Figure 1

Simplified energy level scheme of HD${}^{+}$ with transitions relevant to this work. Full thin arrows, laser-induced transitions; dashed arrows, some relevant spontaneous emission transitions; and dotted double arrows, some relevant black-body-radiation-induced transitions. The terahertz wave (thick arrow) is tuned so that the four hyperfine states in $(v=0,N=0)$ are excited to corresponding hyperfine states in $(v^{\prime }=0,N^{\prime }=1).$ Resonant laser radiation at ${\lambda }^{\prime }$ (1420 nm) and nonresonant radiation at ${\lambda }^{\prime \prime }$ (266 nm) transfer the rotationally excited molecules to a vibrationally excited level $(v^{\prime \prime }=4,N^{\prime \prime }=0)$ and then further to electronically excited molecular states (predominantly 2p$\sigma$), from which they dissociate. Rotational cooling is performed by radiation at ${\lambda }_p$ (5.5 µm) and ${\lambda }_p^{\prime }$ (2.7 µm). The level energy differences are not to scale. Hyperfine structure is indicated very schematically for the levels $(v=0,N=0,1)$ and as thick lines for some other participating levels. The waves at ${\lambda }^{\prime },{\lambda }^{\prime \prime },{\lambda }_p,{\lambda }_p^{\prime }$ have relatively large spectral linewidths.Reuse & Permissions

Figure 2

Energy diagram of the hyperfine states and main electric-dipole transitions in zero magnetic field. Left side, rovibrational ground level $(v=0,N=0)$; right side, rotationally excited level $(v^{\prime }=0,N^{\prime }=1)$. The hyperfine states are labeled by the (in part approximate) quantum numbers $(F,S,J)$. The degeneracy factor of each hyperfine state is $(2J+1)$. Transitions that do not change the quantum numbers $F,S$ are relatively strong and are indicated, starting from the top of the figure, by red, black, green, and blue lines. The four transitions addressed consecutively in this work are indicated by arrows.Reuse & Permissions

Figure 3

Section of the theoretical stick spectrum of the rotational transition in the frequency range relevant to this work, showing the Zeeman splittings and shifts in a 1 G magnetic field. Dashed lines are $\pi$ transitions; full lines are $\sigma$ transitions. $f_{0,\mathrm{theor}}$ is the theoretical “spinless” transition frequency. The four terahertz frequencies of list A (see Table ) are indicated by the arrows. The colors used correspond to those used in Fig. 2.Reuse & Permissions

Figure 4

Schematic of the apparatus and beams. GC, Golay cell; FM, flip mirror; DM, dichroic mirror; and dotted lines, electrically controlled laser beam shutters. The double arrow indicates the polarization of the terahertz wave. Not to scale.Reuse & Permissions

Figure 5

Atomic fluorescence signal during continuous secular excitation of the HD${}^{+}$ ions (method I, liquid state). The time axis starts after the 2.7 µm rotational cooling laser is turned off and the two REMPD lasers and terahertz radiation are turned on. The upper (black) trace, where the terahertz radiation is detuned from resonance, shows the molecular ion number decay due mainly to the effect of BBR-induced rotational excitation. Lower (blue) trace is for terahertz radiation on resonance. Each trace is the average of 10 individual decays. The lines are exponential fits to the first 10 s of the data.Reuse & Permissions

Figure 6

Frequency dependence of the rotational excitation. Top, in the liquid state, at ca. 100–200 mK, using method I. ${\overline{\Gamma }}_{500}$ is the average decay rate when the terahertz radiation frequency is detuned by 500 MHz. Each data point results from nine individual decays. Bottom, in the crystallized state, at 10–15 mK, using method II. Each data point represents the mean of nine or ten measurements. The two close points were taken with the same list $A$ on different days and are shown separated for clarity. The error bars in both plots show the standard deviations of the data, not of the mean. The lines are guides for the eye.Reuse & Permissions