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.
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.
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section.The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances.While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density.As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations.However, significant progress has also been made with purely analytical methods.Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role.Recently, C has also been found to determine the prefactor of the high-frequency power-law decay of correlators as well as the right-hand-sides of shear-and bulk viscosity sum rules.The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium.In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.
The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.
We study the universal relations and normal-phase thermodynamics of a two-component ultracold Fermi gas with coexisting s- and p-wave interactions. Due to the orthogonality of two-body wave functions of different scattering channels, the universal thermodynamic relations of the system appear to be direct summations of contributions from each partial-wave scattering channel. These universal relations are dictated by a set of contacts, which can be associated with either s- or p-wave interactions. Interestingly, due to the interplay of s- and p-wave interactions on the many-body level, the contacts, and hence all the relevant thermodynamic quantities, behave differently from those with only s- or p-wave interactions. These are manifest in our numerical calculations based on second-order virial expansions for 40K atoms under typical experimental parameters. A particularly interesting finding is that, due to the coexistence of s- and p-wave scatterings, the interaction energy of the repulsive branch features abrupt changes across the p-wave resonances. Our results can be readily checked experimentally for 40K atoms near the 198Gp-wave Feshbach resonance, where multiple partial-wave scatterings naturally coexist.
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 was extended to higher partial waves; in particular, the p-wave contacts have been experimentally probed in recent experiments. 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 the high-temperature and low-density limit, we calculate 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 is given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three- and two-dimensional Fermi gases and discuss possible experimental realization of a two-dimensional Fermi gas with p-wave interactions.
The experimental realization of stable, ultracold Fermi gases near a Feshbach resonance allows to study gases with attractive interactions of essentially arbitrary strength. They extend the classic paradigm of BCS into a regime which has never been accessible before. We review the theoretical concepts which have been developed in this context, including the Tan relations and the notion of fixed points at zero density, which are at the origin of universality. We discuss in detail the universal thermodynamics of the unitary Fermi gas which allows a fit free comparison between theory and experiment for this strongly interacting system. In addition, we adress the consequences of scale invariance at infinite scattering length and the subtle violation of scale invariance in two dimensions. Finally we discuss the Fermionic excitation spectrum accessible in momentum resolved RF-spectroscopy and the origin of universal lower bounds for the shear viscosity and the spin diffusion constant.