Few/Many-body physics

A Tunable Atomic and Molecular Quantum Gas in Optical Lattices


Optical lattices, constructed by the interference pattern of laser beams, provide a periodic potential for ultracold particles. Cold atoms/molecules in optical lattices can therefore simulate electrons in condensed matter systems. Novel features of the optical lattices include

  • The lattice configuration is adjustable.
  • The atomic(molecular) interaction is tunable.
  • The lattice site occupacy number can be much higher or lower than one.
  • Atoms and molecules have richer internal structures than electrons.

Full Proposal 

Formation and condensation of composite bosons by pairing fermionic atoms open the door to the exploration of superfluidity in different regimes. In the strong-coupling limit, atoms form short ranged molecules, which undergo Bose-Einstein condensation (BEC) at low temperatures. In the weak-coupling regime, Cooper-pairing of atoms occurs in the Bardeen-Cooper-Schrieffer (BCS) state. In the crossover regime, the two types of superfluid smoothly connect to a “resonance superfluid”, for which a universal behaviour is predicted.

I propose to study ultracold atomic and molecular gases in an optical lattice potential, which can simulates general condensed matter systems and introduces novel quantum phases with long range correlation. For an interacting Fermi gas in a weak optical lattice potential, a d-wave pairing phase and an anti-ferromagnetic phase are expected to exist [1], which could provide new perspectives to high-Tc superconductivity. In a strong confining lattice with a few atoms or molecules localized in each lattice site, reactive scattering processes at ultralow temperatures can be realized with a full control over the internal and external degrees of freedom.

There are three primary goals of this work:  

  1. Superfluid-Mott insulator quantum phase transition in the BEC-BCS crossover regime For a Bose-Einstein condensate, the quantum phase transition occurs when it is loaded into optical lattices with strong confining force. When the coupling between neighbouring sites is sufficiently weak, the system can form a Mott insulator. In the BEC-BCS crossover regime where atoms and molecules form a strongly interacting quantum gas, I will investigate the breakdown of the fermionic superfluidity in the optical lattices and the spatial correlation and the matter-wave coherence of the atoms and molecules.
  2. D-wave pairing of atoms and spin-correlated state in a 2D optical lattice Based on an interacting Fermi gas in different optical lattice configurations, new quantum phases are predicted with novel properties. In particular, I will look into the D-wave pairing and the anti-ferromagnetic order of atoms, which are predicted at an appropriate range of the mean occupancy number and the binary interaction strength. These parameters can be externally controlled by tuning the lasers which form the lattice potential and the magnetic field which tunes the interaction strength.
  3. Controlled chemical reactions and Bose-Einstein condensation of complex molecules In a Mott insulator phase described in 1, a few particles are pinned into the lowest states of every lattice site. This system provides a key step to a full internal and external control of the few-body reactive processes. Furthermore, by adiabatically removing the lattice potential, the system will recover its superfluidity. This conversion opens up fascinating possibilities to explore the many-body effects on the atom-molecule system.

One example would be the formation of atomic trimers or quadrumers by pairing the dimers and/or the atoms in optical lattices. Possible schemes to induce the pairing will be investigated. By lowering the lattice potential, the bosonic quadrumers can possibly undergo Bose-Einstein condensation and the fermionic trimers can possibly be Cooper paired at low temperatures. The realization of the above pairing processes will provide a common testing ground for the studies of chemical physics, few-body physics and condensed matter physics.


[1] W.H. Hofstetter, J.I. Cirac, P.Zoller, E. Demler and M.D. Lukin, Phys. Rev. Lett. 89, 220407 (2002)

Related: cesium experiment.