Generally speaking, I am interested in understanding the interactions between (quantum) light and matter: how light modifies the electronic properties of matter, and how matter modifies the propagation of light pulses. Two main focuses are the non-perturbative regime and the case with quantum light. The latter case appears in the laser-driven materials where a (strong) light pulse dresses the material to manipulate their physical properties; the latter arises in the emerging field of polaritonic chemistry and quantum plasmonics. Both pose significant challenges to the current theories for light-matter interaction. Therefore, novel theoretical tools, both analytical and numerical, are required.

So far, my research experience has been focused on the following areas.

## Cavity femtochemistry

Is it possible to engineer the photonic environment of a molecule to alter its physical properties? The answer is positive! Recent experiments has shown that by placing molecules into an optical cavity such that the molecules feel a different “vacuum”, a large variety of chemical processes such as energy transfer and ground state reactions can be altered significantly.

We are interested in understanding to what extent can we employ optical cavities to control a chemical process and which chemical process is most sensitive to cavity control.

## Electronic properties of materials far from equilibrium

We develop general theories and perform computations to understand electronic properties of materials (e.g. semiconductors and molecules) driven far from equilibrium by lasers.

A current project is to understand the optical properties of laser-dressed materials. The main challenge for this project is that we cannot directly use the linear response theory that is defined for systems in thermal equilibrium because, for laser-driven materials, the strong laser-matter interaction drives the system constantly far from equilibrium.

## Open quantum systems and decoherence

We aim to develop general theories and exact numerical simulations (using hierarchal equations of motion method) to understand decoherence dynamics of systems interacting with Markovian, non-Markovian environments.

In a recent paper [J. Phys. Chem. Lett., 8, 4289-4294 (2017)], we construct a theory that shows that the physics behind the early-time loss of coherence is *fluctuations*.

Among the decoherence processes, electronic decoherence in molecular systems and condensed phase environments is of ubiquitous importance that influences lots of chemical processes such as electron transfer and energy transfer, photochemistry, photophysics, etc.

## Method developments for quantum dynamics

Methods for adiabatic and non-adiabatic quantum dynamics which incorporates nuclear quantum effects but still scalable to the molecular size is one of the main challenges in theoretical chemistry.

In response to this challenge, we focus on the following ideas:

(i) Quantum trajectory methods – Based on the hydrodynamic formulation of quantum mechanics (i.e. de Broglie-Bohm mechanics), one can recast the quantum dynamics with quantum trajectories. These trajectories are just like classical trajectories except that they are coupled with each other through the so-called quantum potential.

(ii) Adaptive basis functions – The problem of representing a high-dimensional nuclear wavefunction with a static basis is that as the nuclear wavepacket undergoes a large amplitude motion, the number of required static basis functions has to increase very quickly. In order to alleviate this problem, one can instead use adaptive basis functions. For example, moving Gaussian wave packets. These Gaussian wave packets can move like classical trajectories, and provide a convenient basis to approximate the time-dependent wavefunction. Consider that one only needs a *single* Gaussian basis to describe the motion of a coherence state in a harmonic potential.