Local-field approach to the interaction of an ultracold dense Bose gas with a light field

Abstract

The propagation of the electromagnetic field of a laser through a dense Bose gas is examined and nonlinear operator equations for the motion of the center of mass of the atoms are derived. The goal is to present a self-consistent set of coupled Maxwell-Bloch equations for atomic and electromagnetic fields generalized to include the atomic center-of-mass motion. Two effects are considered: The ultracold gas forms a medium for the Maxwell field which modifies its propagation properties. Combined herewith is the influence of the dipole-dipole interaction between atoms which leads to a density dependent shift of the atomic transition frequency. It is expressed in a position dependent detuning and is the reason for the nonlinearity. This results in a direct and physically transparent way from the quantum field theoretical version of the local-field approach to electrodynamics in quantum media. The equations for the matter fields are general. Previously published nonlinear equations are obtained as limiting cases. As an atom optical application the scattering of a dense beam of a Bose gas is studied in the Raman-Nath regime. The main conclusion is that for increasing density of the gas the dipole-dipole interaction suppresses or enhances the scattering depending on the sign of the detuning.

Electromagnetically induced left-handedness in a dense gas of three-level atoms

“…Multiple scattering of photons as well as higher order many body correlations may contribute in addition to the local field correction. Such effects are argued to be about the same order with the local field correction [21,22,23,24,25,26,27]. It is an intriguing possibility that the present result of induced left-handedness could improve and benefit from contributions arising from the quantum correlations in a dense Bose-Einstein condensate or in a dense degenerate Fermi gas.…”

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

“…Furthermore, since we are interested in the stationary behaviour of the system and we have already assumed a stationary form for the electromagnetic field, we will consider Ψ(r, t) = Φ(r) exp(−iω a t). The atom equation was already derived in [6] within a fully quantum model and it is important to underline that, once the limitations of the semi-classical reasoning are taken into account, the two derivations lead to the same equation.…”

“…The time averaged force (over laser cycles) is F = 1 16π ∇ |E| 2 ∂ǫ ∂n = −∇V d . Here ǫ(ω, n) is the medium dielectric constant with atom density n and is given by ǫ(ω, n) = 1 + 4παn 1− 4π 3 αn , where, as derived from quantum theory, α(ω) = −d 2 /h∆ is the atomic polarizability at the laser frequency ω L , with ∆ = ω L − ω a being the detuning from the nearest atomic resonance frequency ω a , and d is the dipole matrix element of the resonant transition, [6,13]. The relative semplicity of the semi-classical derivation comes at the price of restricting the validity of the model to a well defined range of parameters: The concept of force is purely classical, therefore quantum fluctuations, stochastic heating and any incoherent process are to be neglected.…”

“…This corresponds exactly to the optics case where the medium through which radiation propagates can bring about nonlinear effects for the electromagnetic field: Nonlinear effects in the dynamical evolution of the atoms and of the radiation are then a consequence of the atom-light interactions. Models of this interaction were presented by several authors, [2,5] and Krutitsky et al, [6], gave a full derivation of the equa- * f.cattani1@physics.ox.ac.uk tions describing it starting from first principles within the framework of quantum field theory. 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.…”

Slow light propagation in trapped atomic quantum gases

“…It is then possible to recognize that E D is given by [ P t ], the retarded transverse polarization field [15,17]. We obtain…”