Several Quantum Phenomena In Ultracold Atoms

We studied several quantum phenomena in Cold Atoms in this thesis. These include itinerant ferromagnetism in Fermi gases, two-dimensional BKT transition in a synthetic magnetic field, radio frequency spectrum in a narrow Feshbach resonance, and topological effects in ultracold Fermi gases.First, we suggest to use a double-well trap to observe the itinerant ferromagnetic transition. Comparing with previous experiments with a single trap, our proposal can produce more stable domain structures and is easier to observe. The transition happens when each component occupies in each well. Our calculation shows that this transition agrees with the Stoner model.Next, we consider the two-dimensional BKT transition in a synthetic magnetic field. We map our system to a frustrated XY model and calculate the transition temperature using Metropolis Monte Carlo method. Our results show a complicated relationship between the critical temperature and the magnetic field.Then, we solve the problem of radio frequency spectrum in a narrow Feshbach resonance. We give qualitative behavior of the spectrum by sum rules and the give more rigorous results by summing infinite terms. Our results can explain the experiment results by O’Hara’s group in Penn State.At last, we propose a tuning experiment in6Li to observe the anticipated topological edge modes. We suggest to use the lowest four hyperfine states in this system. Our proposal solves the heating problem in current experiments.