Coupling Two Laser-Cooled Ions via a Room-Temperature Conductor

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of $620\mu \mathrm{m}$. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

Figure 1

(a) Schematic of two harmonically bound ions connected with a wire. (b) Equivalent circuit model of two ions coupled with a wire. The ion motion is modeled as inductance $L_i$ and capacitance $C_i$ while the current $I_i$ corresponds to the ion velocity [15]. The coupling wire has Ohmic resistance $R$ and capacitance $C_w$ to the rest of the trap.

Figure 2

The dual surface-electrode trap consists of two trapping sites, each composed of four rf electrodes (cyan) driven out of phase and eight independently controlled dc electrodes (blue). The two sites are linked with an electrically floating wire (red) which is engineered to maximize ion-wire coupling. Ions are separated by $620\mu \mathrm{m}$ and the vertical motion of each ion induces image currents in the wire and vice versa.

Figure 3

Heating rate (${\dot{\overline{n}}}_{2,z}$) spectroscopy for the vertical mode of ion 2 in the presence of ion 1, which is held at ${\overline{n}}_{1,z}\gtrsim 10000$ quanta and ${\omega }_{1,z}=2\pi \times 1.3680(6)\mathrm{MHz}$. Error bars represent one standard deviation. Near the resonance condition, ion 2 is sympathetically heated by ion 1. The blue curve represents a Gaussian fit ($527\pm 160\mathrm{Hz}$ width) taking into account also the observed $1/f$ frequency scaling of background electric-field noise.

Figure 4

Mean motional occupation (${\overline{n}}_{1,z}$) of ion 1 is plotted with error bars representing one standard deviation. The baseline ${\overline{n}}_{1,z}$ heating of an uncoupled ion 1 is plotted as filled circles, along with a heating rate fit of $206(20)\mathrm{quanta}/\mathrm{ms}$ (red). In this case, the initial ${\overline{n}}_{1,z}$ is arbitrary and does not affect the heating rate. A second experiment, shown with data plotted as unfilled diamonds, demonstrates sympathetic reduction of ion 1’s temperature induced by resonant wire-mediated coupling with ion 2 held at 182(15) quanta. The resulting reduced heating rate is calculated to be $102(12)\mathrm{quanta}/\mathrm{ms}$ (blue).