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Physical Review A

Dipole-dipole interaction in three-dimensional optical lattices

Elena V. Goldstein, Paul H. Pax, Pierre Meystre

Published Apr 1, 1996• 32 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.53.2604

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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 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 study the coupling of resonant electronic excitations to vibrational center-of-mass motion of ultracold atoms in an optical lattice, when ground- and excited-state optical potentials differ. On-site excitation-vibration coupling can be approximately treated by renormalizing the effective transition energy, which appears, e.g., in lattice clock setups. In addition the dipole-dipole coupling between neighboring sites mediates emission and absorption of vibrational quanta in conjunction with optical transitions. This mechanism for excitation of vibrations can lead to significant heating of the lattice atoms motion during resonant light interaction. We calculate estimates of the corresponding parameters for a gas in the Mott-insulator state from a perturbation expansion in small atomic displacements.
We study the near-resonant dipole-dipole interaction between two atoms in a broadband squeezed vacuum. We show that this ``vacuum'' modifies the rate of spontaneous emission of the atoms so that it may depend not merely on their relative position, as is normally the case, but also on their center-of-mass position. The explicit form of this latter dependence is a function of the way squeezing is achieved. We also show that in contrast to the spontaneous decay rate, squeezed vacua do not modify the dipole-dipole potential between the atoms as compared to its usual form. Finally, we develop a Monte Carlo wave-function description of the interaction between atoms with an arbitrary internal structure and a squeezed vacuum and apply this formalism to the case of off-resonant excitation of the atoms. We find that in addition to the usual light shift, the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground states. \textcopyright{} 1996 The American Physical Society.
At the most fundamental level of quantum electrodynamics, there is no such thing as two-body interactions between atoms. The potentials that describe these interactions are effective potentials resulting from a series of approximations whose validity depends on the precise situation at hand. Considering a one-dimensional geometry for simplicity, we discuss under which conditions the familiar form of the near-resonant dipole-dipole interaction is valid, paying particular attention to the effects of interatomic propagation of light, and to what extent it can be modified in the tailored electromagnetic environments provided by optical resonators. We find that once the atoms have established that they are inside a resonator, the dipole-dipole potential may or may not remain a useful concept, depending upon the strength of the atom-field interaction. In the weak-coupling regime, one finds a two-body dipole-dipole interaction that can be enhanced or inhibited by varying the atom-field detuning. In the strong-coupling regime, by contrast, the two-body dipole-dipole potential ceases to be meaningful.
In condensed matter of densities such that there are many atoms within a cubic atomic resonance wavelength, induced near dipole-dipole interactions (NDD) effects can cause dynamic frequency chirp in near resonant electromagnetic field-matter interactions.1 Using semiclassical theory for two-level atomic systems and a Green's function solution to the wave equation, we derive a self-consistent set of renormalized Bloch–Maxwell equations, useful for discussion of nonlinear optical processes in condensed matter systems, and discuss some of their implications. The strength of the induced near dipole-dipole coupling is found to be ε = (4π/3) u2n, and it causes inversion-dependent frequency chirp in the system. Here, u is the matrix element of the transition dipole moment and n is the density of atoms.
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.