Universal Properties of the Ultra-Cold Fermi Gas

Abstract

We present some general considerations on the properties of a two-component ultra-cold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the ground state energy can be written in terms of a single dimensionless function $h(\xi ,\tau )$, where $\xi =-(k_F{a}_s{)}^{-1}$ and $\tau =T/T_F$. The function $h(\xi ,\tau )$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the RF-spectroscopy shift $\bar{\dø}(ξ,τ)$ and the molecular fraction $f_c(\xi ,\tau )$ in the closed channel can be expressed in terms of $h(\xi ,\tau )$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.

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• Theory of ultracold Fermi gases
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• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Strongly paired fermions: Cold atoms and neutron matter
• Renormalization group fixed points, universal phase diagram, and 1/N expansion for quantum liquids with interactions near the unitarity limit
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• Theory of RF-spectroscopy of strongly interacting Fermions
• Large-N expansion for unitary superfluid Fermi gases
• Fermi gas near unitarity around four and two spatial dimensions
• Coherence and clock shifts in ultracold Fermi gases with resonant interactions
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• Thermodynamics of a Trapped Unitary Fermi Gas
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• BEC-BCS Crossover in the Epsilon Expansion
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Cited by in corpus (143)

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• Contact Measurements on Atomic BEC
• Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
• Universal behavior of pair correlations in a strongly interacting Fermi gas
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Number of closed-channel molecules in the BEC-BCS crossover
• Spectral Functions and rf Response of Ultracold Fermionic Atoms
• Tan relations in one dimension
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Universal Relations for Identical Bosons from 3-Body Physics
• Transverse Demagnetization Dynamics of a Unitary Fermi Gas
• Viscosity of strongly interacting quantum fluids: spectral functions and sum rules
• Particle distribution tail and related energy formula
• Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly-interacting Fermi Gas
• Evidence for universal relations describing a gas with $p$-wave interactions
• Temperature dependence of the contact in a unitary Fermi gas
• Quenching to unitarity: Quantum dynamics in a 3D Bose gas
• Universal Short-Distance Structure of the Single-Particle Spectral Function of Dilute Fermi Gases
• Universal Properties of a Strongly Interacting Fermi Gas at a $p$-wave Resonance
• Universal relations for the two-dimensional spin-1/2 Fermi gas with contact interactions
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases
• Universal high-momentum asymptote and thermodynamic relations in a spinless Fermi gas with a resonant $p$-wave interaction
• Universal contact of strongly interacting fermions at finite temperatures
• Concept of contact spectrum and its applications in atomic quantum Hall states
• Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
• Pseudogaps in strongly interacting Fermi gases
• Dynamic spin response of a strongly interacting Fermi gas
• Yang-Yang thermometry and momentum distribution of a trapped one-dimensional Bose gas
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• Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion
• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Universal One-dimensional Atomic Gases Near Odd-wave Resonance
• Ground-state thermodynamic quantities of homogeneous spin-$1/2$ fermions from the BCS region to the unitarity limit
• Stability Condition of a Strongly Interacting Boson-Fermion Mixture across an Inter-Species Feshbach Resonance
• Dynamics of correlations in a dilute Bose gas following an interaction quench
• Physics of ultracold Fermi gases revealed by spectroscopies
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• Breathing mode of two-dimensional atomic Fermi gases in harmonic traps
• Strongly Interacting p-wave Fermi Gas in Two-Dimensions: Universal Relations and Breathing Mode
• Large-momentum distribution of a polarized Fermi gas and p-wave contacts
• The Unitary Gas and its Symmetry Properties
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• The contact in the unitary Fermi gas across the superfluid phase transition
• Universal Tan relations for quantum gases in one dimension
• Critical behaviours of contact near phase transitions
• Strongly interacting Bose-Fermi mixtures in one dimension
• Universal Bose Gases Near Resonance: A Rigorous Solution
• High Sensitivity RF Spectroscopy of a Strongly-Interacting Fermi Gas
• Absence of heating in a uniform Fermi gas created by periodic driving
• Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model
• Cold Atom Quantum Simulator for Dilute Neutron Matter
• Contact matrix in dilute quantum systems
• Bose Gases Near Resonance: renormalized interactions in a condensate
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Short range asymptotic behavior of the wave-functions of interacting spin-half fermionic atoms with spin-orbit coupling: a model study
• P-Wave Contact Tensor -- Universal Properties of Axisymmetry-Broken P-Wave Fermi Gases
• Viscosity Sum Rules at Large Scattering Lengths
• Correlation functions of one-dimensional strongly interacting two-component gases
