Molecular Entanglement Witness by Absorption Spectroscopy in Cavity QED

TL;DR

This work introduces a generalized QFI-based entanglement witness applicable to non-identical local perturbations, enabling detection of inter-molecular entanglement in cavity QED systems at room temperature. It provides an analytical solution to the squeezed Dicke model, derives thermodynamic-limit expressions for QFI per molecule, and validates the witness via exact diagonalization for finite sizes, linking QFI to bounded-mode absorption measurements. By connecting QFI to dipole correlations observable in absorption spectra, the authors propose a feasible protocol to detect multipartite entanglement in molecular systems and polaritonic chemistry, with implications for exciton transport and quantum sensing. The framework combines rigorous upper bounds, phase-transition insights, and practical measurement strategies to illuminate long-lived many-body entanglement in macroscopic chemical ensembles.

Abstract

Producing and maintaining molecular entanglement at room temperature and detecting multipartite entanglement features of macroscopic molecular systems remain key challenges for understanding inter-molecular quantum effects in chemistry. Here, we study the quantum Fisher information, a central concept in quantum metrology, as a multipartite entanglement witness. We generalize the entanglement witness functional related to quantum Fisher information regarding non-identical local response operators. We show that it is a good inter-molecular entanglement witness for ultrastrong light-matter coupling in cavity quantum electrodynamics, including near the superradiant phase transition. We further connect quantum Fisher information to the dipole correlator, which suggests that this entanglement could be detected by absorption spectroscopy. Our work proposes a general protocol to detect inter-molecular entanglement in chemical systems at room temperature.

Figures (8)

• Figure 1: (a) Cavity QED setup, where the $N_{\mathrm{B}}$ molecules of excitation energy $\omega_{\mathrm{m}}$ are collectively coupled to the monochromatic cavity mode $\omega_{\mathrm{c}}$. (b) Bound mode absorption spectrum $A_{\mathrm{b}}\left( \omega \right)$, for pumping laser driving $I_{\mathrm{p}}\left( \omega \right)$ with in-plane wave-vector beyond the threshold of total internal reflection herrera2017absorption.
• Figure 2: (a)(b) Eigenspectrum $E_n$ as a function of $G$ for minimal coupling model $H^{\left( 1 \right)}$ and Dicke model $H^{\left( 0 \right)}$, for $N_B=3$. (c)(d) Maximized QFI for the room-temperature thermal state and the single lower polariton (the first excited eigenstate) as a function of $G$ for $H^{\left( 1 \right)}$ and $H^{\left( 0 \right)}$. The dashed horizontal lines are the thresholds $F\left(K\right)$ for EW. Parameters: $\omega_{\mathrm{m}}=\omega_{\mathrm{c}}=1~eV$. Photon number truncation is 70.
• Figure 3: QFI for thermal states of infinite system. (a) $f_{\mathrm{Q}}\left[ \rho \left( T=0\mathrm{K} \right) ,S^{\mathrm{x}} \right]$ as a function of $G$ for different $\kappa$ and (b) the zoomed-in figure with the arrows representing the trends with increasing $\kappa$. (c) Zero-temperature phase diagram. Solid lines are $G_{\mathrm{c}}$ and $G_{\mathrm{ew}}$ as a function of $\kappa$ that divides the figure into three areas. Dashed lines are the asymptotes at $\kappa_{\mathrm{c}}=1$ and $\kappa _{\mathrm{ew}}=\sqrt{\left( \sqrt{5}-1 \right) /2}$, above which $G_{\mathrm{c}}$ and $G_{\mathrm{ew}}$ are not well defined. (d) $f_{\mathrm{Q}}^{\mathrm{Max}}\left[ \rho \left( T=0\mathrm{K} \right)\right]$ as a function of $G$ and $\kappa$ (cutoff around 110). (e) and (f) show nonzero temperatures: $f_{\mathrm{Q}}^{\mathrm{Max}}\left[ \rho \left( T \right) \right]$ as a function of $G$ and $T$ in the density profile with certain cutoff. The area enclosed by white dotted curves represents the validity of multi-molecular entanglement witness for certain entanglement depth $K$. (e) $\kappa=0$, $G_{\mathrm{c}}/\omega_{\mathrm{m}}=1/2$ and $K>4$, (f) $\kappa=0.84$, $G_{\mathrm{c}}/\omega_{\mathrm{m}}=5/4$ and $K>16$. Parameters: $\omega_{\mathrm{m}}=\omega_{\mathrm{c}}=1~eV$.
• Figure 4: QFI for pure eigenstates for $N_B\rightarrow\infty$, focusing on the upper polariton branch ($\Omega_{+}$, purple) and the lower polariton branch ($\Omega_{-}$, orange). (a), (c) Minimal coupling model without phase transition ($\kappa=1 \ge \kappa_{\mathrm{c}}$). (b), (d) Dicke model with phase transition ($\kappa=0 < \kappa_{\mathrm{c}}$).
• Figure S1: Analytical solution for $H^{\mathrm{\kappa}}$ as a function of $G$. From left to right: mode frequencies of upper polariton ($\Omega^{\prime}_{+}$) and lower polariton ($\Omega^{\prime}_{-}$); zero-point energy $E_{0_+,0_-}$ (insets are the same data in larger scale); Dicke state rotation angle $\theta$; photon state displacement $\alpha$. From up to down: $\kappa=0$; $\kappa=0.36$; $\kappa=0.84$; $\kappa=1$; $\kappa=2$. Parameters: $\omega_{\mathrm{m}}=\omega_{\mathrm{c}}=1eV$.

Theorems & Definitions (18)

• Definition 1: $k$-producible
• Definition 2: entanglement depth $K$
• Definition 3: $k^{\prime}$-producible in $N_{\mathrm{B}}$ particles
• Definition 4: entanglement depth $K^{\prime}$ in $N_{\mathrm{B}}$ particles
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof