© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1702.02935 · Physical Review Letters

Quasiparticle Energy in a Strongly Interacting Homogeneous Bose-Einstein Condensate

Raphael Lopes, Christoph Eigen, Adam Barker, Konrad Viebahn, Martin Robert-De-Saint-Vincent, Nir Navon, Zoran Hadzibabic, Robert P. Smith

Published May 23, 2017• 47 citations

Abstract

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.

DOI: 10.1103/physrevlett.118.210401

Related papers

Bragg spectroscopy of a strongly interacting Bose-Einstein condensate

J. J. Kinnunen, M. J. Holl

We study Bragg spectroscopy of a strongly interacting Bose–Einstein condensate using time-dependent Hartree–Fock–Bogoliubov theory. We include approximatively the effect of the momentum-dependent scattering amplitude which is shown to be the dominant factor in determining the spectrum for large momentum Bragg scattering. The condensation of the Bragg scattered atoms is shown to alter significantly the observed excitation spectrum by creating a novel pairing channel of mobile pairs.

•Jan 1, 2009•11 citations

Bragg spectroscopy of a strongly interacting Bose–Einstein condensate

J J Kinnunen, M J Holland

We study Bragg spectroscopy of a strongly interacting Bose–Einstein condensate using time-dependent Hartree–Fock–Bogoliubov theory. We include approximatively the effect of the momentum-dependent scattering amplitude which is shown to be the dominant factor in determining the spectrum for large momentum Bragg scattering. The condensation of the Bragg scattered atoms is shown to alter significantly the observed excitation spectrum by creating a novel pairing channel of mobile pairs.

arXiv:0807.2602•New Journal of Physics•Jan 20, 2009•12 citations

Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate

P. B. Blakie, R. J. Ballagh, Crispin W. Gardiner

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at $T=0 \mathrm{K}.$ We demonstrate that within the linear-response regime, both a quantum-field-theory treatment and a mean-field Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a mean-field formalism. We analyze the behavior of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (mean field, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the mean-field treatment, and can be interpreted in terms of the interference of the u and $v$ quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear-response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.

arXiv:cond-mat/0108480•Physical Review A•Feb 4, 2002•73 citations

Testing universality of Feynman-Tan relation in interacting Bose gases using high-order Bragg spectra

Yunfei Wang, Huiying Du, Yuqing Li +5 more

Abstract The Feynman-Tan relation, obtained by combining the Feynman energy relation with the Tan’s two-body contact, can explain the excitation spectra of strongly interacting 39 K Bose-Einstein condensate (BEC). Since the shift of excitation resonance in the Feynman-Tan relation is inversely proportional to atomic mass, the test of whether this relation is universal for other atomic systems is significant for describing the effect of interaction in strongly correlated Bose gases. Here we measure the high-momentum excitation spectra of 133 Cs BEC with widely tunable interactions by using the second- and third-order Bragg spectra. We observe the backbending of frequency shift of excitation resonance with increasing interaction, and even the shift changes its sign under the strong interactions in the high-order Bragg spectra. Our finding shows good agreement with the prediction based on the Feynman-Tan relation. Our results provide significant insights for understanding the profound properties of strongly interacting Bose gases.

Light Science & Applications•Feb 28, 2023•43 citations

Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas

J. M. M. J. Vogels, K. Xu, Chandra Raman +2 more

Summary form only given. Phonons with wavevector q//spl planck/-were optically imprinted into a Bose-Einstein condensate. Their momentum distribution was analyze using Bragg spectroscopy with a high momentum transfer. The wavefunction of these elementary excitations was shown to be a superposition of +q and -q free particle momentum states, in agreement with the Bogoliubov quasiparticle picture.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•7 citations

Excitation of Phonons in a Bose-Einstein Condensate by Light Scattering

Dan Stamper-Kurn, A. P. Chikkatur, Axel Görlitz +4 more

Stimulated small-angle light scattering was used to measure the structure factor of a Bose-Einstein condensate in the phonon regime. The excitation strength for phonons was found to be significantly reduced from that of free particles, revealing the presence of correlated pair excitations and quantum depletion in the condensate. The Bragg resonance line strength and line shift agreed with predictions for the homogeneous Bose gas using a local density approximation.

arXiv:cond-mat/9906035•Physical Review Letters•Oct 11, 1999•451 citations

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.

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at

T=0 \mathrm{K}.

We demonstrate that within the linear-response regime, both a quantum-field-theory treatment and a mean-field Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a mean-field formalism. We analyze the behavior of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (mean field, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the mean-field treatment, and can be interpreted in terms of the interference of the u and

v

quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear-response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.

Abstract The Feynman-Tan relation, obtained by combining the Feynman energy relation with the Tan’s two-body contact, can explain the excitation spectra of strongly interacting 39 K Bose-Einstein condensate (BEC). Since the shift of excitation resonance in the Feynman-Tan relation is inversely proportional to atomic mass, the test of whether this relation is universal for other atomic systems is significant for describing the effect of interaction in strongly correlated Bose gases. Here we measure the high-momentum excitation spectra of 133 Cs BEC with widely tunable interactions by using the second- and third-order Bragg spectra. We observe the backbending of frequency shift of excitation resonance with increasing interaction, and even the shift changes its sign under the strong interactions in the high-order Bragg spectra. Our finding shows good agreement with the prediction based on the Feynman-Tan relation. Our results provide significant insights for understanding the profound properties of strongly interacting Bose gases.