Individual Addressing of Trapped Ions and Coupling of Motional and Spin States Using rf Radiation

Individual electrodynamically trapped and laser cooled ions are addressed in frequency space using radio-frequency radiation in the presence of a static magnetic field gradient. In addition, an interaction between motional and spin states induced by an rf field is demonstrated employing rf optical double resonance spectroscopy. These are two essential experimental steps towards realizing a novel concept for implementing quantum simulations and quantum computing with trapped ions.

Figure 1

Individual addressing in frequency space of one (top), two (middle), and three (bottom) trapped ions, respectively. The frequency separation between neighboring ions is extracted by fitting a sum of Lorentzian line profiles and is 91(3) kHz for two ions and 79(4) kHz (middle, left) and 80(4) kHz (middle, right) for three ions. The average ratio of these frequency separations is 1.15(7), which is in good agreement with the analytical prediction of $\sqrt[3]{8/5}\approx 1.17$ for a constant gradient. Together with the extracted FWHM of 49(5) kHz, the spurious excitation of adjacent ions is 6.7(8)% in the case of two ions.

Figure 2

Individually addressing a particular ${}^{172}\mathrm{Yb}$ ion that is part of a linear Coulomb crystal composed of four ${}^{172}\mathrm{Yb}$ ions. Six images of the same ion string are shown. These were taken successively from top to bottom. The uppermost and lowermost image, labeled NoOP, are recorded with no optical pumping; that is, all ions scatter light. For the intermediate pictures, the magnetic field direction is rotated to coincide with the polarization of the repumper, allowing optical pumping. In addition, the rf frequency was set to the expected resonance of one particular ion. The detuning $\Delta 1$ or $\Delta 2$ of the rf frequency necessary to address a desired ion is indicated on the left-hand side of the graph and is given relative to the Zeeman resonance of a single ion. Here, $\Delta 1=26.3\mathrm{kHz}$ and $\Delta 2=83.2\mathrm{kHz}$. Here the amount of spurious excitation of adjacent ions is comparable to the crosstalk visible in Fig. 1.

Figure 3

A spectrum recorded with a single ion exposed to a magnetic field gradient (right-hand side) compared to one recorded with a single ion without a field gradient (left-hand side). The solid line represents a fit using two Lorentzian lines (right-hand side), and the dashed lines represent fits using a single Lorentzian (left-hand side and right-hand side). The motional sideband accompanying the spin resonance signifies coupling between spin degrees of freedom and the motion of the trapped ${\mathrm{Yb}}^{+}$ ion.