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Light Science & Applications

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

Yunfei Wang, Huiying Du, Yuqing Li, Feng Mei, Ying Hu, Liantuan Xiao, Jie Ma, Suotang Jia

Published Feb 28, 2023• 43 citations
Publisher

Abstract

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.

DOI
10.1038/s41377-023-01103-8

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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.
We present a comprehensive experimental study of Tan's universal contact parameter in a two-component ultracold Fermi gas, using Bragg spectroscopy. The contact uniquely parameterizes a number of universal properties of Fermi gases in the strongly interacting regime. It is linked to the spin-antiparallel component of the static structure factor S ↑↓ ( k ) at high momenta, which can readily be obtained via Bragg scattering. Contact depends upon the relative interaction strength 1/( k F a ) and temperature T / T F , where k F is the Fermi wave vector, a is the s-wave scattering length and T F is the Fermi temperature. We present measurements of both of these dependencies in a cloud of 6 Li atoms and compare our findings to theoretical predictions. We also compare Bragg spectroscopic methods based on measuring the energy and momentum transferred to the cloud and examine the conditions under which the energy transfer method provides improved accuracy. Our measurements of the dynamic structure factor and contact are found to be in good agreement with theoretical predictions based on the quantum virial expansion.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
This paper presents studies of the universal properties of strongly interacting Fermi gases using Bragg spectroscopy. We focus on pair-correlations, their relationship to the contact C introduced by Tan, and their dependence on both the momentum and temperature. We show that short-range pair correlations obey a universal law, first derived by Tan through measurements of the static structure factor, which displays a universal scaling with the ratio of the contact to the momentum C/q . Bragg spectroscopy of ultracold 6 Li atoms is employed to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We show that calibrating our Bragg spectra using the f -sum rule leads to a dramatic improvement in the accuracy of the structure factor measurement. We also measure the temperature dependence of the contact in a unitary gas and compare our results to calculations based on a virial expansion.
We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tan's relations. This is achieved through measurements of the static structure factor which displays a universal scaling proportional to the ratio of Tan's contact to the momentum C/q. Bragg spectroscopy of ultracold 6Li atoms from a periodic optical potential is used to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We calibrate our Bragg spectra using the f-sum rule, which is found to improve the accuracy of the structure factor measurement.
A powerful set of universal relations, centered on a quantity called the contact, connects the strength of short-range two-body correlations to the thermodynamics of a many-body system with zero-range interactions. We report on measurements of the contact, using rf spectroscopy, for an (85)Rb atomic Bose-Einstein condensate (BEC). For bosons, the fact that contact spectroscopy can be used to probe the gas on short time scales is useful given the decreasing stability of BECs with increasing interactions. A complication is the added possibility, for bosons, of three-body interactions. In investigating this issue, we have located an Efimov resonance for (85)Rb atoms with loss measurements and thus determined the three-body interaction parameter. In our contact spectroscopy, in a region of observable beyond-mean-field effects, we find no measurable contribution from three-body physics.
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.