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Physical Review A

Dipole-dipole interaction in the near-resonant Kapitza-Dirac effect

Paul H. Pax, Georg Lenz, Pierre Meystre

Published May 1, 1995• 4 citations
Publisher

Abstract

We study the near-resonant Kapitza-Dirac diffraction of two atoms interacting via the dipole-dipole interaction within the framework of an effective one-dimensional model. We concentrate mostly on the Stern-Gerlach regime of diffraction, where the atomic wave functions are sufficiently well localized that a good physical understanding of the system dynamics in terms of local potentials can be achieved. In general, the dipole-dipole interaction can lead to substantial modifications of the Stern-Gerlach diffraction pattern. We find in particular that under appropriate conditions, bound states of the atomic system can be established, with the two atoms separated by a distance of the order of hundreds of nanometers. However, spontaneous emission eventually destroys the binding between these states via a heating mechanism somewhat similar to strong-field Sysiphus heating. In this respect, the behavior of the ``diatom'' bound state under the influence of spontaneous emission is similar to that of the atomic solitons predicted to occur in near-resonant Kapitza-Dirac diffraction in the framework of nonlinear atom optics.

DOI
10.1103/physreva.51.3972

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We study the near-resonant Kapitza-Dirac diffraction of two atoms interacting via the dipole-dipole interaction within the framework of an effective one-dimensional model. We concentrate mostly on the Stern-Gerlach regime of diffraction, where the atomic wave functions are sufficiently well localized that a good physical understanding of the system dynamics in terms of local potentials can be achieved. In general, the dipole-dipole interaction can lead to substantial modifications of the Stern-Gerlach diffraction pattern. We find in particular that under appropriate conditions, bound states of the atomic system can be established, with the two atoms separated by a distance of the order of hundreds of nanometers. However, spontaneous emission eventually destroys the binding between these states via a heating mechanism somewhat similar to strong-field Sysiphus heating. In this respect, the behavior of the ``diatom'' bound state under the influence of spontaneous emission is similar to that of the atomic solitons predicted to occur in near-resonant Kapitza-Dirac diffraction in the framework of nonlinear atom optics.
Kapitza-Dirac scattering, the diffraction of matter waves from a standing light field, is widely utilized in ultracold gases, but its behavior in the strongly interacting regime is an open question. Here we develop a numerically-exact two-body description of Kapitza-Dirac scattering for two contact-interacting atoms in a one-dimensional harmonic trap subjected to a pulsed optical lattice, enabling us to obtain the numerically exact dynamics. We map how interaction strength, lattice depth, lattice wavenumber, and pulse duration reshape the diffraction pattern, leading to an interaction-dependent population redistribution in real and momentum-space. By comparing the exact dynamics to an impulsive sudden-approximation description, we delineate the parameter regimes where it remains accurate and those, notably at strong attraction and small lattice wavenumber, where it fails. Our results provide a controlled few-body benchmark for interacting Kapitza-Dirac scattering and quantitative guidance for Kapitza-Dirac-based probes of ultracold atomic systems.
In contrast to electromagnetic fields, matter-wave fields are intrinsically interacting due to the presence of atom-atom collisions. Hence, matter-wave optics becomes effectively nonlinear as soon as the atomic densities are high enough that collisions can no longer be ignored. The goal of this dissertation is to study selected aspects of atom optics under such conditions. Specifically, Chapter 2 studies the near-resonant dipole-dipole interaction between two atoms in tailored vacua. In contrast to spontaneous emission, whose rate is known to be influenced by the type of vacuum the atom interacts with, we find that the dipole-dipole potential is determined only by the free space vacuum and is not modified either by thermal or squeezed vacua. In addition in the far off-resonance regime we find that the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground state. In the second part of the dissertation, which comprises Chapter 3, we then study several aspects of the many-body theory of atomic ultracold systems in situations where the nonlinearity arises due to the two-body dipole-dipole interaction. After a formal theoretical development we discuss the possibility of using atomic phase conjugation off Bose condensates as a diagnostic tool to access the spatial coherence properties and to measure the lifetime of the condensate. We argue that phase conjugation provides an attractive alternative to the optical methods of probing condensate proposed in the past. We further study the elementary excitations in a multicomponent Bose condensates and determine the quasi-particle frequency spectrum. We show that in that case interferences resulting from cross-coupling between the condensate components can lead to a reversal of the sign of the effective two-body interaction and to the onset of spatial instabilities.
It has been shown that nonlinear near-field optical resonances occur in diatomic nanostructures consisting of identical or different two-level atoms in the presence of a radiation field when the dipole-dipole interaction is taken into account. The frequencies of these resonances depend strongly on the intensity of the external optical radiation, on the initial conditions, on the polarization of the external field with respect to the axis of the nanostructure, and on the interatomic distance. The interatomic interaction is taken into account beyond perturbation theory. For this reason, the effective polarizabilities of the atoms of the nanostructure are expressed in terms of the polynomials of both the interatomic distance and the electric field strength of the external optical wave. A “falling tower” effect that is caused by the nonlinear behavior of the local dipole moments of atoms in the nanostructure is predicted.
The exchange of momentum between atoms and photons in a deflection experiment is usually described by different formalisms depending on whether the interaction time T is shown or long compared with the radiative lifetime tau R . The authors present a new approach to this problem leading to a single theoretical expression valid in both limits and therefore allowing the transition between them to be studied. They interpret in this way the resonant Kapitza-Dirac effect and the optical Stern and Gerlach effect appearing in the short-time limit (T<< tau R ) as well as the deflection profiles usually deduced from a Fokker-Planck equation in the long-time limit (T>> tau R ). The transition between these two regimes is interpreted in terms of momentum transfer due to absorption and stimulated emission of laser photons, convoluted by the distribution of recoil due to spontaneously emitted photons.