Enantiodetection in a cavity QED setup with finite chiral molecules

TL;DR

This work addresses enantiodetection by engineering interference in a cavity-QED system where $N_L$ left-handed and $N_R$ right-handed $\\Delta$-type molecules couple to a driven cavity mode. The authors exploit a global $\\pi$ phase difference between enantiomers to create interference between a direct cavity-drive pathway and molecule-mediated pathways, making the steady-state intracavity photon number a readout of enantiomeric composition. To treat finite-size ensembles beyond mean-field, they develop and apply the generalized discrete truncated Wigner approximation (GDTWA), enabling scalable simulations that capture fluctuations and correlations in mesoscopic systems. They show that enantiomeric excess $\\mathcal{P}=(N_R-N_L)/(N_R+N_L)$ can be inferred from photon-number readout with errors below $5\%$, tunable by the drive strength $\\eta$, offering a practical route to quantum-optical enantiodetection in realistic experimental settings.

Abstract

We investigate enantiodetection for both a single cyclic three-level chiral molecule and finite ensembles of such molecules by monitoring the steady-state intracavity photon number in a cavity-QED platform. Our scheme exploits the intrinsic global $π$-phase difference between opposite enantiomers to engineer destructive and/or constructive interference pathways, enabling a direct readout of enantiomeric excess with an error below $5\%$. To capture mesoscopic many-molecule effects beyond mean field while avoiding brute-force master-equation simulations, we employ a generalized discrete truncated Wigner approximation, which is well suited for systems with many yet finite molecules. These results pave the way for implementing enantiodetection in realistic quantum-optical settings.

Figures (5)

• Figure 1: Schematic of the enantiodetection setup. A Fabry-Pérot cavity hosts $N_R$ right-handed and $N_L$ left-handed cyclic three-level ($\Delta$-type) molecules. Each molecule couples to two classical control fields with Rabi amplitudes $\Omega_{31}$ and $\Omega_{32}$ and to the quantized cavity mode with strength $g$. The closed-loop product of dipole couplings acquires a $\pi$-phase difference between opposite enantiomers. The cavity is driven coherently at frequency $\nu_{p}$ with amplitude $\eta$ and experiences photon loss at rate $\kappa$.
• Figure 2: (a) and (b) photon and molecular dynamics, respectively. The parameters are set as $\Delta_{31}=\Delta_{32}=\Delta_{c}=0,\Omega_{32}=5g,\Omega_{31}=g,\kappa=5g,\eta=4g,\phi_{L}=0$, and $\phi_{R}=\pi$ in the main panel of (a) and (b). In the inset of (a), all parameters remain unchanged except for $\eta = 0$.
• Figure 3: Comparison between the exact numerical results of the master equation and the GDTWA under simulations with 10000 trajectories. The parameters are set as $\Delta_{31}=\Delta_{32}=\Delta_{c}=0,\Omega_{32}=5g,\Omega_{31}=g,\kappa=5g,\eta=4g,\phi_{L}=0$, and $\phi_{R}=\pi$.
• Figure 4: Steady-state photon number as a function of the number of left-handed molecules $N_{L}$ for different strengths $\eta$. The other parameters are set as $\Delta_{31}=\Delta_{32}=\Delta_{c}=0,\Omega_{32}=5g,\Omega_{31}=g,\kappa=5g,\phi_{L}=0$, and $N_{R}=0$.
• Figure 5: (a) and (b) Steady-state intracavity photon number $\langle \hat{a}^{\dagger}\hat{a}\rangle_{\mathrm{ss}}$ and detection uncertainty $\Delta\mathcal{P}$ as functions of enantiomeric excess $\mathcal{P}$ and several drive strengths $\eta$. The red circles mark the minimum uncertainty for each $\eta$ in panel (b). Other parameters we set as $\Delta_{31}=\Delta_{32}=\Delta_{c}=0, \Omega_{32}=5g, \Omega_{31}=g, \kappa=5g, \phi_{L}=0,\phi_{R}=\pi$, and $N_{R}+N_{L}=200$.