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Revista Colombiana de Física

Interacción dipolo-dipolo en redes ópticas

Ángela M. Guzmán, Pierre Meystre

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

Ultracold atoms trapped in optical lattices interact through the dipole -dipole interaction potential that takes place through the photon exchange of the electromagnetic vacuum field. In this paper we propose a method based on Floquet’s theory to determine matrix elements of the dipole -dipole interaction in 3D optical lattices. Numerical calculations are displayed for the case of 1D optical lattices. Bragg dispersion occurs for elastic scattering when the momentum transfer between the interacting atoms in the lattice is a primitive reciprocal lattice vector. The higher dipole -dipole interaction matrix elements correspond to elastic scattering without spin flip and to case when the Bragg condition is satisfied.

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Ultracold atoms trapped in optical lattices interact through the dipole -dipole interaction potential that takes place through the photon exchange of the electromagnetic vacuum field. In this paper we propose a method based on Floquet’s theory to determine matrix elements of the dipole -dipole interaction in 3D optical lattices. Numerical calculations are displayed for the case of 1D optical lattices. Bragg dispersion occurs for elastic scattering when the momentum transfer between the interacting atoms in the lattice is a primitive reciprocal lattice vector. The higher dipole -dipole interaction matrix elements correspond to elastic scattering without spin flip and to case when the Bragg condition is satisfied.
We present a many-body theory of the dipole-dipole interaction in three-dimensional optical lattices generated by a four-beam configuration, specializing to the case of ${J}_{g}=\frac{1}{2}\ensuremath{\rightarrow}{J}_{e}=$32\frac{3}{2}23​ transitions. We construct a many-body interaction Hamiltonian in coordinate representation for an antiferromagnetic fcc optical lattice, the Schr\"odinger field operators being expanded on a basis of Wannier functions. We discuss the main characteristics of the dipole-dipole matrix elements giving rise to bound-bound and bound-free atom interactions in the lattice. Because of the anisotropy of the dipole-dipole interaction, specific directions can be favored for transport and scattering processes. Furthermore, since the dipole-dipole interaction depends on atomic magnetic quantum numbers, the dipole-dipole potential resembles a spin-dependent potential, and can give rise to atomic hopping with simultaneous change in the magnetic quantum number.
We compute the near-resonant dipole-dipole interaction between atoms in a three-dimensional optical lattice. After a general derivation, we concentrate specifically on the case of a J=1/2\ensuremath{\rightarrow}J=3/2 off-resonant transition, in which case the excited electronic states can be adiabatically eliminated. We present in detail the spatial dependence of the resulting effective dipole-dipole potential, and discuss the physical origin of its anisotropy. In addition to impacting the center-of-mass motion of the atoms, the effective dipole-dipole potential can induce electronic transitions within one or both atoms. The symmetries of the matrix elements corresponding to these various mechanisms are also commented upon. \textcopyright{} 1996 The American Physical Society.
We use a coherent Bragg diffraction method to impart an external momentum to ultracold bosonic atoms trapped in a one-dimensional optical lattice. This method is based on the application of a single light pulse, with conditions where scattering of photons can be resonantly amplified by atomic density grating. An oscillatory behavior of the momentum distribution resulting from the time evolution in the lattice potential is then observed. By measuring the oscillating frequencies, we extract multiband energy structures of single-particle excitations with zero pseudomomentum transfer for a wide range of lattice depths. The excitation energy structures reveal the interaction effect through the whole range of lattice depths.
We study Bragg scattering at one-dimensional (1D) optical lattices. Cold atoms are confined by the optical dipole force at the antinodes of a standing wave generated inside a laser-driven high-finesse cavity. The atoms arrange themselves into a chain of pancake-shaped layers located at the antinodes of the standing wave. Laser light incident on this chain is partially Bragg reflected. We observe an angular dependence of this Bragg reflection which is different from what is known from crystalline solids. In solids, the scattering layers can be taken to be infinitely spread (three-dimensional limit). This is not generally true for an optical lattice consistent of a 1D linear chain of pointlike scattering sites. By an explicit structure factor calculation, we derive a generalized Bragg condition, which is valid in the intermediate regime. This enables us to determine the aspect ratio of the atomic lattice from the angular dependance of the Bragg scattered light.
We investigate theoretically light scattering of photons by ultracold atoms in an optical lattice in the linear regime. A full quantum theory for the atom-photon interactions is developed as a function of the atomic state in the lattice along the Mott-insulator--superfluid phase transition, and the photonic-scattering cross section is evaluated as a function of the energy and of the direction of emission. The predictions of this theory are compared with the theoretical results of a recent work on Bragg scattering in time-of-flight measurements [A.M. Rey et al., Phys. Rev. A 72, 023407 (2005)]. We show that, when performing Bragg spectroscopy with light scattering, the photon recoil gives rise to an additional atomic site-to-site hopping, which can interfere with ordinary tunneling of matter waves and can significantly affect the photonic-scattering cross section.