic bias field is also indicated. (b) Reduced level scheme for ${}^{40}{\mathrm{Ca}}^{+}$ with indication of the transitions addressed under Doppler and sideband cooling. For details, see the main text.

Figure 2

(a) First-order red sideband excitation spectra before (red solid squares) and after (blue solid circles) sideband cooling at an axial oscillation frequency of $585\mathrm{kHz}$. (b) Corresponding first-order blue sideband excitation spectrum after sideband cooling (blue solid circles). $\Delta \nu$ is the frequency detuning with respect to the carrier, and the vertical axis indicates the population transfer to the $D_{5/2}$ level due to the sideband excitation pulse. A quantitative analysis of the measured strengths indicates a $0.99\pm 0.01$ population of the motional ground state. The presented curves are fits to a Gaussian and Rabi line shape, respectively.

Figure 3

(a) The mean occupation number of motional excitation $\langle n\rangle$ vs time ${\tau }_d$ after ended sideband cooling with an axial oscillation frequency ${\nu }_z=585\mathrm{kHz}$. The red solid squares (blue solid circles) represent data points without (with) a mechanical shutter for blocking 397-nm light (see text for details). The solid red and dashed blue lines are best linear fits to the two data sets, resulting in heating rates of $d\langle n\rangle /dt=0.83\pm 0.10{\mathrm{s}}^{-1}$ and $d\langle n\rangle /dt=0.84\pm 0.05{\mathrm{s}}^{-1}$. (b) Measured heating rates vs axial oscillation frequency. The navy blue circles represent data points obtained the same day, while the light blue triangular data points are obtained during a period of 2 months. The red squares represent alternative rf voltages to rule out parametric resonances. A constant fit to all data points except the ones at the “resonance” at 295 kHz gives a heating rate of $1.1\pm 0.35\mathrm{s}$${}^{-1}$.

Figure 4

Heating rate measurements in terms of the spectral noise density multiplied by the oscillation frequency ($\omega S_E$) versus the shortest distance ($d$) between the ion and the trap electrodes. Previous results from cooled ( and ) and room temperature traps (all others) are presented together with some of our results (${\nu }_z=585\mathrm{kHz}$ and ${\nu }_z=280\mathrm{kHz}$). Obviously, the value of $\omega S_E$ for our experiments with ${\nu }_z=280\mathrm{kHz}$ are more than one order of magnitude lower than previously measured, while at the same time our results generally follow the $1/d^4$ scaling (dashed line) expected for fluctuating patch potentials. ${}^{24}{\mathrm{Mg}}^{+}$, Au [34]; ${}^{111}{\mathrm{Cd}}^{+}$, GaAs [35]; ${}^{137}{\mathrm{Ba}}^{+}$, Be-Cu [36]; ${}^{198}{\mathrm{Hg}}^{+}$, Mo [2]; ${}^{40}{\mathrm{Ca}}^{+}$, Mo [4]; ${}^{40}{\mathrm{Ca}}^{+}$, Au [37]; ${}^{171}{\mathrm{Yb}}^{+}$, Mo [38]; ${}^{174}{\mathrm{Yb}}^{+}$, Au [39]; ${}^9{\mathrm{Be}}^{+}$, Au [17]; ${}^{88}{\mathrm{Sr}}^{+}$, Ag 6K [19]; ${}^{88}{\mathrm{Sr}}^{+}$, Al 6K [40]; ${}^{43}{\mathrm{Ca}}^{+}$, St. Steel [41]; ${}^9{\mathrm{Be}}^{+}$, Au [20]; ${}^{40}{\mathrm{Ca}}^{+}$, Au ${}^{40}{\mathrm{Ca}}^{+}$, Au.