Quantum tunneling of ultracold atoms in optical traps

We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.