## Research Interests

**Ongoing NRF Investigatorship Award research project (2017-2022): **

Quantum Control Approach to New Topological Phases of Matter

**Ongoing MOE-funded (Tier-I) research project (2015-2018):**

Floquet Topological Phases of Matter: Generation, Detection, and Application

**Ongoing MOE-funded (Tier-II) research projects (2015-2018): **

Realization, Optimization, and Control of Nano Heat Engines

**Long-term research interest I: Theoretical aspects of quantum chaos and their connections with experiments of cold-atoms in pulsed optical lattices **

One central interest of my research programme is in quantum effects in classically chaotic systems. Theoretically this involves a number of important issues such as quantum-classical correspondence in chaotic systems and the foundations of quantum and classical statistical mechanics. A particular class of model dynamical systems along this avenue is low-dimensional periodically driven quantum systems, which can be realized by cold-atoms in pulsed optical lattice potentials. Such type of experiments were studied, or still being studied, by many cold-atom laboratories worldwide. Experimental tools have also advanced, from using thermal cold atoms to using a Bose-Einstein condensate that has large coherence length. Encouraged by the progress in cold-atom experiments, over the years we have been persistently exploring novel quantum features in classically chaotic systems.

In particular, back in the year of 2008 we put forward a theoretical proposal to realize a quantum driven system with Hofstadter's butterfly Floquet spectrum, which also successfully exposed the direct connection between two important paradigms of quantum and classical chaos. Ever since we have invested our theoretical studies heavily on such driven systems with Hofstadter's butterfly Floquet spectrum, an endeavor that also echoes strongly with current vast experimental interests in synthesizing and observing Hofstadter's butterfly spectrum in time-independent cold-atom or solid-state systems. Our recent discoveries include the possibility of long-last exponential spreading in quantum dynamics, the quantized acceleration due to Floquet band topology, and the topological equivalence between two quantum chaos models.

**Long-term research interest II: Coherent control of quantum dynamics in open or closed systems **

On the most fundamental level quantum mechanics is still not well understood. Yet there is no doubt that quantum mechanics will only be more useful if we continue to enlighten how we can actively control the dynamics of quantum systems. The direction of coherent control of quantum dynamics advocates the use of quantum coherence to manipulate quantum systems for good and to even generate new frontiers for other fields of research. Specific applications of coherent control include a better understanding of the quantum mechanical nature of light and matter, the development of novel spectroscopy and metrology tools, as well as quantum information processing that relies upon our ability to steer the quantum evolution of a quantum computer. For example, the control of quantum state transfer, entanglement propagation, and quantum signal amplification in spin chain systems (which we have been working on) would be relevant to solid-state based quantum information processing.

Along this second research direction we have two long-term questions. The first is on the fundamental aspects of quantum open systems. In reality a quantum system under control is always in the presence of an environment. Hence it is important to understand environment-induced decoherence. Even more importantly, how to protect a quantum state or a quantum process from environment-induced decoherence effects, considering the fact that in many cases we do not even know beforehand in what form and capacity a quantum system of interest is interacting with its environment? The second question is to understand the quantum-classical correspondence in the coherent control context. That is, to what extent a particular coherent control scheme relies on subtle quantum coherence effects, and if there is a classical analog in the classical dynamics, then how to better understand and exploit such type of quantum control? One recent contribution we made is the finding of a classical analog to the so-called shortcuts to quantum adiabatic control.

** Long-term research interest III: Quantum simulation with controlled quantum systems **

By designing a desired interaction between a quantum system of interest and some tailored external control fields, it is now possible to use such quantum systems under control to simulate, and directly examine, a variety of important problems from many different contexts, including condensed-matter physics, chemical physics, quantum physics, chaos theory, and even field theory. For example, an NMR system under a carefully tailored control field may be used to simulate the whole process of a chemical reaction with a high fidelity. Cold atoms in optical lattices can be used to simulate fundamental many-body problems involving electrons, and cold atoms in a rotating frame can simulate the vortex dynamics in superconductors subject to a strong magnetic field. Cold atoms with particular internal level structure can be even used to simulate fundamental issues in spintronics and in the emerging field of topological insulators.

Along this direction, earlier my group considered ultracold systems to study directed transport in dissipationless systems, to simulate quantum dynamics in the presence of Abelian and non-Abelian gauge fields, and to simulate many-body systems with long-range interactions using the dynamics of dipolar Bose-Einstein condensates. In more recent years we are fascinated by the possibility to use periodically driven systems to explore and simulate the physics behind (and beyond) the Quantum Hall Effect and to create new topological states of matter. This is particularly exciting because on one hand Hofstadter's butterfly spectrum is a paradigmatic object in the studies of the Integer Quantum Hall Effect and on the other hand the dynamical systems we have been studying do have Hofstadter's butterfly (Floquet) spectrum (with unusually large band Chern numbers).