Unraveling Geometric-phase at Conical Intersection by Cavity-enhanced Two-dimensional Electronic Spectroscopy

TL;DR

Addressing the challenge of directly observing the geometric phase ($GP$) associated with conical intersections ($CI$) in nonadiabatic molecular dynamics, this work proposes cavity-enhanced two-dimensional electronic spectroscopy (2DES) to control and detect GP effects through vibrational strong coupling. The authors construct a four-state pentacene dimer model with two vibronic coordinates ($Q_t$, $Q_c$) and a $CI$ between excited states, showing that GP causes amplitude cancellation in excited-state absorption via interference of wave-packet pathways, which can be tuned by the cavity coupling strength $\eta$. The 2DES simulations reveal GP signatures as the restoration or suppression of a cross-peak (peak B) and distinct coherence features at frequencies around $250$ and $1200\,\mathrm{cm^{-1}}$, with their lifetimes modulated by $\eta$, establishing a practical route to observe topological effects in ultrafast molecular dynamics. These results offer a pathway to quantum-control strategies and inform the design of optoelectronic materials, linking GP, nonadiabatic dynamics, and cavity quantum electrodynamics in a tangible experimental framework.

Abstract

The geometric phase is a fundamental quantum mechanical phenomenon uniquely associated with conical intersections (CI) between potential energy surfaces and serves as a definitive signature of their presence. In this study, we propose a novel spectroscopic approach to directly detect the geometric phase using two-dimensional electronic spectroscopy (2DES) enhanced by strong light-matter interactions within an optical cavity. Focusing on a prototypical pentacene dimer undergoing singlet fission, we model the nonadiabatic wave packet dynamics as it evolves through a CI between electronically excited states. The optical cavity enables dynamic modulation of the coupling between the optical field and molecular vibrational modes, allowing precise control over the wave packet pathways. Importantly, we identify a cancellation in the spectral amplitude, arising from phase differences accumulated along different trajectories, which serves as a clear spectroscopic manifestation of the geometric phase (GP). This cavity-enhanced 2DES framework not only enables direct observation of GP effects but also offers a versatile platform for probing ultrafast nonadiabatic processes. Our results provide fundamental insights into topological effects in molecular dynamics and pave the way for experimental strategies in quantum control, photochemistry, and the design of advanced optoelectronic materials.

Figures (4)

• Figure 1: (a) Schematic representation of a pentacene molecular dimer coupled to an infrared cavity mode. (b) Conceptual energy landscape illustrating vibronic transitions and wave packet evolution.
• Figure 2: (a, b) nuclear reduced density matrix associated with state $\ket{e_{1}}$ (lower electronic excited state in adiabatic basis) at $\eta$ = 0 cm$^{-1}$ and $\eta$ = 100 cm$^{-1}$, respectively. The blue dashed lines indicate the position of degenerate point between two PESs. (c, d) Corresponding nuclear reduced density matrix along the coupling coordinate Q$_c$ (lower excited state). The black dashed boxes manifest the wave-packet cancellation along the center coordinate of Q$_{c}$.
• Figure 3: Two-dimensional electronic spectroscopy and wavelet analyses for varying $\eta$. Panels (a, b) show 2DES maps at T = 50 fs for $\eta$ = 0 and 100 cm$^{-1}$, revealing ESA-induced spectral changes. Panels (c, d) depict time-domain traces of Peaks A and B. Panels (e-h) show wavelet-transformed coherence maps, highlighting frequency- and time-resolved modulations due to GP effects under vibronic-cavity coupling.
• Figure 4: Extracted coherence lifetimes of vibrational modes for Peaks A (a) and B (b) as a function of cavity-molecule coupling strength $\eta$. Peak A reflects GSB dynamics, while Peak B captures ESA behavior. Enhanced lifetimes, especially for low-frequency modes, indicate GP effects near a CI under strong coupling.