State detection using coherent Raman repumping and two-color Raman transfers

We demonstrate state detection based on coherent Raman repumping and a two-color Raman state transfer. The Raman coupling during detection selectively eliminates unwanted dark states in the fluorescence cycle without compromising the immunity of the desired dark state to off-resonant scattering. We demonstrate this technique using ${}^{137}{\mathit{Ba}}^{+}$ where a combination of Raman coupling and optical pumping leaves the metastable state, $D_{3/2}$ $|F^{\prime \prime }=3,m_F^{\prime \prime }=3\rangle$, optically dark and immune to off-resonant scattering. All other states are strongly coupled to the upper $P_{1/2}$ levels. We achieve a single-shot state-detection efficiency of $89.6\left(3\right)\%$ in a 1-ms integration time, limited almost entirely by technical imperfections. Shelving to $|F^{\prime \prime }=3,m_F^{\prime \prime }=3\rangle$ before detection is performed via a two-color Raman transfer with a fidelity of $1.00\left(3\right)$.

Figure 1

State-detection scheme. We fluoresce on the transitions from the ground states, $|F=1,2\rangle$, to the excited state, $|F^{\prime }=1\rangle$, via beams $D_1$ and $D_2$ and use $|F^{\prime \prime }=3,m_F^{\prime \prime }=3\rangle$ as the dark state. By using near-resonant $\pi$ polarized beams $D_3$–$D_5$ and coherent coupling via the Raman pair $R_1$ and $R_2$, we are able to repump out of the $5D_{3/2}$ metastable manifold without compromising the immunity of the dark state to off-resonant excitations. Hyperfine splittings between the levels are also indicated.

Figure 2

Coherent Raman repumping. We use $\pi$-polarized light near resonance with the $F^{\prime \prime }=0,1,2$ to $F^{\prime }=1$ transitions to repump out of the $5D_{3/2}$ manifold. This leaves three unwanted metastable states indicated by filled circles. To clear these, we use a pair of Raman beams which are detuned by $\approx$1 THz from the $6P_{1/2}$ levels. The beams are polarized $\pi$ and ${\sigma }^{+}$ and couple $|F^{\prime \prime },m_F^{\prime \prime }\rangle$ to $|F^{\prime \prime },m_F^{\prime \prime }-1\rangle$ via the $6P_{1/2}$ levels for all values of $F^{\prime \prime }$ and $m_F^{\prime \prime }$ with the exception of the dark state, $|F^{\prime \prime }=3,m_F=3\rangle$. Raman coupling to this state is only achieved via the $P_{3/2}$, which is a further $50\mathit{THz}$ from resonance with the Raman lasers. Furthermore, since all of the detection lasers near 650 nm are polarized $\pi$ or ${\sigma }^{+}$, off-resonant scattering out of the dark state is eliminated. We also note that the Landé $g$ factor, $g_F$, does not depend on $F$ for the $D_{3/2}$ states. Thus, the Zeeman splittings due to the quantizing magnetic field shifts all the Raman resonances by an equal amount and so the Raman resonances are the same for all $|F^{\prime \prime },m_F^{\prime \prime }\rangle$ to $|F^{\prime \prime },m_F^{\prime \prime }-1\rangle$ transitions.

Figure 3

Histogram of photon counts for three cases: one in which the ion is first optically pumped to $|F^{\prime \prime }=3,m_F^{\prime \prime }=3\rangle$ (dark, $\circ$), one in which the ion is optically pumped to $S_{1/2}$ levels (bright, $\times$), and one in which the ion is not present (background, $▵$). Each distribution corresponds to $10000$ detection events, each with a 1-ms duration. For comparison, we plot the ideal Poisson distribution for $\overline{n}=0.44$ (solid line) and $\overline{n}=8.7$ (dashed line). The vertical line indicates the threshold used to determine the detection efficiency.

Figure 4

Rabi oscillation induced by two-photon Raman transition between the $S_{1/2}$ $|F=2,m_F=2\rangle$ state and the $D_{3/2}$ $|F^{\prime \prime }=3,m_F=3\rangle$ state. Each point represents 1000 detection events, and the probability of being in the $|F=2,m_F=2\rangle$ state is based on a standard least squares fit [17] to the photon distributions using dark- and bright-state reference histograms as a basis. The solid curve is a fit assuming a thermal distribution along the axial direction of the trap. Fitting parameters are the mean vibrational number, $\overline{n}$, and the Raman Rabi rate, ${\Omega }_R$. We find $\overline{n}=14\left(2\right)$, and $\Omega =2\pi \times 2.60\left(1\right)$ MHz. The Lamb-Dicke parameter is determined from the measured trap frequency of 90 kHz and the beam geometry, giving $\eta =0.044$.