Figure 1

Schematic diagrams for the electrodes of the two ion traps used in this experiment. (a) Asymmetric quadrupole trap with closest electrode distance $d=150\mu \mathrm{m}$ (fork electrode). Both electrodes are constructed from $125\text{−}\mu \mathrm{m}$-thick molybdenum sheets. (b) Three-layer linear trap with closest electrode distance $d=100\mu \mathrm{m}$ (middle rf electrode). The rf layer (gray) is $125\mu \mathrm{m}$ thick, while the top and bottom segmented layers are $250\mu \mathrm{m}$ thick; the gold-plated alumina layers are separated by alumina spacers (not shown) with a thickness of $125\mu \mathrm{m}$. The outer segments of the top and the bottom layers are separated by $400\mu \mathrm{m}$. The evaporated gold coating on each electrode is approximately $0.3\mu \mathrm{m}$ thick. The electrodes in both traps are not shielded from the atomic $\mathrm{Cd}$ sources.Reuse & Permissions

Figure 2

(a) Relevant ${}^{111}\mathrm{Cd}^{+}$ energy levels (not to scale). The ground-state hyperfine levels used in the experiment are $\mid \downarrow ⟩\equiv \mid 1,0⟩$ and $\mid \uparrow ⟩\equiv \mid 0,0⟩$ (expressed in the $\mid F,M_F⟩$ basis). (b) Both Raman beams R1 and R2 are linearly polarized and are red detuned $\sim 300\mathrm{GHz}$ from the $S_{1∕2}\to P_{3∕2}$ transition.Reuse & Permissions

Figure 3

Raman spectra for an ion in the quadrupole trap with a secular frequency of ${\omega }_x∕2\pi =5.8\mathrm{MHz}$. Both plots show probability for population transfer to the “bright state" $P(\mid \downarrow ⟩\equiv \mid F=1,M_F=0⟩)$ vs $\delta$ or frequency of the beatnote from a carrier transition. Both lower (left) and upper (right) sidebands are displayed following (a) Doppler cooling to $\overline{n}\simeq 5\left(3\right)$, and (b) subsequent Raman cooling to $\overline{n}\simeq 0.03\left(2\right)$where the upper sideband vanishes. The strength of the transitions are ${\Omega }_0∕2\pi \approx 100\mathrm{kHz}$ and ${\Omega }_{0,1}∕2\pi \approx 10\mathrm{kHz}$. The Raman probe pulse is exposed for $80\mu \sec$. The lines are a fit to the data.Reuse & Permissions

Figure 4

An example of heating data taken in the quadrupole trap, with trap frequency ${\omega }_x∕2\pi =5.8\mathrm{MHz}$. Mean motional quanta $\overline{n}$ is plotted vs time delay. The insets show sideband Rabi oscillations from which $\overline{n}$ is inferred; the black points represent the lower sideband and the open points represent the upper sideband. The solid line is a linear fit to the data from which a heating rate of $\dot{\overline{n}}\approx 0.0248\left(3\right)$ quanta/msec is obtained.Reuse & Permissions

Figure 5

Observed heating rates $\dot{\overline{n}}$ vs trap frequency in the ${}^{111}\mathrm{Cd}^{+}$ ion system. The solid line is a fit to the heating rates in the linear trap where the rf electrode voltage $V_0$ is constant. The fit to the data in this trap shows a trap frequency scaling of ${\omega }_x^{-2.4}$, yielding a frequency dependence for the spectral density of electric-field noise of $S_E\left(\omega \right)\propto {\omega }^{-1.4}$. The heating measurements were taken over a period of five months in the quadrupole trap and two months in the linear trap.Reuse & Permissions

Figure 6

(a) Observed heating rate $\dot{\overline{n}}$ vs distance to nearest electrode $d$ in several trapped-ion systems with trap frequencies between 2.9 and $6.2\mathrm{MHz}$. In addition to the ${}^{111}\mathrm{Cd}^{+}$ measurements reported here, previous measurements in ${}^9\mathrm{Be}^{+}$ (I,III) [10], ${}^9\mathrm{Be}^{+}$ (II) [11],${}^{198}\mathrm{Hg}^{+}$ [4], ${}^{40}\mathrm{Ca}^{+}$ [22], and ${}^{137}\mathrm{Ba}^{+}$ [12] are also indicated for reference. Data set ${}^9\mathrm{Be}^{+}$ (III) represents heating measurements in a particular trap that exhibited anomalously low heating [10]. (b) Spectral density of electric-field noise $S_E\left({\omega }_x\right)$ at the ion inferred from the heating rate in (a) also vs distance to nearest electrode $d$. The dashed line is a guide to the eye for the $1∕d^4$ scaling of the heating rate predicted by a model of microscopic potential fluctuations [10].Reuse & Permissions