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Reviews of Modern Physics

Colloquium: Bulk Bogoliubov excitations in a Bose-Einstein condensate

Roee Ozeri, Nadav Y. Katz, Jeff Steinhauer, Nir Davidson

Published Apr 8, 2005• 187 citations
Publisher

Abstract

Bogoliubov theory for excitations in Bose-Einstein condensates was formulated over 50 years ago to qualitatively explain strongly interacting superfluids. Quantitative experimental verification of this theory came with the long-awaited realization of gaseous, weakly interacting condensates. This Colloquium reviews recent experimental advances in the study of Bogoliubov bulk excitations in Bose-Einstein condensates, obtained using two-photon Bragg scattering.

DOI
10.1103/revmodphys.77.187

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Bogoliubov theory for excitations in Bose-Einstein condensates was formulated over 50 years ago to qualitatively explain strongly interacting superfluids. Quantitative experimental verification of this theory came with the long-awaited realization of gaseous, weakly interacting condensates. This Colloquium reviews recent experimental advances in the study of Bogoliubov bulk excitations in Bose-Einstein condensates, obtained using two-photon Bragg scattering.
This colloquium surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to occur. Nevertheless, experimental indications supporting the formation of a condensate in low-dimensional systems have recently been obtained. This unexpected behavior appears to be due to the nonuniformity introduced into a system by the external trapping potential. Theoretical predictions, made for homogeneous systems, require therefore careful reexamination. A number of popular theoretical treatments of the dilute weakly interacting Bose gas are presented and their regions of applicability are discussed. The possibility of Bose-Einstein condensation in a two-dimensional gas, the validity of the perturbative ttt-matrix approximation, and the diluteness condition are issues also discussed in detail.
© The Author(s) 2025.Bose-Einstein Condensation is a phenomenon at the heart of many of the past century’s most intriguing and fundamental manifestations, such as superfluidity and superconductivity: it was discovered theoretically some 100 years ago, and unequivocally experimentally demonstrated in the context of weakly-interacting gases 30 years ago. Since then, it has revolutionised our understanding of the collective quantum behaviour of matter. Such a phenomenon manifests itself across all physical scales, from the nuclear and atomic, all the way to the astrophysical, and has paved the way for novel technological applications.
Bose-Einstein Condensation is a phenomenon at the heart of many of the past century's most intriguing and fundamental manifestations, such as superfluidity and superconductivity: it was discovered theoretically some 100 years ago, and unequivocally experimentally demonstrated in the context of weakly-interacting gases 30 years ago. Since then, it has revolutionised our understanding of the collective quantum behaviour of matter. Such a phenomenon manifests itself across all physical scales, from the nuclear and atomic, all the way to the astrophysical, and has paved the way for novel technological applications.
Using two-photon Bragg spectroscopy, we study the energy of particlelike excitations in a strongly interacting homogeneous Bose-Einstein condensate, and observe dramatic deviations from Bogoliubov theory. In particular, at large scattering length a the shift of the excitation resonance from the free-particle energy changes sign from positive to negative. For an excitation with wave number q, this sign change occurs at a≈4/(πq), in agreement with the Feynman energy relation and the static structure factor expressed in terms of the two-body contact. For a≳3/q we also see a breakdown of this theory, and better agreement with calculations based on the Wilson operator product expansion. Neither theory explains our observations across all interaction regimes, inviting further theoretical efforts.