Enantiomer-Specific State Transfer of Chiral Molecules

State-selective enantiomeric excess is realized using microwave-driven coherent population transfer. The method selectively promotes either $R$ or $S$ molecules to a higher rotational state by phase-controlled microwave pulses that drive electric-dipole allowed rotational transitions. We demonstrate the enantiomer-specific state transfer method using enantiopure samples of 1,2-propanediol. This method of state-specific enantiomeric enrichment can be applied to a large class of asymmetric, chiral molecules that can be vaporized and cooled to the point where rotationally resolved spectroscopy is possible, including molecules that rapidly racemize. The rapid chiral switching demonstrated here allows for new approaches in high-precision spectroscopic searches for parity violation in chiral molecules.

Figure 1

Left: Level diagram of the rotational states of 1,2-propanediol used for enantiomer-specific enrichment of a chosen rotational state. The relevant states are labeled $|A⟩$, $|B⟩$, $|C⟩$, and $|D⟩$. In our method, state $|C⟩$ is populated on two paths: directly from $|A⟩\to |C⟩$ and indirectly $|A⟩\to |B⟩\to |C⟩$. Depending on the phases ${\varphi }_1$, ${\varphi }_2$, and ${\varphi }_3$ of the driving transitions, $|C⟩$ is populated or depopulated for opposite enantiomers. The final population in the target state $|C⟩$ is probed by using an additional, radiating transition $|C⟩\to |D⟩$. Right: Molecular structure of the lowest energy conformer of $S$ and $R$ 1,2-propanediol [17].

Figure 2

(a) Sketch (not to scale) and (b) picture of the experimental setup. 1,2-propanediol molecules are evaporated in front of the cell entrance and enter the cell through a hole in the microwave mirror. The cryogenic buffer gas cell is cooled by a closed-cycle pulse tube refrigerator (4 K). The hot molecules enter the cell and rapidly cool to approximately 10 K. Microwave pulses of $\widehat{y}$ and $\widehat{z}$ polarization are introduced via microwave horns. An electric field of $\widehat{x}$ polarization is produced between the microwave mirror and the opposite face of the buffer gas cell. A third microwave horn drives a transition from $|C⟩\to |D⟩$ for probing the population in state $|C⟩$. The resulting FID is collected with an additional microwave horn, amplified with a cryogenic low noise amplifier, mixed down and sent to recording electronics.

Figure 3

Applied microwave pulses and predicted state-specific enantiomeric enrichment signal. (a) The applied four-pulse sequence used for the state transfer. The first three pulses selectively promote either $R$ or $S$ enantiomers to the excited state $|C⟩$. The fourth pulse ($|C⟩\to |D⟩$) is used for probing the population in the target state. (b) The predicted amplitude of the signal at $f_{CD}$ as a function of the phase ${\varphi }_3$ of the drive pulse $|B⟩\to |C⟩$. Similar sinusoidal behavior is predicted as a function of ${\varphi }_1$ and ${\varphi }_2$. For the simulation, field-free Hamiltonian and transition matrices are calculated [19], and the time-dependent Schrödinger equation is numerically integrated.

Figure 4

Enantiomer-specific enrichment of the rotational state $|C⟩$ of chiral 1,2-propanediol. Variations in the amplitude $S$ of the FID signal of the $|C⟩\to |D⟩$ transition reflect the changing population in $|C⟩$. The red and blue data show the signal from enantiopure $S$ and $R$ 1,2-propanediol, respectively. The data show the change in the population of state $|C⟩$, represented by the quantity $S/S_0-\mathrm{mean}(S)/S_0$, as a function of the phase ${\varphi }_3$ of the $|B⟩\to |C⟩$ drive. Here, $S_0$ is the signal amplitude for the transition $|C⟩\to |D⟩$ with all of the drive pulses off and the $|C⟩\to |D⟩$ probe pulse on, and $\mathrm{mean}(S)=(1/N)\sum _i(S_i)$ is the mean measurement $S$ over all phases ${\varphi }_3$ with $N$ being the number of measurements and $i$ being the index of the measurement. For further information see the Supplemental Material [20]. The enantiomer-specific phase dependence is clearly visible. The red and blue lines show sinusoidal fits to the data of $S$ and $R$ molecules, with root mean squared errors of $7.0\times {10}^{-4}$ and $7.3\times {10}^{-4}$, respectively. With an initially racemic sample, the maximum achieved state-specific enrichment is proportional to the peak-to-peak amplitude of the sinusoidal fit and amounts to $\epsilon =0.54\pm 0.05\%$ (Supplemental Material [20]).