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arXiv:cond-mat/9701088 · Physical Review A

Lorentz-Lorenz shift in a Bose-Einstein condensate

Janne Ruostekoski, Juha Javanainen

Published Sep 1, 1997• 49 citations
arXivHTMLPDF

Abstract

We study the quantum field theory of light-matter interactions for quantum degenerate atomic gases at low light intensity. We argue that the contact interactions between atoms emerging in the dipole gauge may be ignored. Specifically, they are canceled by concurrent infinite level shifts of the atoms. Our development yields the classic Lorentz-Lorenz local-field shift of the atomic resonance.

DOI
10.1103/physreva.56.2056

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We study the quantum field theory of light-matter interactions for quantum degenerate atomic gases at low light intensity. We argue that the contact interactions between atoms emerging in the dipole gauge may be ignored. Specifically, they are canceled by concurrent infinite level shifts of the atoms. Our development yields the classic Lorentz-Lorenz local-field shift of the atomic resonance.
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We study the interactions of a possibly dense and/or quantum degenerate gas with driving light. Both the atoms and the electromagnetic fields are represented by quantum fields throughout the analysis. We introduce a field-theory version of Markov and Born approximations for the interactions of light with matter, and devise a procedure whereby certain types of products of atom and light fields may be put to a desired, essentially normal, order. In the limit of low light intensity we find a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, three, five, etc., ground-state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for a coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of noncooperative atoms by presenting a mathematical example in which this approach is exact.
The study of systems formed from ultracold atomic gases has emerged to become one of the most active research fields within the condensed matter landscape. These highly controllable macroscopic systems amalgamate ideas from many sub disciplines of physics, including the study of low temperatures, quantum optics and quantum information theory as well as the seemingly disparate field of high energy physics. The central concept of this thesis is gauge theories as applied to systems of bosonic atoms, which at temperatures close to absolute zero form Bose-Einstein condensates. To simulate the mathematical structure of a gauge theory, the geometric (Berry) phase formalism is adopted. This is in turn accomplished by considering the adiabatic following of the eigenstates of the light-matter coupling for an ensemble of atoms forming a Bose-Einstein condensate. These concepts are then applied to show how one can generate a spin-orbit coupling in a one-dimensional condensate, which additionally features a random mass term that allows us to study the physics of Anderson localization in an intriguing “quasi” relativistic regime. One of the features of light induced gauge potentials is that they are static; in the sense that there is no feedback between the light-matter interaction and the matter field. In the second part of this thesis it is demonstrated how such a feedback mechanism can be induced by the appropriate modification of the light-matter interaction. The consequences this has for the condensate are then described at the mean-field level, including the expected experimental signatures of the resulting ‘interacting’ gauge theory, in terms of the expansion of the condensate and also the structure of the solitons of this nonlinear system. Finally, this nonlinear model is applied to a double well system, from which the associated Bose-Hubbard model is derived and analysed; and the nonlinear Josephson problem studied.
We measure the coherent scattering of light by a cloud of laser-cooled atoms with a size comparable to the wavelength of light. By interfering a laser beam tuned near an atomic resonance with the field scattered by the atoms, we observe a resonance with a redshift, a broadening, and a saturation of the extinction for increasing atom numbers. We attribute these features to enhanced light-induced dipole-dipole interactions in a cold, dense atomic ensemble that result in a failure of standard predictions such as the "cooperative Lamb shift". The description of the atomic cloud by a mean-field model based on the Lorentz-Lorenz formula that ignores scattering events where light is scattered recurrently by the same atom and by a microscopic discrete dipole model that incorporates these effects lead to progressively closer agreement with the observations, despite remaining differences.
We calculate the spectrum of the scattered light from quantum degenerate atomic gases obeying Bose-Einstein statistics. The atoms are assumed to occupy two ground states, which are optically coupled through a common excited state by two low-intensity off-resonant light beams. In the presence of a Bose condensate in both ground states, the atoms may exhibit light-induced oscillations between the two condensates analogous to the Josephson effect. The spectrum of the scattered light is calculated in the limit of a low oscillation frequency. In the spectrum we are able to observe qualitative features depending on the phase difference between the macroscopic wave functions of the two condensates. Thus, our optical scheme could possibly be used as an experimental realization of the spontaneous breakdown of the U(1) gauge symmetry in the Bose-Einstein condensation.