Dynamic Spin Response of a Strongly Interacting Fermi Gas

Abstract

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 provide 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 ω is the probe energy. Two-component Fermi gases near Feshbach resonances provide a well controlled setting to explore many-body phenomena in highly correlated quantum systems [1,2]. When the interparticle interactions are sufficiently strong, ultracold atomic gases display universal features, where macroscopic parameters become independent of the microscopic details of the interatomic potential [3][4][5]. Most studies to date have focussed on static aspects of universality [6][7][8][9][10]; however, certain dynamical properties can also become universal. Key among these are dynamic susceptibilities which describe the way a system responds to a perturbation. Recent theoretical work has shown that the dynamic structure factor, which is connected to the imaginary part of susceptibility through the fluctuation-dissipation theorem, shows a universal high frequency tail both at high momentum [11][12][13] and low momentum where it depends on the frequency dependent shear viscosity [14,15].Bragg spectroscopy is a well established tool to measure dynamic and static density response functions [16][17][18][19]. Previous work on Fermi gases has shown that the static structure factor follows a universal law which arises from Tan's relation for the density-density correlator [20]. Several theoretical studies have also investigated the dynamic spin response [12,13,[21][22][23]] and a recent study of universal spin transport examined the static spin susceptibility [24,25], yet the dynamic spin susceptibility has not been studied experimentally.In this letter we present the first measurements of the dynamic spin response of a strongly interacting Fermi gas. Two-photon Bragg scattering is used to probe either the spin or density response by appropriate choice of the Bragg laser detuning. This allows full characterisation of the spin-parallel and spin-antiparallel components of the dynamic and static structure factors through the application of the f -sum rule [26,27]. The spin response is suppressed at low energies due to pairing and displays a universal high frequency tail, decaying as ω −5/2 , where ω is the probe energy (Bragg frequency) [13].The key to accessing the spin response in two-photon scattering experiments is to use Bragg lasers with a different coupling to each of the two s...

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

“…However, we observe that, as it happens in three-dimensions [37], the intensity of the peak is smaller on the BEC side of the crossover, and the position of the peak is shifted towards higher energies. This corresponds to a suppression of the spin susceptibility, related to the increased energy required to remove atoms from the molecules.…”

“…In particular, the high momentum behavior is very interesting as it provides a highly sensitive probe of the BEC-BCS crossover. We focus our attention on k = 4k F , close to the value recently investigated experimentally in three-dimensions [37].…”

“…From these, we apply analytic continuation to obtain the density and spin dynamical structure factors, S ρ ( k, ω) and S S ( k, ω), which can be measured experimentally using two-photons Bragg spectroscopy [37]. In particular, the high momentum behavior is very interesting as it provides a highly sensitive probe of the BEC-BCS crossover.…”

“…This provides a unique approach to excitations and dynamical response functions. Focusing on the BEC-BCS crossover regime, we compute the pairing gap as a function of the interaction strength, the spectral function, which can be measured experimentally in photoemission spectroscopy [25], and the density and spin structure factors, which can be measured in two-photon scattering experiments [37].…”

Precision studies of Fermi gases using Bragg spectroscopy

“…This is analogous to applying a magnetic field so that the perturbation couples toŜ z (k) =ˆ ↑ (k) −ˆ ↓ (k). More generally, we can express the momentum transferred via the Bragg lasers, P(k, ), at arbitrary detunings in terms of the spin-parallel and spinantiparallel components of the dynamic structure factor, S ↑↑ (k, ) and S ↑↓ (k, ) respectively, as [15] …”