Method for collective excitation of a Bose-Einstein condensate

Spectacular experimental realizations of the BoseEinstein condensate ~BEC! in cooled and trapped atomic gases @1–3# stimulated intensive investigations of possible modifications, control, and manipulations of this new state of matter. Here a macroscopic sample of atoms is in a well defined quantum state. Thus several typically quantummechanical phenomena may now be investigated on a macroscopic level. As an example of manipulation of the condensate, one may consider the splitting of the condensate into two parts @4#, well separated in space and yet coherent with each other. The latter property may be tested by superimposing, at some later time, the two parts and an observation of the interference fringes @4–6#. Another example is the leakage of atoms from the condensate that may be used to prepare an ‘‘atom laser’’ @7,8#. Other fascinating possibilities are revealed when one considers possible collective excitations of the condensate. Several schemes have been proposed to create either solitary waves or vortices in the condensate. Both these types of excitations are the solutions of the time-dependent GrossPitayevsky equation ~GPE! as appropriate for the mean-field, effective single-particle description of the gas of weakly interacting bosons in the limit of vanishing temperature ~for reviews see @9,10#!. In analogy to nonlinear optics @11#, one may consider bright solitons ~bell shaped structures propagating without dispersion!, dark solitons ~with a node in the middle—an analog of the first excited state in the noninteracting particles picture!, or the intermediate gray solitons. The early propositions for creation of solitions in the BEC utilized collisions between spacially separated condensates @12,13#. Soon it was realized that less violent approaches are also possible. Typical for atomic laser control—resonant Raman excitation scheme—the excitation of vortex states has been proposed @14#. This approach relies on the resonance condition, which is, however, modified during the transfer process due to the nonlinearity of the GPE. Another possibility that takes the nonlinearity fully into account is the adiabatic scheme of Ref. @15#. It effectively utilizes internal atomic transitions combined with appropriate states of the condensate for a controlled laser induced adiabatic transfer, populating solitonic or vortex solutions of GPE, depending on the details of the process. The latter approach seems more robust against typical experimental uncertainties. A yet different approach produces a phase shift between two parts of the condensate—such a phase imprinting method, originally