We consider the nonlinear scattering and transmission of an atom laser or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several physical features beyond the well-known picture from single-particle quantum mechanics. We find numerical evidence for a denumerably infinite string of bifurcations in the transmission resonances as a function of nonlinearity and chemical potential, when the potential barrier is wide compared to the wavelength of oscillations in the condensate. Near the bifurcations, we observe extended regions of near-perfect resonance, in which the barrier is effectively invisible to the BEC. Unlike in the linear case, it is mainly the barrier width, not the height, that controls the transmission behavior. We show that the potential barrier can be used to create and localize a dark soliton or dark-soliton train from a phononlike standing wave.We consider the nonlinear scattering and transmission of an atom laser or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several physical features beyond the well-known picture from single-particle quantum mechanics. We find numerical evidence for a denumerably infinite string of bifurcations in the transmission resonances as a function of nonlinearity and chemical potential, when the potential barrier is wide compared to the wavelength of oscillations in the condensate. Near the bifurcations, we observe extended regions of near-perfect resonance, in which the barrier is effectively invisible to the BEC. Unlike in the linear case, it is mainly the barrier width, not the height, that controls the transmission behavior. We show that the potential barrier can be used to create and localize a dark soliton or dark-soliton train from a phononlike standing wave.

arXiv:1006.5519Physical Review AAug 17, 201214 citations

NONLINEAR RESONANT STATES AND SCATTERING IN A ONE-DIMENSIONAL BEC-MODEL

Andrei Ludu

Computational and Group-Theoretical Methods in Nuclear PhysicsFeb 1, 20041 citation

Nonlinear Scattering of Bose-Einstein Condensates on a Finite Barrier

Rachel Miller, Matthew S. Heller, Daniel R. Bolton +1 more

We seek stationary state solutions to the nonlinear Schrodinger equation (NLS) for piecewise-constant potentials V(x). In this case, we are able to find complete stationary solutions, i.e. exact solutions which are separable in time and space, in terms of Jacobi elliptic functions. These special functions can be defined as an inverse integral and are an interpolation between the circular and hyperbolic trigonometric functions. As an important mathematical application of our exact solutions, we will seek a nonlinear generalization of the transfer matrix. When this matrix, which is commonly used in electromagnetic transmission problems, is applied to the coefficient vector characterizing the solution in the region to the left of the first boundary, it yields the coefficient vector for any region to the right. To solve this general problem, we begin with the nontrivial case of two boundaries, which corresponds to a potential step or barrier. This has a direct physical application to an atom laser incident on such a potential, as occurs in Bose-Einstein condensates on a chip. Our work provides the first step towards formulating a completely general nonlinear scattering theory.We seek stationary state solutions to the nonlinear Schrodinger equation (NLS) for piecewise-constant potentials V(x). In this case, we are able to find complete stationary solutions, i.e. exact solutions which are separable in time and space, in terms of Jacobi elliptic functions. These special functions can be defined as an inverse integral and are an interpolation between the circular and hyperbolic trigonometric functions. As an important mathematical application of our exact solutions, we will seek a nonlinear generalization of the transfer matrix. When this matrix, which is commonly used in electromagnetic transmission problems, is applied to the coefficient vector characterizing the solution in the region to the left of the first boundary, it yields the coefficient vector for any region to the right. To solve this general problem, we begin with the nontrivial case of two boundaries, which corresponds to a potential step or barrier. This has a direct physical application to an atom laser incident on such a potential, as occurs in Bose-Einstein condensates on a chip. Our work provides the first step towards formulating a completely general nonlinear scattering theory.

Bulletin of the American Physical SocietyMar 6, 20070 citations

Scaling of the interaction in BECs at large scattering lengths

Risto Sarjonen, M. Saarela, Ferran Mazzanti

The European Physical Journal DOct 11, 20112 citations

Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth

Lincoln D. Carr, Khan W. Mahmud, William P. Reinhardt

The fundamental question of how Bose-Einstein condensates tunnel into a barrier is addressed. The cubic nonlinear Schr\"odinger equation with a finite square well potential, which models a Bose-Einstein condensate in a trap of finite depth, is solved for the complete set of localized and partially localized stationary states, which the former evolve into when the nonlinearity is increased. An immediate application of these different solution types is tunable tunneling. Magnetically tunable Feshbach resonances can change the scattering length of certain Bose-condensed atoms, such as ${}^{85}\mathrm{Rb},$ by several orders of magnitude, including the sign, and thereby also change the mean field nonlinearity term of the equation and the tunneling of the wave function. We find both linear-type localized solutions and uniquely nonlinear partially localized solutions where the tails of the wave function become nonzero at infinity when the nonlinearity increases. The tunneling of the wave function into the nonclassical regime (and thus its localization) therefore becomes an external experimentally controllable parameter.The fundamental question of how Bose-Einstein condensates tunnel into a barrier is addressed. The cubic nonlinear Schr\"odinger equation with a finite square well potential, which models a Bose-Einstein condensate in a trap of finite depth, is solved for the complete set of localized and partially localized stationary states, which the former evolve into when the nonlinearity is increased. An immediate application of these different solution types is tunable tunneling. Magnetically tunable Feshbach resonances can change the scattering length of certain Bose-condensed atoms, such as ${}^{85}\mathrm{Rb},$ by several orders of magnitude, including the sign, and thereby also change the mean field nonlinearity term of the equation and the tunneling of the wave function. We find both linear-type localized solutions and uniquely nonlinear partially localized solutions where the tails of the wave function become nonzero at infinity when the nonlinearity increases. The tunneling of the wave function into the nonclassical regime (and thus its localization) therefore becomes an external experimentally controllable parameter.

arXiv:cond-mat/0102291Physical Review AAug 6, 200143 citations

Experimental studies of BECs in optical lattices: Nonlinear effects

O. Morsch

APSMar 1, 20040 citations

{}^{85}\mathrm{Rb},

by several orders of magnitude, including the sign, and thereby also change the mean field nonlinearity term of the equation and the tunneling of the wave function. We find both linear-type localized solutions and uniquely nonlinear partially localized solutions where the tails of the wave function become nonzero at infinity when the nonlinearity increases. The tunneling of the wave function into the nonclassical regime (and thus its localization) therefore becomes an external experimentally controllable parameter.