In this letter, we have studied quantum tunneling of two-species cold bosonic atoms in an optical lattices. When the optical lattice is not infinitely long and the spin excitations are not in the long-wavelength limit, quantum tunnelings are presented.
In this letter, the superfluid-Mott-insulator phase transition of two-species cold bosonic atoms in an optical lattices is studied. The Hamiltonian of this model is diagonalized by means of Bogliubov transformations and by the inversion symmetry of the optical lattice, the energy spectrum of this system is obtained. From the energy gap of the excitation spectrum, the quantum phase transition condition is obtained and it is determined by the competition between the interatomic repulsions and the tunnel coupling. It is found that there exists an ordinary fluid phase when taking the zero wave-vector limit.
We study quantum tunneling of a dipolar Bose-Einstein condensate in optical lattice when the spin system initially is prepared in a squeezed coherent state. It is found that there exists quantum tunneling between lattices l and l + 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, quantum tunneling disappears between lattices l and l + 1, and that l and l - 1. Correspondingly, the magnetic soliton appears.
In this letter, we have studied the tunneling effects and fluctuations of spinor Bose–Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l + 1, l and l − 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices l and l + 1, and l and l − 1. In this case the fluctuations are a constant, and the magnetic soliton appears.
Quantum tunneling is a quantum phenomenon in which a microscopic object crosses through a potential barrier even if its energy cannot overcome the barrier. A general belief is that tunneling occurs only when the barrier width is comparable to, or smaller than the de Broglie’s wavelength of the object. Here, we study the tunneling of an ultracold atom among N far-separated trapping potentials in a state-selective optical lattice and present a mechanism to realize long-range tunneling. We find that, mediated by the propagating matter wave emitted from the atom, coherent tunneling of the atom to the remote lattices occurs as long as bound states are present in the energy spectrum of the system formed by the atom and its matter-wave. Going beyond the Markovian approximation, and breaking through the conventional distance constraint, our result opens another avenue to realizing tunneling and gives a guideline for developing tunneling devices. It is generally believed that quantum tunneling cannot occur when the distance is larger than the particle’s wavelength. This paper reveals that a long-range quantum tunneling of the atom to the remote trapping potentials mediated by its emitted matter wave occurs as long as bound states are present in the energy spectrum of the total system formed by the atom and its matter-wave.