We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross-Pitaevskii equationwith the Kronig-Penney potential (KPP) of period d,which governs a repulsive Bose-Einstein condensate.Under thezero a...We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross-Pitaevskii equationwith the Kronig-Penney potential (KPP) of period d,which governs a repulsive Bose-Einstein condensate.Under thezero and periodic boundary conditions,we show how to determine n exact stationary eigenstates {R_n} correspondingto different chemical potentials {μ_n} from the known solutions of the system.The n-th eigenstate R_n is the Jacobianelliptic function with period 2d/n for n=1,2,…,and with zero points containing the potential barrier positions.So R_nis differentiable at any spatial point and R_n^2 describes n complete wave-packets in each period of the KPP.It is revealedthat one can use a laser pulse modeled by a δ potential at site x_i to manipulate the transitions from the states of {R_n}with zero point x ≠x_i to the states of {R_n′} with zero point x=x_i.The results suggest an experimental scheme forapplying BEC to test the BVP and to observe the macroscopic quantum transitions.展开更多
基金The project supported by the National Natural Science Foundation of China under Grant Nos.10575034 and 10875039
文摘We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross-Pitaevskii equationwith the Kronig-Penney potential (KPP) of period d,which governs a repulsive Bose-Einstein condensate.Under thezero and periodic boundary conditions,we show how to determine n exact stationary eigenstates {R_n} correspondingto different chemical potentials {μ_n} from the known solutions of the system.The n-th eigenstate R_n is the Jacobianelliptic function with period 2d/n for n=1,2,…,and with zero points containing the potential barrier positions.So R_nis differentiable at any spatial point and R_n^2 describes n complete wave-packets in each period of the KPP.It is revealedthat one can use a laser pulse modeled by a δ potential at site x_i to manipulate the transitions from the states of {R_n}with zero point x ≠x_i to the states of {R_n′} with zero point x=x_i.The results suggest an experimental scheme forapplying BEC to test the BVP and to observe the macroscopic quantum transitions.
