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.
Reply to the Comment by Galanakis \textit{et al} on the paper \textquotedblleft Exact bosonization for an interacting Fermi gas in arbitrary dimensions"
We study depletion dynamics of an open system of weakly interacting fermions with two-body random interactions. In this model fermions are escaping from the high-energy one-particle orbitals, that mimics the evaporation process used in laboratory experiments with neutral atoms to cool them to ultra-low temperatures. It is shown that due to dynamical thermalization the system instantaneously adjusts to the new chemical potential and temperature, so that occupation numbers of the one-particle orbitals always obey the Fermi-Dirac distribution. In this way we are able to describe the evaporation p…
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…
Many-body \textit{T}-matrix theory of a strongly interacting spin-orbit coupled Fermi gas: Momentum-resolved radio-frequency spectroscopy and fermionic pairing
Universal relations are important for understanding strongly interacting Fermi gases, the study of which have been mostly limited to cases with a single scattering channel. Here we discover a series universal relations for strongly interacting Fermi gases with multiple scattering channels. Unlike its counterpart across a single channel wide magnetic Feshbach resonance, a new kind of contact which we call the cross-channel contact naturally appears in this system, this contact is related to varies thermodynamic quantities as well as short range correlation functions.
Interacting Fermi systems in the strongly correlated regime play a fundamental role in many areas of physics and are of particular interest to the condensed matter community. Though weakly inter- acting fermions are understood, strongly correlated fermions are difficult to describe theoretically as there is no small interaction parameter to expand about. Existing strong coupling theories rely heavily on the so-called many-body T-matrix approximation that sums ladder-type Feynman diagrams. Here, by acknowledging the fact that the effective interparticle interaction (i.e., the vertex function) b…
We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov process in low temperature strongly interacting Fermi gases using quantum hydrodynamics, correcting and extending the original calculation of Landau and Khalatnikov [ZhETF, 19 (1949) 637]. Our predictions can be tested in state-of-the-art experiments with cold atomic gases in the collisionless regime.
We study one-dimensional strongly interacting Bose-Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the one-dimensional Bose-Fermi gas with equal boson-boson and boson-fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose-Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the…
We investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including $p$-wave pairing fluctuations within the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that, in the weak-coupling side, $C_V$ exhibits a dip-hump behavior as a function of the temperature. While the dip is associated with the pseudogap phenomenon near $T_{\rm c}$, the hump structure is found to come from the suppression of Fermi quasiparticle scattering into a $p$-wave molecular state in the Fermi degenerate regime. Since the latter phenomenon do…
We measure the free decay of a spatially periodic density profile in a normal fluid strongly interacting Fermi gas, which is confined in a box potential. This spatial profile is initially created in thermal equilibrium by a perturbing potential. After the perturbation is abruptly extinguished, the dominant spatial Fourier component exhibits an exponentially decaying (thermally diffusive) mode and a decaying oscillatory (first sound) mode, enabling independent measurement of the thermal conductivity and the shear viscosity directly from the time-dependent evolution.
In this work we study the particle conductance of a strongly interacting Fermi gas through a quantum point contact. With an atom-molecule two-channel model, we compute the contribution to particle conductance by both the fermionic atoms and the bosonic molecules using the Keldysh formalism. Focusing on the regime above the Fermi superfluid transition temperature, we find that the fermionic contribution to the conductance is reduced by interaction compared with the quantized value for the non-interacting case; while the bosonic contribution to the conductance exhibits a plateau with non-univers…
A gas of interacting ultracold fermions can be tuned into a strongly interacting regime using a Feshbach resonance. Here we theoretically study quasiparticle transport in a system of two reservoirs of interacting ultracold fermions on the BCS side of the BCS-BEC crossover coupled weakly via a tunnel junction. Using the generalized BCS theory we calculate the time evolution of the system that is assumed to be initially prepared in a non-equilibrium state characterized by a particle number imbalance or a temperature imbalance. A number of characteristic features like sharp peaks in quasiparticle…
Quantum many-body systems in one dimension (1D) exhibit some peculiar properties. In this article, we review some of our work on strongly interacting 1D spinor quantum gas. First, we discuss a generalized Bose-Fermi mapping that maps the charge degrees of freedom to a spinless Fermi gas and the spin degrees of freedom to a spin chain model. This also maps the strongly interacting system into a weakly interacting one, which is amenable for perturbative calculations. Next, based on this mapping, we construct an ansatz wavefunction for the strongly interacting system, using which many physical qu…
We analytically study quantum dissipative dynamics described by the Caldirola-Kanai model with inter-particle interactions. We have found that the dissipative quantum dynamics of the Caldirola-Kanai model can be exactly mapped to a dissipationless quantum dynamics under a negative external harmonic potential, even when the particles are strongly interacting. In particular, we show that the mapping is valid for the unitary Fermi gas, which is relevant for cold atoms and nuclear matters.
