Coherent nonlinear optical probe for cavity-dressed vibrational mode mixing: multidimensional double-quantum coherence and photon-echo spectroscopy

TL;DR

The paper develops a microscopic framework for cavity-dressed interacting vibrons (vibron-polaritons) that includes both one- and two-vibron states and a dissipative phonon bath. It derives a full vibron-polariton Hamiltonian, constructs a tensor-product basis, and obtains polariton Green's functions to describe transport and dephasing under realistic dissipation. Two complementary three-pulse MDCS techniques, double-quantum coherence and photon-echo spectroscopy, are formulated and simulated to resolve polariton correlations and transport across one- and two-polariton manifolds, with simulations demonstrating tunable spectral weight among resonances by adjusting pulse parameters. The approach reveals how cavity coupling strengths comparable to vibron couplings can modulate excited-state delocalization and vibrational energy redistribution while preserving vibrational identity, offering a pathway to control IVR in dissipative molecular systems and a framework extensible to broader cavity-controlled nonlinear spectroscopy.

Abstract

Cavity dressing of molecular vibrational dynamics expands the role of characteristic vibrations as spectroscopic markers of underlying ultrafast dynamics. Interacting vibrational modes exhibit a pronounced excited state delocalization due to the interaction with the cavity mode, which is reflected in the ultrafast dynamics. We characterize the ultrafast dynamics of these cavity-dressed characteristic vibrations in the presence of dissipation. Specifically, we present two complementary three-pulse coherent multidimensional spectroscopic techniques capable of monitoring one- and two-quantum cavity-dressed vibrational excitations. Dissipative properties, such as transport and dephasing, are described using a microscopic theory that includes low- and high-energy phonon modes. Simulations were performed with finite laser pulses. The cavity coupling strengths fall within a range similar to vibrational mode couplings, hinting towards a possibility of control of intermolecular vibrational energy redistribution. The framework is extendable to a broad range of cavity-controlled nonlinear spectroscopies of dissipative molecular systems.

Figures (8)

• Figure 1: Illustration of cavity-vibron configurations. The first row (A1–A3) represents single-excitation exchange processes, whereas the second and third rows (B1–B6) represent two-excitation processes. The gray background represents configuration mixing facilitated by cavity-vibron coupling, while the white background indicates mixing via vibron hopping. The ground states correspond to the absence of excitations. The one-polariton states comprise weighted contributions from three configurations: the pure one-photon cavity ( $|00\rangle |1\rangle_c$) and the mixed cavity-vibron configurations ($|10\rangle |0\rangle_c, |01\rangle |0\rangle_c$)the first row. The two-polariton states comprise weighted contributions from six configurations: the pure two-vibron states ($|20\rangle |0\rangle_c, |02\rangle |0\rangle_c, |11\rangle |0\rangle_c$), the pure two-photon cavity state ($|00\rangle |2\rangle_c$), and the mixed cavity-vibron configurations ($|10\rangle |1\rangle_c, |01\rangle |1\rangle_c$).
• Figure 2: Parametric dependence of one- and two-polariton energies on the cavity mode detuning (defined via the scanning parameter $\Omega_c)$ for three distinct coupling strengths. The coupling strength increases from left to right, resulting in a marked increase in state repulsion. For any combination of cavity detuning and coupling strength, a specific energetic ordering of states is obtained. By selecting appropriate laser parameters, the time-dependent fluctuations of the polariton energy gaps can be monitored. Notably, the relaxation parameters are also determined by these gaps.
• Figure 3: (A) Schematic diagram of the pulse configuration for multidimensional coherent spectroscopy, including the heterodyning stage (adapted from hochstrasser2007two). For clarity, relative dimensions are exaggerated. The sample consists of a cavity-encapsulated system of vibrons, polaritons, and phonons. (B) The cavity mode interacts with two interacting vibron modes. Each has distinct two-vibron nonlinearities, illustrated in the local mode description. C) Two plausible dynamical pathways (in Albrecht notation) displaying polariton excited-state absorption, depicted in the polariton eigenbasis. The pathways on the left are pertinent to photon echo spectroscopy, while those on the right are pertinent to double-quantum coherence spectroscopy.
• Figure 4: Displayed are the Liouville space Feynman diagrams that describe the polariton pathways contributing to the PE and DQC signal. The time evolution of the polariton density operator, denoted $|ab\rangle\rangle \rightarrow |a\rangle\langle b|$, is depicted by vertical pairs of arrows. Wiggly lines pointing toward or away from the density operator indicate the resonant absorption or emission of a single excitation, respectively. Diagrams labeled (a1)–(a3) denote photon-echo pathways, while (b1)–(b2) denote double-quantum coherence pathways.
• Figure 5: Simulated two-dimensional double-quantum coherence (DQC) spectra presented for six variations of the driving laser parameters. These variations explore the temporal width of the excitation pulses, the excitation frequencies, and the final projection frequencies. Off-diagonal spectral features represent correlations between the one-polariton resonances. A careful selection of pulse parameters can amplify or suppress particular features which shows the accumulation of spectral weight in specific resonances. The expression in Eq. \ref{['eqn:dqc']} and the pathways depicted in Fig. \ref{['fig:vibpolfeyn']} rationalize the observed spectral features. For a detailed discussion, see section \ref{['subsubsec:dqcsim']}.