Figure 1

The relevant energy levels of ${{}^9\mathrm{B}\mathrm{e}}^{+}$. The ground-state $2s$ ${}^{2}S_{1/2}$ manifold consists of the $F=1$ and $F=2$ hyperfine levels. Superposition states are composed of the $|F=1,m_F=1⟩\equiv |\uparrow ⟩$ and $|F=2,m_F=0⟩\equiv |\downarrow ⟩$ states. The excited-state $2p$ ${}^{2}P$ manifold consists of the $J=1/2$ and $J=3/2$ fine-structure levels, separated by ${\Delta }_f/2\pi =197.2\mathrm{GHz}$. The laser frequency, illustrated by the dashed arrow, is detuned by $\Delta$ from the $|\downarrow ⟩$ to ${}^{2}P_{1/2}$ transition frequency.Reuse & Permissions

Figure 2

Coherence relaxation pulse sequence. Two Ramsey pulses surround a sequence of spin-echo $\pi$ pulses of alternating phase. The spin-echo pulses are separated by a time $2{\tau }_{\mathrm{echo}}$, during which the ion is illuminated by a decohering beam, illustrated by the gray-filled arrows.Reuse & Permissions

Figure 3

Coherence and population relaxation data for a decohering beam detuning of $\Delta /2\pi \simeq 227.5\mathrm{GHz}$. The difference between the two filled circles curves is proportional to the superposition coherence at different times in the presence of the decohering beam light. The difference between the two open circles curves is proportional to the coherence in the absence of light. The gray-filled squares are proportional to the $|\uparrow ⟩$ state population at different times. Very similar data were recorded for the $|\downarrow ⟩$ state population. Every point in the figure is the average photon count of 400 experiments.Reuse & Permissions

Figure 4

Ratios of the different scattering rates and the decoherence rate to the differential Stark shift for different decohering beam detunings. The dashed line is the calculated ${\Gamma }_{\mathrm{total}}/{\Delta }_{\mathrm{St}}$, which at large detunings is seen to asymptotically reach a constant value of $\simeq 0.0154$. The solid line is the calculated ${\Gamma }_{\mathrm{Raman}}/{\Delta }_{\mathrm{St}}$. The empty circles are the measured values of ${\Gamma }_{\mathrm{Raman}}/{\Delta }_{\mathrm{St}}$ which are seen to be in reasonable agreement with the calculated curve. The filled circles are the measured values of $1/({\tau }_{\mathrm{dec}}{\Delta }_{\mathrm{St}})$. The two sets of data are seen to be in good agreement, thus demonstrating that Raman scattering of photons is the dominant cause of decoherence. The suppression of the decoherence rate relative to the total scattering rate is evident for large detunings.Reuse & Permissions