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arXiv:2605.19770

Quantum master equation approach for the multiphonon up-pumping model

Jiong Cheng, Yanqiang Yang, Wenlin Li, Xun Li

quant-phphysics.chem-phSubmitted May 19, 2026• Announced May 20, 2026
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Abstract

A fully quantum multiphonon up-pumping model is proposed to characterize coherent energy transfer in energetic materials (EMs) subjected to external shock. After eliminating the degrees of freedom of the phonon bath within a mean-field approximation, we derive a quantum master equation governing the energy transfer among vibrational modes. Our analysis reveals that doorway modes of different frequencies undergo distinct levels of effective coherent driving and dissipation, induced by the shocked phonon environment. This not only clarifies the microscopic origin of coherent phonon generation, but also reveals the possibility of modulating such coherent driving and dissipation. Based on numerical simulations of a simplified model using the master equation, we demonstrate how doorway modes extract energy from the phonon environment and subsequently excite higher-frequency molecular vibrational modes. This work offers a renewed perspective for understanding the mechanisms of energy transfer in energetic materials.

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A fully quantum multiphonon up-pumping model is proposed to characterize coherent energy transfer in energetic materials (EMs) subjected to external shock. After eliminating the degrees of freedom of the phonon bath within a mean-field approximation, we derive a quantum master equation governing the energy transfer among vibrational modes. Our analysis reveals that doorway modes of different frequencies undergo distinct levels of effective coherent driving and dissipation, induced by the shocked phonon environment. This not only clarifies the microscopic origin of coherent phonon generation, but also reveals the possibility of modulating such coherent driving and dissipation. Based on numerical simulations of a simplified model using the master equation, we demonstrate how doorway modes extract energy from the phonon environment and subsequently excite higher-frequency molecular vibrational modes. This work offers a renewed perspective for understanding the mechanisms of energy transfer in energetic materials.
We have developed a unified quantum optical master equation that includes the dissipative mechanisms of an impurity molecule in crystals. Our theory applies generally to polyatomic molecules where several vibrational modes give rise to intramolecular vibrational redistributions. The usual assumption on identical shapes of the nuclear potentials in ground and excited electronic states and the rotating wave approximation have been relaxed, i.e. the vibrational coordinates are different in the ground and excited states, with counter-rotating terms included for generality. Linear vibrational coupling to the lattice phonons accounts for dissipations via non-radiative transitions. The interaction of a molecule with photons includes Herzberg-Teller coupling as the first order non-Condon interaction where the transition dipole matrix elements depend linearly on vibrational coordinates. We obtain new cross terms as the result of mixing the terms from the zeroth-order (Condon) and first-order (non-Condon) approximations. The corresponding Lamb shifts for all Liouvilleans are derived explicitly including the contributions of counter-rotating terms. The computed absorption and emission spectra for carbon monoxide is in good agreement with experimental data. We use our unified model to obtain the spectra for nitrogen dioxide, demonstrating the capability of our theory to incorporate all typical dissipative relaxation and decoherence mechanisms for polyatomic molecules. The molecular quantum master equation is a promising theory for studying molecular quantum memory.
Abstract Quantum simulation offers a route to study open-system molecular dynamics in non-perturbative regimes by programming the interactions among electronic, vibrational, and environmental degrees of freedom on similar energy scales. Trapped-ion systems possess this capability, with their native spins, phonons, and tunable dissipation integrated within a single platform. Here, we demonstrate an open-system quantum simulation of charge and exciton transfer in a multi-mode linear vibronic coupling model. Employing tailored spin-phonon interactions alongside reservoir engineering techniques, we emulate a system with two dissipative vibrational modes coupled to donor and acceptor electronic sites and follow its non-equilibrium dynamics. We continuously tune the system from the charge transfer (CT) regime to the vibrationally assisted exciton transfer (VAET) regime by controlling the vibronic coupling strengths. We find that degenerate modes enhance CT and VAET rates at large energy gaps, while non-degenerate modes activate slow-mode pathways that reduce the energy-gap dependence, thus enlarging the window for efficient transfer. These results show that the presence of one additional vibration introduces interfering vibrationally assisted pathways and reshapes non-perturbative quantum excitation transfer. Our work establishes a scalable route to simulating chemically relevant, many-mode vibronic processes with engineered environments, guiding the design of next-generation organic photovoltaics and molecular electronics.
