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Register a new userVerification of universal relations in a strongly interacting Fermi gas
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Many-body fermion systems are important in many branches of physics, including condensed matter, nuclear, and now cold atom physics. In many cases, the interactions between fermions can be approximated by a contact interaction. A recent theoretical advance in the study of these systems is the derivation of a number of exact universal relations that are predicted to be valid for all interaction strengths, temperatures, and spin compositions. These equations, referred to as the Tan relations, relate a microscopic quantity, namely, the amplitude of the high-momentum tail of the fermion momentum distribution, to the thermodynamics of the many-body system. In this work, we provide experimental verification of the Tan relations in a strongly interacting gas of fermionic atoms. Specifically, we measure the fermion momentum distribution using two different techniques, as well as the rf excitation spectrum and determine the effect of interactions on these microscopic probes. We then measure the potential energy and release energy of the trapped gas and test the predicted universal relations.
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Transport of strongly interacting fermions governs modern materials -- from the high-$T_c$ cuprates to bilayer graphene --, but also nuclear fission, the merging of neutron stars and the expansion of the early universe. Here we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting Fermi gas of atoms by studying sound propagation and its attenuation via the coupled transport of momentum and heat. In the normal state, the sound diffusivity ${D}$ monotonically decreases upon lowering the temperature $T$, in contrast to the diverging behavior of weakly interacting Fermi liquids. As the superfluid transition temperature is crossed, ${D}$ attains a universal value set by the ratio of Plancks constant ${h}$ and the particle mass ${m}$. This finding of quantum limited sound diffusivity informs theories of fermion transport, with relevance for hydrodynamic flow of electrons, neutrons and quarks.
The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact has been extended to higher partial waves, in particular, the p-wave contacts have been experimentally probed in recent experiment. So far discussions on p-wave contacts have been limited to three-dimensions. In this paper, we generalize the p-wave contacts to two-dimensions and derive a series of universal relations, including the adiabatic relations, high momentum distribution, virial theorem and pressure relation. At high temperature and low density limit, we calculated the p-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing mode frequency and the p-wave contacts are given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three and two dimensional Fermi gas and discuss possible experimental realization of two dimensional Fermi gas with p-wave interactions.
We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tans relations. This is achieved through measurements of the static structure factor which displays a universal scaling proportional to the ratio of Tans contact to the momentum $C/q$. Bragg spectroscopy of ultracold $^6$Li 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.
We study the spin-mixing dynamics of a one-dimensional strongly repulsive Fermi gas under harmonic confinement. By employing a mapping onto an inhomogeneous isotropic Heisenberg model and the symmetries under particle exchange, we follow the dynamics till very long times. Starting from an initial spin-separated state, we observe superdiffusion, spin-dipolar large amplitude oscillations and thermalization. We report a universal scaling of the oscillations with particle number N^1/4, implying a slow-down of the motion and the decrease of the zero-temperature spin drag coefficient as the particle number grows.
We study the spin-Seebeck effect in a strongly interacting, two-component Fermi gas and propose an experiment to measure this effect by relatively displacing spin up and spin down atomic clouds in a trap using spin-dependent temperature gradients. We compute the spin-Seebeck coefficient and related spin-heat transport coefficients as functions of temperature and interaction strength. We find that when the inter-spin scattering length becomes larger than the Fermi wavelength, the spin-Seebeck coefficient changes sign as a function of temperature, and hence so does the direction of the spin-separation. We compute this zero-crossing temperature as a function of interaction strength and in particular in the unitary limit for the inter-spin scattering.
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