Introduction

The interaction of atomic or molecular matter with light carrying quantized orbital angular momentum (OAM)[1], is of considerable research interest[2, 3, 4]. New tools are becoming increasingly available for creation[5, 6, 7], manipulation[8], detection[9, 10], and application[11] of the orbital angular momentum (OAM) states of light. However, there is a caveat—due to the size mismatch between the atoms and the spatial features of the phase structures in the OAM beams of light—it is difficult to couple the OAM degrees of freedom of light to the internal states of single atoms. As a result, one needs to look for macroscopic coherent objects that could interact with the OAM carrying beams of light. In this context, Bose−Einstein condensates (BEC)[12, 13, 14] come to mind for the obvious reason that they are macroscopic coherent objects that are obtained by trapping atoms in particular, internal states, and cooling them further so that all the atoms have the same motional and internal states. The excitation of vortices in BECs, that have the phase structure similar to light carrying OAM, have been traditionally achieved via stirring of the BEC cloud with a laser beam[15]. These vortex states are fairly stable and could be candidates for qubits in quantum information[16], if appropriate means to manipulate them are developed.

To recall, the OAM states of light have unique amplitude and phase structures. Monochromatic OAM beams have an azimuthal phase dependence of the type exp(ilø). Laguerre−Gaussian (LG) laser modes are an example of such OAM states[17]. The normalized LG mode at the beam waist (z = 0) and beam size w0at the waist is given in cylindrical coordinates (p,ø,z) by

w0 is the beam width, p is the number of non-axial radial nodes of the mode, and the index l, referred to as the winding number, describes the helical structure of the wave front around a phase dislocation. For further discussion, we consider only pure LG modes with charge ` and p = 0. We denote such a state of the light field by |l such that ˂r|l˃ = LGl0(p,ɸ). Thus it can be easily seen that the states |+l and |-l, with ` being a whole number, differ only in the sense of the winding of the phase either clockwise or counter-clockwise.