1. Atomic spin entanglement in optical lattices

Based on our former experiment of generating a large amount of entangled atom pairs, we will optimize the temperature of the atoms, and connect the entangled pairs to form multipartite entangled state, further study its application in quantum information processing

2. Quantum simulation and low-dimension physics with optical lattices

Lattice structure of a defined geometry can be engineered with a diffraction-limited objective and a spatial light modulator. We can then study the physics of quantum fluctuations, topological quantum states, quantum magnetism in square lattices, triangular lattices, and Kagome lattices etc. Low-dimensional systems of 1D or 2D will be created and the quantum criticality will be studied.

3. Quantum simulation of the physics around the critical point.

Around the critical point of the phase transition between superfluid-to-Mott insulator, the correlation length gets divergent. It is very hard to describe the system by numerical simulation with classical computers. New physical phenomena emerge rather than predicted per the atomic theory based on reductionism. Well, quantum simulator built by the quantum system itself will answer the questions when one measures relevant observables of the quantum system.

## Related Publications

- Four-body ring-exchange interactions and anyonic statistics within a minimal toric-code Hamiltonian. Nature Physics 13, 1195-1200 (2017).
- Geometrical characterization of reduced density matrices reveals quantum phase transitions in many-body systems. Science China Physics, Mechanics \& Astronomy 60, 060331 (2017).
- Quantum criticality and the Tomonaga-Luttinger liquid in one-dimensional Bose gases. Physical Review Letters 119, 165701 (2017).
- Spin-dependent optical superlattice. Physical Review A 96, 011602 (2017).
- Generation and detection of atomic spin entanglement in optical lattices. Nature Physics 12, 783-787 (2016).