Quasiparticle Energy in a Strongly Interacting Homogeneous Bose-Einstein Condensate

Abstract

Using two-photon Bragg spectroscopy, we study the energy of particle-like 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 wavenumber 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.PACS numbers: 03.75. Hh, 67.85.De, 67.85.Hj Spectroscopy of elementary excitations in a many-body system is one of the primary methods for probing the effects of interactions and correlations in the ground state of the system, which are at the heart of macroscopic phenomena such as superfluidity [1,2]. In ultracold atomic gases, two-photon Bragg spectroscopy provides a measurement of the excitation energy ω at a well defined wavenumber q [3-9]. For a weakly interacting homogeneous Bose-Einstein condensate (BEC), the excitation spectrum is given by the Bogoliubov dispersion relation [10], with low-q phonon excitations and highq particle-like excitations. Predictions of the Bogoliubov theory have been experimentally verified both in harmonically trapped gases, invoking the local density approximation [4,5], and in homogeneous atomic BECs [9].Much richer physics, including phenomena traditionally associated with superfluid liquid helium, such as the roton minimum in the excitation spectrum [11], is expected in strongly interacting atomic BECs (for a recent review see [12]). The strength of two-body interactions, characterised by the s-wave scattering length a, can be enhanced by exploiting magnetic Feshbach resonances [13]. However, this also enhances three-body inelastic collisions, making the experiments on strongly interacting bulk BECs [6,[14][15][16] challenging and still scarce [17]. A deviation from the Bogoliubov spectrum was observed in Bragg spectroscopy of large-q excitations in a harmonically trapped 85 Rb BEC [6], and has inspired various theoretical interpretations [6,12,[18][19][20][21][22], with no consensus or complete quantitative agreement with the experiments being reached so far.In this Letter, we use Bragg spectroscopy to study the large-q, particle-like excitations in a strongly interacting homogeneous 39 K BEC, produced in an optical box trap [24]. Our homogeneous system allows more direct comparisons with theory, and we also explore stronger interactions than in previous experiments. We show that at large a the excitation-energy shift from the free-particle dispersion relation strongly deviates from the Bogoliubov theory and even changes sign from positive to negative. For a 3/q our measurements are ...

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