Arkajit Mandal

In this work, we develop two many-body quantum electrodynamic methods to calculate the ground-state energies of strongly coupled light-matter molecular systems. Specifically, we extend the second-order many-body Green’s function theory (GF2) for electronic systems to incorporate electron–boson couplings. We employ two ansätze to treat the bosonic part of the system, namely, the coherent-state (CS) and Lang–Firsov (LF) transformed vacuum state. These are combined with the GF2 method to construct two new approaches, which we refer to as CS-GF2 and LF-GF2. We benchmark CS- and LF-GF2 by studying various molecular systems inside an optical cavity. We investigate H2 and LiH potential energy surfaces, keto–enol tautomerization energy barrier, van der Waals interactions between two H2 molecules, and the torsional potential energy surface of the ethylene molecule, C2H4. Both methods provide similar energy profiles, with relatively small differences between CS-GF2 and LF-GF2. Comparisons with the reference calculations also reveal remaining limitations at stretched bond lengths and near the twisted ethylene configuration. We additionally benchmark CS-GF2 against exact diagonalization for a two-site Hubbard–Holstein model and observe that it closely reproduces the coupling-induced energy change in the weakly interacting regime while improving upon CS-MP2 in the strongly interacting regime. Overall, the results demonstrate that CS-GF2 and LF-GF2 provide self-consistent descriptions of correlated molecular electron–boson systems, offering a many-body Green’s function alternative for studying ground-state cavity-modified systems.

Recent experiments demonstrate the modification of chemical dynamics via cavity-enhanced vibrational energy transport. Here, we provide a microscopic account of both photonic and mode-selective energy transport using direct mesoscale on-the-fly simulations of cavity-modified transport under vibrational strong coupling. We find that molecular anharmonicity leads to nonlinear driving-dependent photonic transport and localization, which we demonstrate in cavity-coupled water by tuning the photon frequency close to either the harmonic bending or the anharmonic stretching modes. We reproduce these effects in simple model systems, suggesting that the underlying mechanism extends beyond the specific case of cavity-coupled water. We also demonstrate that the diffusion of mode-selective temperature, quantified via the variance of the H–O–H bond angle or O–H bond length, depends on the cavity frequency, which we rationalize using an analytical model. Our results highlight the rich dynamical interplay of molecular and photonic degrees of freedom that persist in real atomistic systems.

In this work, we introduce Quantum Ninjas vs Laser Robots, a board game designed to cultivate quantum intuition in learners across a variety of backgrounds through interactive gameplay and tangible analogies. The game introduces familiar and approachable characters, ninjas and robots, which help to model key ideas of quantum mechanics, including probabilistic measurement, discrete energy levels, excitation and relaxation processes, and wave function collapse. The game was introduced to a group of undergraduate students at Texas A&M University, and their postgame perceptions were collected via a survey. The results indicate a positive reception of the game, engagement, and collaborative learning. Our findings suggest that game-based learning has the potential to serve as an effective complement to traditional teaching methods for abstract and math-heavy subjects such as quantum mechanics by lowering barriers to entry.

Coupling excitons with quantized radiation has been shown to enable coherent ballistic transport at room temperature inside optical cavities. Previous theoretical works employ a simple description of the material, depicting it as a one-dimensional single-layer placed in the middle of an optical cavity, thereby ignoring the spatial variation of the radiation field. In contrast, in most experiments, the optical cavity is filled with organic molecules or multiple layers of two-dimensional materials. Here, we develop an efficient mixed-quantum-classical approach, introducing a bright layer description, that enables the simulation of exciton-polariton quantum dynamics in all three dimensions. Our simulations reveal that, for the same Rabi splitting, a multilayered material extends the quantum coherence lifetime and enhances transport compared to a single-layer material. We find that this enhanced coherence can be traced to a synchronization of phonon fluctuations over multiple layers, wherein the collective light-matter coupling in a multilayered material effectively suppresses the phonon-induced dynamical disorder.

Exciton-polaritons are light-matter hybrid quasi-particles that have emerged as a flexible platform for developing quantum technologies and engineering material properties. However, the fundamental mechanistic principles that govern their dynamics and relaxation remain elusive. In this work, we provide the microscopic mechanistic understanding of the exciton-polariton relaxation process that follows from an excitation in the upper polariton. Using both mixed quantum-classical simulations and analytical analysis, we reveal that phonon-induced upper-to-lower polariton relaxation proceeds via two steps: the first step is a vertical interband transition from the upper to the lower polariton, which is followed by a second step that is a phonon-induced Fröhlich scattering within the lower polariton. We find that in materials of finite thickness (which include filled cavities), phonon-induced polaritonic intraband Fröhlich scattering is significantly suppressed. We show that the microscopic origin of this suppression is phonon-fluctuations synchronization (or self-averaging) due to the polaritonic spatial delocalization in the quantization direction. Finally, we show that the same phonon fluctuation-synchronization effect plays a central role across polaritonic relaxation pathways, and we derive simple analytical expressions that relate a material's finite thickness to the corresponding relaxation rate constants.

