Scaling and Suppression of Anomalous Heating in Ion Traps

We measure and characterize anomalous motional heating of an atomic ion confined in the lowest quantum levels of a novel rf ion trap that features moveable electrodes. The scaling of heating with electrode proximity is measured, and when the electrodes are cooled from 300 to 150 K, the heating rate is suppressed by an order of magnitude. This provides direct evidence that anomalous motional heating of trapped ions stems from microscopic noisy potentials on the electrodes that are thermally driven. These observations are relevant to decoherence in quantum information processing schemes based on trapped ions and perhaps other charge-based quantum systems.

Figure 1

(a) Schematic of double-needle rf ion trap. The needles are separated by variable distance $2z_0$ controlled by external translation stages. The needle tips are approximately spherical with a radius of $r_0\approx 3\mu \mathrm{m}$ and supported by a conical shank of half-angle $\theta \sim 4°$. Each surrounding cylindrical grounded sleeve of inner diameter 3.0 mm is recessed 2.3 mm from the needle tip and electrically isolated from the needles with an alumina tube. (b) Equivalent circuit for the ion trap, including a discrete model of the helical resonators providing rf potentials on each electrode. The rf resonators are independently biased with static potentials applied through $\pi$-network filters consisting of rf chokes of inductance $L_F=100\mu \mathrm{H}$ and resistance $R_F=3\Omega$ between $C_F=0.1\mu \mathrm{F}$ capacitors to ground. The outputs of the two rf resonators are shunted with a $C_S=0.1\mu \mathrm{F}$ capacitor just outside of the vacuum feedthrough. The resistance of each electrode lead within the vacuum chamber is approximately $r\sim 0.1\Omega$. Each needle electrode exhibits capacitance $C\sim 5\mathrm{pF}$ to its grounded sleeve through the alumina spacer.

Figure 2

Average thermal occupation number $\overline{n}$ measured after various amounts of delay time $\tau$. The axial trap frequency is ${\omega }_z/2\pi =2.07\mathrm{MHz}$ with an ion-electrode spacing of $z_0=64\mu \mathrm{m}$. The linear growth in time indicates a motional heating rate of $\dot{\overline{n}}=2260\pm 210\mathrm{\text{quanta}}/\mathrm{s}$.

Figure 3

Measured axial heating rate $\dot{\overline{n}}$ as a function of axial motional trap frequency $\omega$. For these data, the ion-electrode spacing is fixed at $z_0=103\mu \mathrm{m}$ and the trap strength is varied by changing only the static potential $U_0$ while fixing $V_0$, except for the highest frequency point where $V_0$ is 15% higher. The line is a fit to a power law, yielding $\dot{\overline{n}}\sim {\omega }^{-1.8\pm 0.2}$, implying that the electric field noise spectral density varies roughly as $S_E(\omega )\sim {\omega }^{-0.8\pm 0.2}$ over this frequency range.

Figure 4

Axial heating rate $\dot{\overline{n}}$ as a function of distance $z_0$ from trapped ion to each needle electrode, for warm and cold electrodes. The solid points are measured for 300 K electrodes, and the trap frequency is ${\omega }_z/2\pi =2.07\mathrm{MHz}$ for this data, with the rf and static trapping potentials increased as the trap is made larger. The measurements fit well to a scaling of heating rate with trap dimension of $\dot{\overline{n}}\sim z_0^{-3.5\pm 0.1}$ (dashed line). The lower set of measurements (open points) are acquired with the needle electrodes cooled to approximately 150 K through contact with a liquid nitrogen reservoir. These three points were measured on the same trapped ion at a trap frequency of ${\omega }_z/2\pi =2.07\mathrm{MHz}$. (The $z_0=42\mu \mathrm{m}$ cold measurement was performed at ${\omega }_z/2\pi =4.9\mathrm{MHz}$ and has been scaled upward by a factor of $\sim 3$ to the expected heating rate at ${\omega }_z/2\pi =2.07\mathrm{MHz}$.) The shaded band at bottom, scaling as $z_0^{-2}$, is the expected range of heating from thermal Johnson noise in the trap circuitry.