# Transfer of orbital angular momentum superposition from asymmetric Laguerre-Gaussian beam to Bose-Einstein Condensate

## TL;DR

This paper develops a theory for transferring orbital angular momentum from an asymmetric Laguerre-Gaussian beam to a Bose-Einstein condensate, resulting in superposed vortex states with enhanced quadrupole Rabi frequencies.

## Contribution

It introduces a novel asymmetric LG beam model and demonstrates how multiple quantized circulations are transferred to BEC, creating superpositions of vortex states with unique coherence properties.

## Key findings

- Multiple quantized circulations are transferred to BEC.
- Enhanced quadrupole Rabi frequency for higher vorticity states.
- Distinct superposition features and coherence variations observed.

## Abstract

In this paper, we have formulated a theory for the microscopic interaction of the asymmetric Laguerre-Gaussian (aLG) beam with the atomic Bose-Einstein condensate (BEC) in a harmonic trap. Here the asymmetry is introduced to an LG beam considering a complex-valued shift in the Cartesian plane keeping the axis of the beam and its vortex states co-axial to the trap axis of the BEC. Due to the inclusion of the asymmetric nature, multiple quantized circulations are generated in the beam. We show how these quantized circulations are transferred to the BEC resulting in a superposition of matter vortex states. The calculated Rabi frequencies for the dipole as well as quadrupole transitions during the transfer process show distinct variability with the shift parameters of the beam. A significant enhancement of the quadrupole Rabi frequency for higher vorticity states is observed compared to symmetric single orbital angular momentum (OAM) mode beam at a particular range of the shift parameters. We also demonstrate the variation of superposition of matter vortex states and observe its distinct feature compared to the superposition of the LG modes for different shift parameters. The first order spatial correlation of the superposed states supports this feature and highlights asymmetry in degree of transverse coherence along orthogonal directions on the surface.