Interest in vibrational polaritonic chemistry, where ground-state chemical kinetics are modified via confined optical modes in a cavity, has surged in recent years. Although models have been developed to understand cavity-modified reactions, fully quantum mechanical simulations remain out of reach for the collective regime that involves many molecules, a critical aspect of the phenomenon. Mixed quantum–classical (MQC) simulations offer a scalable alternative, but their accuracy requires testing and potential improvements even in the single-molecule limit. In this work, we take this step by first introducing the mapping approach to surface hopping (MASH) to address the limitations of traditional MQC methods. Second, we incorporate a quantum treatment of the cavity mode, moving beyond the classical approximations often employed in previous studies. Results for a single-molecule model of vibrational polaritonic chemistry show that combining MASH with a quantum cavity mode yields the most accurate rates. However, this scheme may produce different long-time population dynamics at zero coupling depending on whether the cavity mode is quantized; a problem known as size-inconsistency in MASH. We address this problem by proposing the ɛ-MASH approach, which forbids hopping between states with negligible nonadiabatic couplings (NACs). Combining MASH with a quantum cavity mode thus provides a promising approach for scalable and accurate MQC simulations in the collective regime.

We develop a mesoscale on-the-fly approach, and a computational package CavOTF, to simulate the cavity modified chemical dynamics.

Exciton-polaritons are light-matter hybrid quasi-particles that have emerged as a flexible platform for developing quantum technologies and engineering material properties. However, the fundamental mechanistic principles that govern their dynamics and relaxation remain elusive. In this work, we provide the microscopic mechanistic understanding of the exciton-polariton relaxation process that follows from an excitation in the upper polariton. Using both mixed quantum-classical simulations and analytical analysis, we reveal that phonon-induced upper-to-lower polariton relaxation proceeds via two steps: the first step is a vertical inter-band transition from the upper to the lower polariton, which is followed by a second step that is a phonon-induced Fröhlich scattering within the lower polariton. We find that in materials of finite thickness (which include filled cavities), phonon-induced polaritonic intraband Fröhlich scattering is significantly suppressed. We show that the microscopic origin of this suppression is phonon-fluctuations synchronization (or self-averaging) due to the polaritonic spatial delocalization in the quantization direction. Finally, we show that the same phonon fluctuation-synchronization effect plays a central role across polaritonic relaxation pathways, and we derive simple analytical expressions that relate a material's finite thickness to the corresponding relaxation rate constants.

In this work, we introduce Quantum Ninjas vs. Laser Robots, a board game designed to cultivate quantum intuition in learners across a variety of backgrounds through interactive gameplay and tangible analogies. The game introduces familiar and approachable characters, ninjas and robots, which help to model key ideas of quantum mechanics, including probabilistic measurement, discrete energy levels, excitation and relaxation processes, and wavefunction collapse. The game was introduced to a group of undergraduate students at Texas A&M University, and their learning outcomes were evaluated using a post-game survey. The results indicate improved familiarity with quantum mechanics as well as high levels of engagement and collaborative learning. Our findings suggest that game-based learning can serve as a very effective complement to traditional teaching methods for abstract and math-heavy subjects such as quantum mechanics by lowering barriers to entry and fostering intuitive understanding.

In this work, we combine the density functional tight-binding (DFTB) approach with a light-matter Hamiltonian beyond the long-wavelength approximation to propagate the dynamics of vibrational polaritons formed by coupling molecular vibrations to confined radiation inside a Fabry-Pérot optical cavity. Here, we develop a parallelized propagation scheme with lightweight inter-CPU communication by exploiting the sparse nature of the light-matter interactions in the real space representation. We find that the computationally expensive Born charges required for our propagation can be replaced with the computationally inexpensive Mulliken charges to obtain qualitatively accurate linear spectra especially when the nonlinearity (arising from molecular vibrations) of the light-matter interaction term is not substantial. However, the same approach may not be suitable to be used for studying cavity modification of energy transport or chemical dynamics as this approximation leads to spurious heating of the light-matter hybrid system. We demonstrate the utility of this on-the-fly approach to compute angle resolved polaritonic spectra of water. We implement our approach as an open-source computational package, CavOTF, which is available on GitHub.