We present a theoretical investigation of the dynamic density structure factor of a strongly interacting Fermi gas near the Feshbach resonance at finite temperature, which can be exploited in two photon Bragg scattering experiments. This study is based on a fully gauge invariant linear response theory, which is consistent with a diagrammatic approach for the equilibrium state taking into account the pair fluctuation effects and respects important restrictions like the f -sum rule. At small incoming momentum, the dynamic density structure factor exhibits various features including the Nambu-Goldstone-mode peak and the quasiparticle-scattering, pairing-breaking continua. At large incoming momentum and at half recoil frequency, the structure factor has a qualitatively similar behavior as the order parameter, which can signify the appearance of the condensate. These results qualitatively agree with the recent Bragg spectroscopy experiments.
We present a theoretical investigation of the dynamic density structure factor of a strongly interacting Fermi gas near the Feshbach resonance at finite temperature, which can be exploited in two photon Bragg scattering experiments. This study is based on a fully gauge invariant linear response theory, which is consistent with a diagrammatic approach for the equilibrium state taking into account the pair fluctuation effects and respects important restrictions like the f -sum rule. At small incoming momentum, the dynamic density structure factor exhibits various features including the Nambu-Goldstone-mode peak and the quasiparticle-scattering, pairing-breaking continua. At large incoming momentum and at half recoil frequency, the structure factor has a qualitatively similar behavior as the order parameter, which can signify the appearance of the condensate. These results qualitatively agree with the recent Bragg spectroscopy experiments.
We develop a microscopic theory of the dynamic structure factor to describe the Bogoliubov-Anderson-Goldstone phonon mode and its damping rate in a strongly interacting Fermi gas at finite temperature. It is based on a density functional approach---the so-called superfluid local density approximation. The accuracy of the theory is quantitatively examined by comparing the theoretical predictions with recent experimental measurements for the local dynamic structure factor of a nearly homogeneous unitary Fermi gas at low transferred momentum [S. Hoinka et al., Nat. Phys. 13, 943 (2017)], without any free parameters. We calculate the dynamic structure factor as functions of temperature and transferred momentum, and determine the temperature evolution of the phonon damping rate, by considering the dominant decay process of the phonon mode via scatterings off fermionic quasiparticles. These predictions can be confronted with future Bragg scattering experiments on a unitary Fermi gas near the superfluid transition.
We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen–Cooper–Schrieffer superfluids to Bose–Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)—the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov–de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s -wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at . The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with 6 Li or 40 K atoms using Bragg spectroscopy.
Sum rules for the dynamic structure factors are powerful tools to explore the collective behaviors in many-body systems at zero temperature as well as at finite temperatures. The recent remarkable realization of synthetic spin-orbit (SO) coupling in quantum gases is opening up new perspective to study the intriguing SO effects with ultracold atoms. So far, a specific type of SO coupling, which is generated by a pair of Raman laser beams, has been experimentally achieved in Bose-Einstein condensates of 87Rb and degenerate Fermi gases of 40K and 6Li. In the presence of SO coupling, the dynamic structure factors for the density fluctuation and spin fluctuation satisfy different sum rules. In particular, in the two-component quantum gases with inter-species Raman coupling, the f-sum rule for the spin fluctuation has an additional term proportional to the transverse spin polarization. Due to the coupling between the momentum and spin, the first moment of the dynamic structure factor does not necessarily possess the inversion symmetry, which is in strong contrast to the conventional system without SO coupling. Such an asymmetric behavior could be observed in both Fermi gases and Bose gases with Raman coupling. As a demonstration, we focus on the uniform case at zero temperature in this work. For the non-interacting Fermi gases, the asymmetric first moment appears only when the Raman detuning is finite. The asymmetric amplitude is quite limited, and it vanishes at both zero detuning and infinite detuning. For the weakly interacting Bose gases, the first moment is asymmetric in momentum space even at zero detuning, when the ground state spontaneously breaks the Z2 symmetry in the plane-wave condensation phase. Using the Bogoliubov method, the dynamic structure factor and its first moment are explicitly calculated for various interaction parameters. We find that the asymmetric behavior in the spin channel could be much more significant than in the density channel, and the asymmetric amplitude is enhanced as the interaction strength increases. Experimentally, the dynamic structure factors can be directly measured through the two photon Bragg scattering. Numeric simulations show that to observe the deviation of inversion symmetry in the first moment, the resolution of the Bragg spectroscopy should reach a required value. For the typical parameters of the rubidium atomic gas, the required resolution is about 10-2Er with Er being the recoil energy. Our predictions can be tested in the future experiment.
The dynamic structure factor of a trapped Bose-Einstein condensed gas is investigated at zero temperature in the framework of Bogoliubov theory. Different values of momentum transfer are considered, ranging from the phonon to the single-particle regime. Various approximate schemes are discussed, including the local density approximation, where the system is locally described as a uniform gas, and the impulse approximation, in which the response is fixed by the momentum distribution of the condensate. A comprehensive approach, based on the eikonal expansion, is presented. The predictions of theory are successfully compared with the results of recent two-photon Bragg scattering experiments, at both low and high momentum transfer. Relevant features of the dynamic structure factor are also discussed using the formalism of sum rules and the concept of scaling. Particular emphasis is given to the regime of high momentum transfer, in which the dynamic structure factor is sensitive to the behavior of the order parameter in momentum space, and some instructive examples showing the consequence of long-range coherence are presented.
We present an experimental investigation of the dynamic spin response of a strongly interacting Fermi gas using Bragg spectroscopy. By varying the detuning of the Bragg lasers, we show that it is possible to measure the response in the spin and density channels separately. At low Bragg energies, the spin response is suppressed due to pairing, whereas the density response is enhanced. These experiments yield the first independent measurements of the spin-parallel and spin-antiparallel dynamic and static structure factors, which provide insight into the different features of density and spin response functions. At high momentum the spin-antiparallel dynamic structure factor displays a universal high frequency tail, proportional to ω(-5/2), where ℏω is the probe energy.
Universality of strongly interacting fermions is a topic of great interest in diverse fields. Here we investigate theoretically the universal dynamic density response of resonantly interacting ultracold Fermi atoms in the limit of either high temperature or large frequency. At high temperature, we use quantum virial expansion to derive universal, nonperturbative expansion functions of the dynamic structure factor; at large momentum, we conjecture that the second-order expansion function gives the Wilson coefficient used in the operator product expansion method. The dynamic structure factor is therefore determined by its second-order expansion function with an overall normalization factor given by Tan's [S. Tan, Ann. Phys. (NY) 323, 2952 (2008); S. Tan, Ann. Phys. (NY) 323, 2971 (2008); S. Tan, Ann. Phys. (NY) 323, 2987 (2008)] contact parameter. We show that the spin-parallel and -antiparallel dynamic structure factors have, respectively, a tail of the form $\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}^{\ensuremath{-}5/2}$ for $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$, decaying slower than the total dynamic structure factor found previously ($\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{-}7/2}$). Our predictions for the dynamic structure factor at high temperature or large frequency are testable using Bragg spectroscopy for ultracold atomic Fermi gases.