We demonstrate that a tight transverse trap with the local frequency, ??, gradually varying in the longitudinal direction (x) induces an effective potential for one-dimensional solitons in a self-attractive Bose-Einstein condensate. An analytical approximation for this potential is derived by means of a variational method. In the lowest approximation, the potential is N(S+1)??(x), with N the soliton's norm (number of atoms), and S its intrinsic vorticity (if any). The results can be used to devise nonuniform traps helping to control the longitudinal dynamics of the solitons. Numerical verification of the analytical predictions will be presented elsewhere.
An effective potential for one-dimensional matter-wavesolitons in an axially inhomogeneous trap
De Nicola S;
2006
Abstract
We demonstrate that a tight transverse trap with the local frequency, ??, gradually varying in the longitudinal direction (x) induces an effective potential for one-dimensional solitons in a self-attractive Bose-Einstein condensate. An analytical approximation for this potential is derived by means of a variational method. In the lowest approximation, the potential is N(S+1)??(x), with N the soliton's norm (number of atoms), and S its intrinsic vorticity (if any). The results can be used to devise nonuniform traps helping to control the longitudinal dynamics of the solitons. Numerical verification of the analytical predictions will be presented elsewhere.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
