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Register a new userContact and sum-rules in a near-uniform Fermi gas at unitarity
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We present an experimental study of the high-energy excitation spectra of unitary Fermi gases. Using focussed beam Bragg spectroscopy, we locally probe atoms in the central region of a harmonically trapped cloud where the density is nearly uniform, enabling measurements of the dynamic structure factor for a range of temperatures both below and above the superfluid transition. Applying sum-rules to the measured Bragg spectra, we resolve the characteristic behaviour of the universal contact parameter, ${cal C}$, across the superfluid transition. We also employ a recent theoretical result for the kinetic (second-moment) sum-rule to obtain the internal energy of gases at unitarity.
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We present measurements of the local (homogeneous) density-density response function of a Fermi gas at unitarity using spatially resolved Bragg spectroscopy. By analyzing the Bragg response across one axis of the cloud we extract the response function for a uniform gas which shows a clear signature of the Bose-Einstein condensation of pairs of fermions when the local temperature drops below the superfluid transition temperature. The method we use for local measurement generalizes a scheme for obtaining the local pressure in a harmonically trapped cloud from the line density and can be adapted to provide any homogeneous parameter satisfying the local density approximation.
We present a theoretical study of the dynamic structure function of a resonantly interacting two-component Fermi gas at zero temperature. Our approach is based on dynamic many-body theory able to describe excitations in strongly correlated Fermi systems. The fixed-node diffusion Monte Carlo method is used to produce the ground-state correlation functions which are used as an input for the excitation theory. Our approach reproduces recent Bragg scattering data in both the density and the spin channel. In the BCS regime, the response is close to that of the ideal Fermi gas. On the BEC side, the Bose peak associated with the formation of dimers dominates the density channel of the dynamic response. When the fraction of dimers is large our theory departs from the experimental data, mainly in the spin channel.
We present an experimental study of a two component Fermi gas following an interaction quench into the superfluid phase. Starting with a weakly attractive gas in the normal phase, interactions are ramped to unitarity at a range of rates and we measure the subsequent dynamics as the gas approaches equilibrium. Both the formation and condensation of fermion pairs are mapped via measurements of the pair momentum distribution and can take place on very different timescales, depending on the adiabaticity of the quench. The contact parameter is seen to respond very quickly to changes in the interaction strength, indicating that short-range correlations, based on the occupation of high-momentum modes, evolve far more rapidly than the correlations in low-momentum modes necessary for pair condensation.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mixtures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be different, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this review, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisticated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach.
The contact ${cal I}$, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter $1/(k_F a)$, where $k_F$ is the Fermi wave-vector and $a$ is the $s$-wave scattering length, and the temperature $T/T_F$, where $T_F$ is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.
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