Figure 1

Schematic energy level scheme of ${\mathrm{HD}}^{+}$ with transitions relevant to this work. Hyperfine structure is shown schematically only for the ($v=0$, $N=0$) and (1,1) levels as lines, but is implied for all other levels as well (thick bars). Full lines: laser-induced transitions, dashed lines: some relevant spontaneous emission transitions; dotted lines: some blackbody induced transitions. The spectrally narrow wave ${\lambda }_f$ selectively excites molecules from a particular hyperfine state ($v=0$, $N=0$, $F$, $S$, $J$) to a single hyperfine state (1,1, $F^{\prime }$, $S^{\prime }$, $J^{\prime }$) Quantum state preparation is performed by irradiating alternatly the appropriately tuned waves ${\lambda }_f$ and ${\lambda }_p$, in conjunction with spontaneous emission from the level (1,1). Resonant laser radiation at ${\lambda }^{\prime }$ and nonresonant radiation at ${\lambda }^{\prime \prime }$ is used to detect that hyperfine-state-selective excitation to the (1,1) level has occurred, by transferring the excited molecules to the electronically excited molecular state $2p\sigma$ from which they dissociate. Initially, rotational cooling is performed by radiation at ${\lambda }_p$ and ${\lambda }_p^{\prime }$. The level energy differences are not to scale. The waves at ${\lambda }^{\prime }$, ${\lambda }^{\prime \prime }$, ${\lambda }_p$, ${\lambda }_p^{\prime }$, have large spectral linewidths and do not excite hyperfine state selectively.Reuse & Permissions

Figure 2

(a) Energy diagram of the hyperfine states and main electric-dipole transitions in zero magnetic field. (b) Stick spectrum of the transitions (in zero magnetic field; values of the squared transition moment $d^2$ are normalized to the strongest transition). The states are labeled by the quantum numbers ($F$, $S$, $J$). Weak transitions are shown in pink [12]. Very weak transitions are not shown, except for $P4$ (dashed). The “spin-independent” transition frequency $f_{0,\mathrm{th}}$ is the value if nuclear and electron spin were zero. $S0$, $S1$, $S2$, $S3$, $S4$, $S5$, $S6$, $W1$, $W2$, $W3$, $W4$, $P2$ are transitions studied here (“$W$, $S$, $P$” mean “weak”, “strong”, and “pumping”, respectively). All were observed except $S4$. $W1$, $W3$ are the transitions used here to achieve population transfer from the hyperfine states ($v=0$, $N=0$, $F=1$, $S=2$, $J=2$, $J_z$) (empty circle) and (0,0,1,1,1,$J_z^{\prime }$) into the hyperfine state (0,0,1,0,0,$J_z^{\prime \prime }$) (filled circle). $P1$, $P2$, $P3$, and $P4$ are proposed optical pumping transitions (with indicated polarizations) for preparation of the molecule in the single quantum state (0, 0, 1, 2, 2, $J_z=+2$) (one of the Zeeman states in the open circled hyperfine state).Reuse & Permissions

Figure 3

Observed hyperfine spectrum of the $(v=0,N=0)\to (1,1)$ fundamental rovibrational transition in cold trapped ${\mathrm{HD}}^{+}$ ions. The effective intensity times irradiation duration product of the $5.1\mu \mathrm{m}$ radiation varied from line to line, and was adapted to avoid saturation. Brown lines are the result of fitting $f_{0,\exp }$, the individual line amplitudes, the Doppler temperature (9.5 mK) and the average magnetic field (0.8 G). The sticks are for illustration purpose and show the theoretical squared transition dipole moments for the Zeeman components at 0.8 G, assuming exciting radiation polarized at 45° to the magnetic field. They are scaled by different factors for presentation purpose. Color coding is as in Fig. 2. $S4$, $S6$ were taken at high intensity-irradiation time product, $S5$ at a lower value. The side peak of $S1$ is probably due to an ion micromotion sideband of $S2/S3$. The $W4$ line required hyperfine-state optical pumping for its detection (see Fig. 4).Reuse & Permissions

Figure 4

Demonstration of hyperfine-state manipulation. The transition $W4$ shown here is observed only when hyperfine optical pumping is implemented. This transition represents the excitation from a single quantum state, (0,0,1,0,0,$J_z=0$). Data shown were taken alternating measurements preceded by hyperfine optical pumping (upper data points joined by line) and not (lower data points). The intensity of the $5.1\mu \mathrm{m}$ laser radiation was set to its maximum both during hyperfine pumping on the $W1$ and $W3$ transitions and subsequent detection of the $W4$ transition. Irradiation time on the $W4$ transition was 3 s. Rotational cooling by the $2.7\mu \mathrm{m}$ and $5.5\mu \mathrm{m}$ laser was used. The zero level corresponds to the relative decrease measured when the $5.1\mu \mathrm{m}$ spectroscopy laser was blocked. The three sticks show, for illustration purposes, the theoretical transition frequencies and strengths in a 0.8 G magnetic field and radiation polarized at 45° to the magnetic field. The shift of the central component is $-0.05\mathrm{MHz}$ relative to the zero-field frequency.Reuse & Permissions