The experimental setup is schematically depicted in Fig. 1. The chiral molecule 1-indanol is heated to \(\sim\)80 °C and seeded into neon. The gas mixture is expanded at \(\sim\) 2 bar backing pressure out of a pulsed valve, operated at 30 Hz, into a vacuum. The thus produced jet-cooled molecular beam has a rotational temperature of \(\sim\)1 K and a speed of \(\sim\)800 m/s. The molecular beam is collimated by two skimmers of 3 mm and 1 mm diameter opening, and subsequently passes through the depletion region (I), the ESST region (II), and the detection region (III), as outlined below. The relevant rotational states and MW frequencies of 1-indanol are depicted in Fig. 2a. Details of the excitation schemes at the interaction regions are illustrated in Fig. 2b and c. As indicated in these figures, states \(\left|{1}_{01}\right\rangle\) and \(\left|{1}_{10}\right\rangle\) are depleted in region (I), population is transferred between all three states in region (II), and the population in the target state \(\left|{1}_{01}\right\rangle\) is monitored in region (III).Fig. 1: Scheme of the experimental setup.Jet-cooled 1-indanol passes through two skimmers and then traverses three distinct regions (I-III). In (I), the molecules interact with both the UV depletion laser and with MW fields that drive the b-type transition. The optical multi-pass setup extends the interaction time to \(\sim\)30 µs. In (II), the molecules interact with a sequence of three orthogonally, linearly polarized MW fields. In (III), the target rotational state is probed using the same UV laser as used for depletion. The laser-induced fluorescence is detected using a photomultiplier tube (PMT).Fig. 2: Schemes of the experimental procedure using 1-indanol.a Illustration of the triad of rotational states of 1-indanol used in this study, shown in standard spectroscopic notation \(\left| \, {J}_{{K}_{a}{K}_{c}}\right\rangle\). All \({M}_{J}\) sub-levels and allowed transitions are represented, with frequencies and types of MW transitions marked. b Depiction of depletion schemes using MW-UV double resonance. Two scenarios are presented: using polarization along \({{\bf{z}}}\) (left) and along x (right), with the respective selection rules. c Time sequences of the applied MW fields (top) and the excitation schemes applied at each stage of the experiment (bottom).In the depletion region (I), about 40 mW of tunable continuous-wave UV laser radiation with a bandwidth of less than 1 MHz crosses the molecular beam perpendicularly in a multi-pass arrangement. In this way, the total interaction time of the molecules with the UV radiation is extended. The laser frequency is set to selectively excite from the target rotational state \(\left|{1}_{01}\right\rangle\) to the electronically excited state on the \({S}_{1}\left({2}_{02}\right)\leftarrow {S}_{0}\left({1}_{01}\right)\) R-branch line31, addressing all \({M}_{J}\) sub-levels. Once excited, the molecules rapidly radiate, predominately to higher vibrational states and other rotational states within the \({S}_{0}\) electronic state32. For the small fraction of molecules that radiates back to the original state, the process is repeated, effectively depleting the \(\left|{1}_{01}\right\rangle\) state. Simultaneously, MW fields that drive the b-type transition are applied to connect state \(\left|{1}_{10}\right\rangle\) to the target state \(\left|{1}_{01}\right\rangle\), thereby depleting both levels via optical pumping. The polarization of these MW fields is switched back and forth between the \(\bf z\)- and \(\bf x\)-, which enables coupling all \({M}_{J}\) sub-levels of the rotational states. This is crucial for complete depletion, as otherwise, according to the selection rules, the \({M}_{J}=0\) sub-level in state \(\left|{1}_{10}\right\rangle\) would remain populated. In Fig. 2b it is shown, how the different \({M}_{J}\) sub-levels are addressed by each MW polarization direction. Further details are given in the Methods.In the ESST region (II), a sequence of three resonant, linearly polarized, and mutually orthogonally polarized MW fields is applied consecutively in the following order: \(\left|{1}_{01}\right\rangle {\leftarrow }^{\pi /2,{\phi }_{a}}\left|{0}_{00}\right\rangle { \to }^{\pi,{\phi }_{c}}\left|{1}_{10}\right\rangle {- \to }^{\pi /2,{\phi }_{b}}\left|{1}_{01}\right\rangle\), where \({\phi }_{i}\) represents the phase of the MW field driving the \(i\)-type transition, with \(i=a,b\) or \(c\). Note that other pulse sequences can be used for ESST if the first MW pulse drives a transition from the initially populated rotational state. Enantiomer-specific state transfer is then achieved between the two rotational states connected by the final MW pulse. In our chosen sequence, enantiomeric enrichment is realized in two excited rotational states, but we only probe the population in the target rotational state. The enantiomer-selectivity of ESST is determined by the relative phases of the MW fields. In the experiment, the phase of the final pulse \({\phi }_{b}\) is scanned in 20° increments from 0° to 720°, while the phases of the first two MW fields, \({\phi }_{a}\) and \({\phi }_{c}\), are kept fixed.In the detection region (III), the same UV laser as used in the depletion region probes the population in the target rotational state, utilizing only about 10% of the laser power to avoid line broadening. The laser is aligned perpendicularly to the molecular beam and parallel to the laser in the depletion region, thus interacting with the same group of molecules as in the depletion region. The laser-induced fluorescence (LIF) emitted by the molecules is detected using a photomultiplier tube (PMT).In this experimental approach, the ESST signal for a given enantiomer, defined as the population in the target state \(\left|{1}_{01}\right\rangle\) at the end of the ESST process, is given by the following expression29:$$\frac{1}{2}\left[{n}_{{0}_{00}}+4{n}_{{1}_{01}}+{n}_{{1}_{10}}\pm \left({n}_{{0}_{00}}-{n}_{{1}_{01}}\right)\sin \left({\phi }_{a}-{\phi }_{c}+{\phi }_{b}\right)\right]$$
(1)
