Recently, many laboratories around the world are using cold atoms in optical lattices to emulate theoretical models for strongly correlated systems in condensed matter physics. There are great challenges for those efforts to succeed. The first challenge is that the required temperatures for studying strongly correlated physics in optical lattices are much lower than what can be achieved in laboratories nowadays. Another one is that, it requires novel schemes to probe thermodynamic properties and macroscopic quantum phenomena of the trapped atoms. This thesis will present theoretical proposals on how to overcome those challenges.
In the first part of this thesis, I will discuss new cooling schemes for trapped atoms in optical lattice so as to construct successful optical lattice emulators. For the bosonic atoms, opening up the confining potential adiabatically can reverse the heating efforts in current experiments, and allow experiments to achieve strongly correlated bosons in optical lattices. For the fermionic atoms, two alternative schemes can be used to decrease the entropy of the systems to a few percent of lowest value obtainable today. Those schemes will allow experimentalist to achieve antiferromagetism or other strongly correlated systems of fermions in optical lattices at the lowest temperature ever in laboratories.
In the second part of this thesis, I will propose new probing schemes to fulfill the goal of optical lattice emulators. I will first explain why a method often used in experiments in the past a few years to probe superfluid from the sharpness of the interference pattern is incorrect. I will show that the normal state in optical lattice can also have a sharp interference pattern. I will then discuss schemes to map out the phase diagrams of quantum models, as well as many important thermodynamic quantities, such as the superfluid density and the entropy density, that have so far eluded experimental measurements.