Enantiosensitive exceptional points in open chiral systems

TL;DR

The paper investigates enantiosensitive exceptional points in open chiral systems, showing that EP positions depend on molecular handedness. It develops a three-color field approach to realize enantiosensitive population transfer by encircling a single enantiomer's EP, and demonstrates a non-Hermitian route to amplify weak chiral effects near resonance via lifetime stabilization and PT-phase contrast. It further proposes a chiral optical-fiber sensor in which enantiomeric excess shifts EPs and yields topologically distinct propagation, enabling high-sensitivity detection. Collectively, the work provides a topologically robust framework for selective chiral control and sensing, with broad implications for non-Hermitian photonics and chiral chemistry.

Abstract

Exceptional points (EPs) are remarkable spectral degeneracies in a non-Hermitian system's parameter space, where both eigenvalues and eigenstates coalesce. Here, we show that in non-Hermitian molecular chiral systems the position of EPs in the parameter space is enantiomer-specific. First, we show that encircling the EP of one enantiomer drives robust topological population transfer in the chiral molecule while its mirror twin remains unaffected, offering a new route for selective chiral control. Second, we reveal how resonant excitation of EPs in chiral molecules can amplify weak chiral effects, offering an alternative approach to the enhancement of chiral interactions. Third, we demonstrate that a twisted chiral fiber immersed in a liquid solution of chiral molecules exhibits topologically different behavior depending on the solution's enantiomeric excess, offering a new approach to the detection of molecular chirality. Our results combine high enantiosensitivity with topological robustness in chiral discrimination and control, paving the way for new approaches in the exploration of non-Hermitian and chiral phenomena.

Figures (6)

• Figure 1: Enantiosensitive exceptional points of a non-Hermitian chiral molecule.(a) Three-level model representing two bound states $|1\rangle$ and $|2\rangle$ of a chiral molecule coupled to each other and the continuum $|E\rangle$ via electric-dipole transitions by a three-color laser field with frequencies $\omega_1=\omega_2+\omega_3$. (b) Position of the EPs in the parameter space $(\Delta,F_3)$ for varying ratios $\eta=F_2/F_1$ and fixed $F_1$. The solid red (blue) lines correspond to the right (left) enantiomer, where the arrows indicate the directions along which the EPs move for increasing $\eta$. The black circles (triangles) correspond to the position of the EPs for $\eta=0$ ($\eta=1$), where enantiosensitivity is lost. The red (blue) circles correspond to the position of the EPs for $\eta=\sqrt{2}$ for the right (left) enantiomer. The dashed red (blue) lines show how the EPs of the right (left) enantiomer move for fixed $\eta=\sqrt{2}$ and varying relative phase $\Delta\Phi\in[0,\pi/2]$ of the three-photon matrix element $\Omega_{123}$. At $\Delta\Phi=\pi/2$ the enantiosensitivity is lost and the EPs of the two enantiomers are on the vertical axis $\Delta=0$.
• Figure 2: Enantiosensitive topological population transfer in non-Hermitian chiral molecules.(a,d) Absolute value of the difference in quasi-energies $|\lambda_+-\lambda_-|$ for the right (a) and left (d) enantiomer in the $(\Delta,F_3)$ parameter space. The black solid line shows the path enclosing one of the exceptional points (white cross) of the right enantiomer. (b,e) Trajectories of the adiabatic solutions for the path in (a,d) for the right (b) and left (e) enantiomers on the quasi-energy surfaces $\mathrm{Re}[\lambda_\pm(\Delta,F_3)]$. Solid (dashed) lines correspond to clockwise (counter-clockwise) encirclement. The right enantiomer in (b) shows the adiabatic flip associated to the encirclement of an EP, leading to a transfer of population from one adiabatic state to the other at the end of the loop, while for the left enantiomer in (e) the initial and final population at the end of the loop coincide. (c,f) Time-dependent populations population inversion $A^{\circlearrowright/\circlearrowleft}_{\pm}(t)$ in the adiabatic states for a dynamical evolution along the path shown in (a,d) for the right (c) and left (f) enantiomer. Red (blue) color corresponds to clockwise (counter-clockwise) encirclement, while solid (dahsed) lines correspond to an initial population in the $|\phi_+\rangle$ ($|\phi_-\rangle$) adiabatic state. The asymmetric enantiosensitive switch is observed for the right enantiomer in (c), where the sign of the population inversion parameter is determined by the sense of encirclement, while for the left enantiomer in (d) the population at the end of the evolution is predominantly in the $|\phi_-\rangle$ regardless of the sense of encirclement and initial conditions.
• Figure 3: Stability of the enantiosensitive asymmetric switch effect.(a)$\alpha$ parameter for paths with a deformed radius $\rho_x=\rho\cdot\rho_x^{(0)}$, where $\rho_x^{(0)}$ is the radius of the path along the $\Delta$ coordinate of the path in Figs. \ref{['Fig2']}a,d). (b)$\alpha$ parameter for paths with a shifted center $\Delta=\delta\cdot\Delta^{(0)}$, where $\Delta^{(0)}$ is the center of the path in Figs. \ref{['Fig2']}a,d). The red and blue lines correspond respectively to the right and left enantiomer. The insets show the deformed paths for different values of $\rho$ and $\delta$, where the dotted line shows the undeformed path and the black cross indicates the position of the EP of the right enantiomer.
• Figure 4: Amplification of weak chiral coupling via non-Hermitian effects.(a) Two levels $|1\rangle$ and $|2\rangle$ of a chiral molecule are coupled by a circularly-polarized field via electric-dipole and magnetic-dipole transitions (orange and green arrows). The upper level is coupled via tunneling through a barrier to the continuum $|E\rangle$ with a decay rate $\Gamma$. $\mathbf{Q}$ represents a general molecular coordinate. (b,c) Real (b) and imaginary (c) parts of the eigenvalues $\lambda_{\pm}$ in Eq. [\ref{['eq:eig0']}] with respect to the scaled decay rate $\Gamma/\Omega_d$. The red and blue colors correspond to right and left enantiomer respectively, and their respective EPs are indicated by colored circles. (d) Time-dependent chiral dichroism $\text{CD}(t)$ for increasing scaled decay rate $\Gamma/\Omega_d$ obtained from the solution of the Time-Dependent Schrödinger Equation (TDSE) with the Hamiltonian in Eq. [\ref{['eq:Ham0']}] at zero detuning $\Delta=0$. (e) Total residual population in the two enantiomers $P_+(t)+P_-(t)$ for selected values of the scaled decay rate $\Gamma/d_{12}$. (f) Time-dependent chiral dichroism for selected values of the scaled decay rate as in panel (d). The horizontal dashed line indicates $\text{CD}(t)=0$.
• Figure 5: (a) A single mode non-Hermitian optical fiber interacting with a solution of chiral molecules via its evanescent modes. (b) The fiber is twsited along its propagation axis $z$ with a torsion rate $\phi_t$, where positive $\phi_t$ indicates clockwise twist. (c) Absolute value of the difference between the eigenmodes of the fiber for enantiomeric excess $ee=100\%$ (top panel), $ee=0\%$ (middle panel) and $ee=-100\%$ (bottom panel). The white crosses indicate the EP. (f,h) Real (f) and imaginary (h) part of the eigenmodes of a fiber with positive torsion rate $\phi_t=|\Delta\Gamma|$. Red and blue areas indicate respectively the $\mathcal{PT}$-broken and $\mathcal{PT}$-symmetric regions. (e,g) Same as in (f,h) for a fiber with negative torsion rate $\phi_t=-|\Delta\Gamma|$.