Co-propagating Bose–Einstein condensates and electromagnetic radiation: formation of mutually localized structures

Abstract

A semi-classical model is derived for describing the interaction between coherent electromagnetic radiation and a Bose-Einstein condensate in the limit of zero temperature, including the back action of the atoms on the radiation. This model is used to analyse the problem of the self-consistent evolution of a laser beam and a BEC atomic beam. The mutual propagation is studied numerically and demonstrates not only the possibility of a stationary regime of mutual guiding, but also of generating a collapse-like phenomenon.

Co-propagating Bose-Einstein condensates and electromagnetic radiation: Emission of mutually localized structures

“…As demonstrated in [7], in the case of red detuning, the system settles down asymptotically to a stationary state with mutually localized atom-laser structures: Starting from a gaussian atom density profile and a super-gaussian laser intensity one, the interaction leads to the formation of two bell-shaped structures which propagate unchanged thereon. This means that atoms and radiation in excess will be shed away, which is the process we would like to elucidate here.…”

“…Details of the semi-classical derivation of both the atom and the laser equations are given in [7,9], here we will only briefly review the two model equations and re-introduce the notation. In a semi-classical derivation, the force exerted by the light on the atoms is written as the gradient of a potential and this potential is used as the atom-laser interaction term in the Hamiltonian for the atoms Schrödinger equation.…”

“…Maxwell's equations for the propagation of radiation in a medium, [7,13,14], yield a wave equation which, under the assumption of L n ≫ λ L or ∇ǫ · E ≃ 0 (L n is the characteristic length scale of transverse density modulations and λ L is the radiation wavelength), gives the three scalar equations (ω L = k L c)…”

“…This last work showed the emergence of a resonant nonlinear term in the system dynamics as a consequence of the laser-atom dipole-dipole interaction, besides the well known Kerrlike nonlinearity. The same equation for the atoms and consequently a coupled system of equations for the laseratom system were rederived in [7], this time starting from a semi-classical theory. It was found there that the response of the "medium", that is of the laser radiation, to the dynamics of the condensate could play an important role in the coupled evolution and even allow for the formation of mutually localizd atom-laser structures capable of propagating with no changes in the atom density and laser intensity, in spite of the assumed repulsive atom-atom interaction.…”

“…Such solitary-like structures are of interest bacause of their properties of self-localization and robust propagation and the effects of these interactions can be seen also in relation to the creation of metalenses and comoving potentials to refocus atom waves, [8]. Their emerging as a result of the coupling during propagation of atoms and laser was studied in [7] while the stationary states of the coupled system and their stability properties were introduced in [9]. However, little is known about their actual mechanism of formation.…”