• Short-distance properties of Coulomb systems
• Expansion of harmonically trapped interacting particles and time dependence of the contact
• Tan's two-body contact across the superfluid transition of a planar Bose gas
• Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover
• Quantum Many-Body Conformal Dynamics: Symmetries, Geometry, Conformal Tower States, and Entropy Production
• The BCS-BEC Crossover
• Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction
• Effective theory and universal relations for Fermi gases near a $d$-wave interaction resonance
• Dynamics of correlations in a quasi-2D dipolar Bose gas following a quantum quench
• Universal relations and normal phase of an ultracold Fermi gas with coexisting $s$- and $p$-wave interactions
• Sigature of the universal super Efimov Effect: three-body contact in two dimensional Fermi gases
• Finite-density corrections to the Unitary Fermi gas: A lattice perspective from Dynamical Mean-Field Theory
• Universal Relation for the Inelastic Two-Body Loss Rate
• Contact interaction in an unitary ultracold Fermi gas
• Normal State Properties of a resonantly interacting p-wave Fermi Gas
• Excitation picture of an interacting Bose gas
• Fermion superfluid with hybridized $s$- and $p$-wave pairings
• A strongly interacting high partial wave Bose gas
• Universal relations for dipolar quantum gases
• $s$-wave Contacts of Quantum Gases in Quasi-one and Quasi-two Dimensions
• Non-Perturbative Dynamical Effects in Nearly Scale Invariant Systems: The Action of Breaking Scale Invariance
• Universal Properties of Fermi Gases in One-dimension
• Structure Function Sum rules for Systems with Large Scattering Lengths
• Universal Short Range Correlations in Bosonic Helium Clusters
• Far-Away-From-Equilibrium Quantum Critical Conformal Dynamics: Reversibility, Thermalization, and Hydrodynamics
• Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries
• Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling
• Maximum Energy Growth Rate in Dilute Quantum Gases
• The Contact in the BCS-BEC crossover for finite range interacting ultracold Fermi gases
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• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• Dynamics of strongly interacting Fermi gases with time-dependent interactions: Consequence of conformal symmetry
• High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance
• Strong-Coupling and Finite Temperature Effects on $p$-wave Contacts
• Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• The self-energy of an impurity in an ideal Fermi gas to second order in the interaction strength
• P-wave contacts of quantum gases in quasi-one-dimensional and quasi-two-dimensional traps
• Universal Relations of Ultracold Fermi Gases with Arbitrary Spin-Orbit Coupling
• Universal relations for spin-orbit coupled Fermi gas near an s-wave resonance
• Non-Universal and Universal Aspects of The Large Scattering Length Limit
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• On the survival of the quantum depletion of a condensate after release from a magnetic trap
• Universal relations for a spin-polarized Fermi gas in two dimensions
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• A new effective interaction for the trapped fermi gas: the BEC-BCS crossover
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Observation of the density dependence of the closed-channel fraction of a ${}^6$Li superfluid
• A Universal Energy Functional for Trapped Fermi Gases with Large Scattering Length
• Isothermal sweep theorems for ultra-cold quantum gases in a canonical ensemble
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Photo-excitation measurement of Tan's contact for a strongly interacting Fermi gas
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• Emergent $s$-wave interactions in orbitally active quasi-two-dimensional Fermi gases
• Spin incoherent liquid and interaction-driven criticality in 1D Hubbard model
• Studies of Single Component Fermi Gas near a $P$-wave Resonance with Lowest Order Constrained Variational Method
• Spin correlations and entanglement in partially magnetised ensembles of fermions
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Three-body contact for fermions. I. General relations
• Dependence of interface conductivity on relevant physical parameters in polarized Fermi mixtures
• Tan's universal contact and collective oscillations of strongly interacting Fermi gases
• Scale Invariance in the Lowest Landau Level
• Universal scattering phase shift in the presence of spin-orbit coupling
• Two-Body Contact Dynamics in a Bose Gas near a Fano-Feshbach Resonance
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• Radio-Frequency Spectroscopy and the Dimensional Crossover in Interacting Spin-Polarized Fermi Gases
• Closed-channel parameters of Feshbach resonances
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• Universal Relations for Fermions with Large Scattering Length
• Dimer-projection contact and the clock shift of a unitary Fermi gas
• An Effective Series Expansion to the Equation of State of Unitary Fermi Gases
• Two-body contact of a Bose gas near the superfluid--Mott-insulator transition
• BEC-BCS Crossover with Feshbach Resonance for a Three-Hyperfine-Species Model
• The normal state of attractive Fermi gases from coupled-cluster theory
• Universal Bound States in Long-range Spin Chains with an Impurity
• Pair-Condensation Peak in Radio-Frequency Dimer-Projection Spectroscopy of a Unitary Fermi Gas
• Universal Relations in Long-range Quantum Spin Chains
• Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids