Quantum simulations with ultracold quantum gases
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This thesis explores Feynman’s idea of quantum simulations by using ultracold quantum gases. In the first part of the thesis we develop a general method applicable to atoms or molecules or even nanoparticles, to decelerate a hot fast gas beam to zero velocity by using an optical cavity. This deceleration method is based on a novel phase stability mechanism in the bad cavity regime, which is very different from the traditional cavity cooling studies where a good cavity is needed. We propose several schemes to decelerate the gas beam based on this new phase stability mechanism. Practical issues for realizing the proposals are also discussed in detail which show that the deceleration schemes are feasible using present experimental techniques. In the second part of this thesis, we show how the concept of quantum simulations is applied to multiple-layered Dirac cones and related phenomena by using multi-component ultracold fermionic atoms in optical lattices where the spin-dependent hopping and on-site spin flipping are both controlled by Raman lasers. By tuning the spin-dependent hopping according to the representations of su(2) algebra, we show that we can simulate the Dirac-Weyl fermions with any arbitrary spin beyond the spin ½ cases found in graphene and topological insulators. These high spin Dirac-Weyl fermions show rich anomalous quantum Hall effects and a remarkable Klein multi-refringent tunnelling. Moreover, when getting rid of the limitations of su(2) algebra and allowing for on-site spin flipping, we further investigate Modified Dispersion Relations (MDRs) and Neutrino Oscillations (NOs) as in Standard Model Extensions (SMEs) by virtue of an analogue between the three-family fermions in particle physics and a three-layered Dirac cones scheme. This thesis shows the important role ultracold quantum gases play in quantum simulations to address some of the most challenging topics in modern physics.