Open quantum batteries (QBs) operate under unavoidable system--environment interactions, where both dissipation and coherent frequency renormalization can affect their dynamics. While dissipative effects have been extensively studied, the role of environment-induced frequency shifts, such as the Lamb shift, remains less explored. Here, we investigate a driven open QB consisting of two coherently coupled quantum harmonic oscillators representing the charger and the battery. By incorporating dissipation and Lamb-shift corrections within a Lindblad master equation, we show that the Lamb shift renormalizes the system eigenfrequencies and modifies the resonance condition with the external drive. We further demonstrate that the resulting frequency renormalization leads to a mode-selective energy-transfer process, producing a redistribution of energy between the charger and the battery. This behavior is characterized through a supermode decomposition of the coupled system, which reveals how the environment-induced frequency shift alters the dominant energy-transfer channel. Our results clarify the role of coherent environmental effects in open quantum batteries and provide a physical framework for understanding work-extraction dynamics beyond purely dissipative descriptions.
This thesis is concerned with modelling the dynamics of open quantum systems in several different contexts. Of principal interest is the manner in which the environment can modify, or even dominate, a system’s quantum behaviour in order to facilitate the transport of energetic excitations. In the first research chapter, a time-local, non-Markovian quantum master equation is derived in a variationally defined reference frame, for networks of two-level systems coupled to bosonic environments. The predictions of this master equation are then compared with those derived using both weak-coupling and polaron approximations. The variational master equation is found to agree with these standard approaches in their regimes of validity, whilst interpolating between them in intermediate parameter regimes. The second research chapter focusses on the dynamics of a superconducting double quantum dot embedded in a resonant circuit. The device is considered in a regime where the ground state consists of a coherent spatial superposition of a single Cooper pair, which can be excited by a variety of interactions with the environment. The relevant transition rates are calculated and the processes responsible are identified. A numerical simulation of the system is then used to explain experimental data, and show that for certain parameters a significant fraction of excitations occur via absorption of photons from the environment. The final chapter considers a model for an olfactory receptor, in which odorant molecules are recognised by their vibrational modes. Electron transfer occurs in the receptor, dependent on the presence of a vibrational mode of the right frequency. A quantum master equation for the system is derived, and the resulting dynamics is compared to earlier semi-classical treatments. The behaviour of the receptor is found to be sensitive not only to the frequency of the vibrational mode, but also to the character of the surrounding environment. Increased dissipation on the odorant mode, as well as the presence of higher frequencies in the environment is found to improve the frequency resolution of the receptor.
We develop a versatile master equation approach to describe the nonequilibrium dynamics of a two-level system in contact with a bosonic environment, which allows for the exploration of a wide range of parameter regimes within a single formalism. As an experimentally relevant example, we apply this technique to the study of excitonic Rabi rotations in a driven quantum dot, and compare its predictions to the numerical Feynman integral approach. We find excellent agreement between the two methods across a generally difficult range of parameters. In particular, the variational master equation technique captures effects usually considered to be nonperturbative, such as multiphonon processes and bath-induced driving renormalization, and can give reliable results even in regimes in which previous master equation approaches fail.
Coherent-state functional-integral methods are used to develop approximation schemes for the description of coupled electron-phonon systems far from equilibrium. We consider an interacting-electron system which is coupled to a system of phonons and subjected to an external---not necessarily weak---perturbation. For systems where the electron-phonon interaction is linear in the phonon variables, the phonon degrees of freedom can be accounted for exactly. From a formally exact representation of a suitable generating function for the expectation value of electronic observables, approximation schemes based on mean-field solutions can be derived. Within the lowest order of approximation, the coupled electron-phonon system may be treated as a self-consistent system of indepenent electrons. Higher-order corrections are shown to give a random-phase approximation based on self-consistent mean fields. This approach is applied to electronic two-level systems coupled to phonons under a large external bias. We find that the coupling to acoustical-phonon modes leads to a damping of the quantum beats and drives the system into a new equilibrium state. The coupling to LO phonons is shown to account correctly for resonance effects which arise when the level splitting is close to the LO-phonon energy.