where \({n}_{{0}_{00}}\), \({n}_{{1}_{01}}\), and \({n}_{{1}_{10}}\) is the initial population of each \({M}_{J}\) sub-level of the states \(\left|{0}_{00}\right\rangle\), \(\left|{1}_{01}\right\rangle\), and \(\left|{1}_{10}\right\rangle\), respectively, at the beginning of the ESST process and where the \(\pm\) sign is used for different enantiomers. Here, the handedness of the coordinate system dictates the handedness of the molecules associated with the \(\pm\) sign. The amplitude-to-mean ratio of this expression is the measure for maximum state-specific enantiomeric enrichment, which refers to the enantiomeric excess achievable in a chosen rotational state when starting from a racemic mixture. For example, an 80% state-specific enantiomeric enrichment means that, starting from a racemic mixture, 80% of the molecules in the target rotational state are one enantiomer, while 20% are the racemic mixture. In other words, this corresponds to a composition of 90% of one enantiomer and 10% of the other enantiomer in the target state. Achieving 100% state-specific enantiomeric enrichment requires that both upper levels are initially empty, i.e., \({{n}_{{1}_{01}}=n}_{{1}_{10}}=0\). It is seen from this expression how any remaining population in states \(\left|{1}_{01}\right\rangle\) and \(\left|{1}_{10}\right\rangle\) adversely affects the state-specific enantiomeric enrichment. Moreover, the population in the target state impacts the mean of the ESST signal four times more than the population in state \(\left|{1}_{10}\right\rangle\).Measurements are performed using commercially available, enantiopure samples of 1-indanol. The enantiopurity for both samples is better than 99.8% as determined by chiral high-performance liquid chromatography. Separate molecular beam sources are used for the two enantiomers to avoid any cross-contamination. To ensure an optimal \(\pi /2-\pi -\pi /2\) pulse sequence, Rabi oscillation curves for each MW transition are measured prior to ESST (see Suppl. Note 3). The \(\pi\)-pulse conditions are determined from the pulse durations that correspond to the first maxima of these curves, as indicated by vertical bars in Fig. 3a. Due to the use of different molecular beam sources, the \(\pi\)-pulse durations are slightly different for the measurements on the (R)- and (S)-enantiomer.Fig. 3: Rabi oscillation curves and ESST results.a Rabi oscillation curves of the MW transitions are shown for (R)−1-indanol. The \(\pi\)-pulse durations are marked by dashed vertical lines. b Normalized ESST signal is shown as a function of the relative MW phase for (R)- and (S)-enantiomers in black and red, respectively. The standard error on each measurement point is indicated by error bars. Calculated normalized ESST curves using expression (1) are shown with dashed lines. The gray shaded areas around the experimental curves show the standard deviation from the sine fit. Two regions of specific interest are shown enlarged in the boxes below.Figure 3b shows the ESST signals, normalized to the thermal population in the target state \(\left|{1}_{01}\right\rangle\), as a function of the relative MW phase. The signals for the (R)- and (S)-enantiomers are shown in black and red, respectively, with error bars representing the standard errors. The mean and amplitude values from sinusoidal fits to the data are given. These values yield a maximum state-specific enantiomeric enrichment of 90.2(1.9)% for the (R)-enantiomer and 92.4(2.1)% for the (S)-enantiomer. This latter value means that when starting from a racemic mixture, we can selectively obtain 92% of one enantiomer in the target rotational state, with the remaining 8% being racemic. Consequently, it results in a final composition where the target state comprises 96% of one enantiomer and 4% of the other. The high degree of state-specific enantiomeric purity is best seen by the proximity of the minima of the sine curve to zero, and two relevant segments are therefore shown enlarged in Fig. 3b.The two ESST curves in Fig. 3b are shown with a phase difference of exactly 180°. When using identical pulse durations for the (R)- and (S)-enantiomer, their ESST curves are indeed confirmed to be 180° out-of-phase (see Suppl. Note 5). However, optimal transfer efficiency for both enantiomers is only obtained when using pulse durations that are optimized for each enantiomer individually. This results in an additional phase offset between the measurements, that has been corrected for in Fig. 3b.In the experiments, ~2% of the original thermal populations in the states \(\left|{1}_{01}\right\rangle\) and \(\left|{1}_{10}\right\rangle\) is measured to be present in the detection region (see Methods). This population is attributed to re-filling as a result of in-beam collisions with the carrier gas atoms while the molecules travel from the depletion region to the detection region27,29. This is confirmed by the observation that reducing the carrier gas density by installing a second skimmer is beneficial, i.e., that it reduces this population. When depleting just in front of the LIF detection region, basically no population is measured to be present. Using this information in a model as described in the Suppl. Note 2, the population in both of these states is estimated to be about 1.4% upon entering the ESST region.Calculated normalized ESST curves using expression (1) and assuming thermal populations at 1.1 K for (R)-indanol and 0.7 K for (S)-indanol, are shown in Fig. 3b (dashed). These calculations incorporate the 1.4% population in the two upper levels as well as the 0.2% enantiomer-impurity. The calculated amplitude and mean of the normalized ESST signal agree very well with those of the experiment, for both enantiomers, indicating that enantiopure substances are not required to determine the absolute enantiomeric excess of a sample. Moreover, with the absolute phases of the three MW fields known, it is possible to determine the absolute configuration, even within a racemic mixture. This sets our approach apart from most other chiral discrimination techniques.
Near-complete chiral selection in rotational quantum states
