Topological quantum phase transition and quantum magnetism simulation are the frontier researches in the field of ultracold atomic physics. Changing a certain parameter of multi-particle systems when under the absolute zero degree, such as the coupling strength, the pressure or the external magnetic field strength, the system can be continuously changed from one ordered state to another. Since the thermodynamic fluctuations are as important as the quantum fluctuations when at the critical point, this kind of phase transition is completely different from the thermodynamic phase transition induced by temperature and is called as the quantum phase transition. But when under the absolute zero degree, another kind of quantum phase transition may also exist in a quantum system. This special kind of quantum phase transition process does not exist of spontaneous symmetry breaking of Landau theory and the behavior is determined by the bulk properties of the wave function for the ground state of the system. The system is in disordered phases at both sides of the phase transition point and there is no localized order parameter to describe or distinguish the two phases. But a non-localized order parameter may exist and this kind of quantum phase transition is called as topological quantum phase transition . For example, the phase transition between the conductance quantum platform in the fractional quantum Hall effect is a typical topological quantum phase transition.However, the manipulation of the parameters of quantum phase transitions in condensed matter physics is very difficult. We can achieve this by using quantum gas in an optical lattice to study the quantum phase transition mechanism and discover novel quantum phase transitions even the implementation of novel states.
FIG.2 The principle diagram of the superexchange interaction The superexchange interaction is the basis for the formation of the quantum magnetic properties in strongly correlated electronic media. The control of the equivalent spin-spin interaction between adjacent lattice sites is also a new way of quantum magnetic simulation. This interaction results from the "virtual" jump between adjacent lattice sites: a particle jumps to adjacent sites, a same particle (or a particle in adjacent sites) jumps back to where it was originally in the lattice at the same time . For the double-spin polarized fermions, such a jump is inhibited by the Pauli exclusion principle. Therefore, two particles of opposite spin can jump and cause a reduction in the total energy of particles.
Ultracold quantum gases in optical lattices
FIG.5 Schematic diagram of one dimensional, two dimensional andthree dimensional optical lattices
FIG.6 Band structure in optical lattice
FIG.7 Hexagonal optical lattices formed by three laser beams with 120 degrees of each other
FIG.9 Quantum phase transition from superfluid to Mott insulating in a three dimensional optical lattice
FIG.10 Quantum Newton’s cradle
Summary of experimental system
FIG.11 Vacuum system
FIG.12 Rubidium 87 D2 transition hyperfine structure
FIG.13 Laser system
FIG.14 Schematic diagram of optical dipole trap
S. Sachdev, Quantum Phase Transition (Cambridge University Press, Cambridge, 1999).
A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer, Berlin, 2006).
S. Trotzky et al., Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices, Science 319, 295 (2008).
I. Bloch et al., Quantum simulations with ultracold quantum gases, Nature Phys. 8, 267 (2012).