Coupling a Single Atomic Quantum Bit to a High Finesse Optical Cavity

The quadrupole $S_{1/2}–D_{5/2}$ optical transition of a single trapped ${\mathrm{C}\mathrm{a}}^{+}$ ion, well suited for encoding a quantum bit of information, is coherently coupled to the standing wave field of a high finesse cavity. The coupling is verified by observing the ion’s response to both spatial and temporal variations of the intracavity field. We also achieve deterministic coupling of the cavity mode to the ion’s vibrational state by selectively exciting vibrational state-changing transitions and by controlling the position of the ion in the standing wave field with nanometer precision.

Figure 1

Schematic experimental setup (left) and ${\mathrm{C}\mathrm{a}}^{+}$ level scheme (right). PZT1 denotes the offset piezo, and PZT2 the scan piezo (see text). A photomultiplier tube (PMT) is used to record fluorescence on the $S_{1/2}–P_{1/2}$ transition, and the CCD camera monitors the ion’s position. The following stabilized laser sources are used in the experiment: two cavity-locked diode lasers at 866 and 854 nm with linewidths of $\approx 10\mathrm{k}\mathrm{H}\mathrm{z}$ and two Ti:Sa lasers at 729 nm ($\approx 1\mathrm{k}\mathrm{H}\mathrm{z}$ linewidth) and 794 nm ($<300\mathrm{k}\mathrm{H}\mathrm{z}$ linewidth), where the 794 nm laser is resonantly frequency doubled to obtain 397 nm. The whole laser system is described in more detail elsewhere [1].The dotted arrows indicate directions of laser beams: 729 nm excitation laser along the direction of the cavity axis and 397 nm cooling laser, 854 and 866 nm auxiliary lasers at a certain angle to the trap axis (shown only schematically).

Figure 2

Excitation spectra of the $S_{1/2}–D_{5/2}$ transition for different cavity scan rates: ${\nu }_L=\pm 0.16$ (a), $\pm 0.23$ (b), and $\pm 0.69$ (c). Blueshifted excitation spectra are drawn as gray lines on the right hand side of the diagrams, and superimposed solid lines show the theoretical simulation. The parameters used for the simulations are excitation laser bandwidth $\Delta {\nu }_{\mathrm{L}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}}=6\mathrm{k}\mathrm{H}\mathrm{z}$, natural linewidth of the $S_{1/2}–D_{5/2}$ transition $\Delta {\nu }_{SD}=0.17\mathrm{H}\mathrm{z}$, maximum Rabi frequency at the transition center wavelength ${\Omega }_{\max }=15.5\mathrm{k}\mathrm{H}\mathrm{z}$ (a), 11 kHz (b), and 25 kHz (c), and the cavity parameters given in the text.

Figure 3

Excitation probability on the $S_{1/2}–D_{5/2}$ transition of a single trapped ${\mathrm{C}\mathrm{a}}^{+}$ ion as a function of the PZT offset voltage, i.e., at various positions in the intracavity standing wave field. The solid line represents a ${sin}^2$ function fitted to the data points.

Figure 4

Integral excitation on the carrier (triangles) and the red axial sideband (circles) of the $S_{1/2}–D_{5/2}$ transition as a function of the PZT offset voltage, i.e., at various positions in the intracavity standing wave field. The solid lines represent fits of ${sin}^2$ functions to the data points.