Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance

Abstract

We address the thermodynamics, density profiles and superfluid density of trapped fermions undergoing BCS-BEC crossover, with and without population imbalance. Our approach represents a fully consistent treatment of "pseudogap effects", which reflect the distinction between the pair formation temperature $T^{\ast }$ and the pair condensation temperature $T_c$ and must be accommodated by modifying the fermionic excitation spectrum. This distinction has been omitted from all other many body approaches in the literature. We show how enforcing this corollary implies that pairing fluctuation contributions enter into both the gap and the number equations; this is necessary in order to be consistent with a generalized Ward identity. Furthermore, we demonstrate that we obtain physical results for the superfluid density $n_s(T)$ at all $T$. In contrast, previous work in the literature has led to ill-behaved $n_s(T)$. The superfluid density is a critical measure of the physicality of a given crossover theory. In order to properly address thermodynamic properties of a trapped Fermi gas, it is necessary to demonstrate that the particle density profiles are consistent with experiment. The lack of demonstrable consistency between theoretical and experimental density profiles, along with problematic behavior found for $n_s(T)$, casts doubt on previous claims in the literature concerning quantitative agreement between thermodynamical calculations and experiment.

19 pages, 14 figures. Submitted to PRB

References in corpus (34)

• Observation of Bose-Einstein Condensation of Molecules
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Weakly bound dimers of fermionic atoms
• Observation of Phase Separation in a Strongly-Interacting Imbalanced Fermi Gas
• Thermodynamics of the BCS-BEC crossover
• Direct Observation of the Superfluid Phase Transition in Ultracold Fermi Gases
• Deformation of a Trapped Fermi Gas with Unequal Spin Populations
• Precision Measurements of Collective Oscillations in the BEC-BCS Crossover
• Finite temperature phase diagram of a polarised Fermi condensate
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Strongly interacting Fermi gases with density imbalance
• Generic Phase Diagram of Fermion Superfluids with Population Imbalance
• Profiles of near-resonant population-imbalanced trapped Fermi gases
• Trapped fermions with density imbalance in the BEC limit
• Pairing fluctuations and the superfluid density through the BCS-BEC crossover
• Trapped Fermions across a Feshbach resonance with population imbalance
• Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures
• Surface Tension in Unitary Fermi Gases with Population Imbalance
• Pairing of a trapped resonantly-interacting fermion mixture with unequal spin populations
• Intermediate temperature superfluidity in an atomic Fermi gas with population imbalance
• Temperature of a trapped unitary Fermi gas at finite entropy
• Superfluid phase diagrams of trapped Fermi gases with population imbalance
• Mean field thermodynamics of a spin-polarized spherically trapped Fermi gas at unitarity
• Stability conditions and phase diagrams for two component Fermi gases with population imbalance
• Breakdown of the local density approximation in interacting systems of cold fermions in strongly anisotropic traps
• Single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell state in BCS--Bose-Einstein condensation crossover
• Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS-BEC Crossover Regime
• Theory of Superfluids with Population Imbalance: Finite Temperature and BCS-BEC Crossover Effects
• Popov approximation for composite bosons in the BCS-BEC crossover
• Non-BCS superfluidity in trapped ultracold Fermi gases
• Finite temperature effects in trapped Fermi gases with population imbalance
• Understanding the superfluid phase diagram in trapped Fermi gases
• Finite Temperature Momentum Distribution of a Trapped Fermi Gas

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• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices
• The Finite Temperature Pairing Gap of a Unitary Fermi Gas by Quantum Monte Carlo Calculations
• Pseudogaps in strongly interacting Fermi gases
• Comparative Study of BCS-BEC Crossover Theories above $T_c$: the Nature of the Pseudogap in Ultra-Cold Atomic Fermi Gases
• Comparison of Different Pairing Fluctuation Approaches to BCS-BEC Crossover
• A Two Energy Gap Preformed-Pair Scenario For the Cuprates: Implications for Angle-Resolved Photoemission Spectroscopy
• Perfect Fluids and Bad Metals: Transport Analogies Between Ultracold Fermi Gases and High $T_c$ Superconductors
• Second sound and the density response function in uniform superfluid atomic gases
• Variational theory of two-fluid hydrodynamic modes at unitarity
• Ground state of the two-dimensional attractive Fermi gas: essential properties from few- to many-body
• Phase separation in imbalanced fermion superfluids beyond mean-field
• Critical Behaviour in Trapped Strongly Interacting Fermi Gases
• Radio Frequency Spectroscopy of Trapped Fermi Gases with Population Imbalance
• Auxiliary field formalism for dilute fermionic atom gases with tunable interactions
• The Josephson relation for the superfluid density in the BCS-BEC crossover
• Dimensional Crossover in a Spin-imbalanced Fermi gas
• The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics
• Conserving T-matrix theory of superconductivity
• The Compressibility in Strongly Correlated Superconductors and Superfluids: From BCS to BEC
• Signatures of pairing and spin-orbit coupling in correlation functions of Fermi gases
• Effect of the particle-hole channel on BCS--Bose-Einstein condensation crossover in atomic Fermi gases
• Reentrant Superfluidity and Pair Density Wave in Single Component Dipolar Fermi Gases
• Equivalence of channel-corrected T-matrix and anomalous propagator approach
• Experimental setup for the production of ultracold strongly correlated fermionic superfluids of ${}^6$Li
• Multiple condensed phases in attractively interacting Bose systems
• Adiabatic cooling of a tunable Bose-Fermi mixture in an optical lattice
• Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids
• Topological effects on transition temperatures and response functions in three-dimensional Fermi superfluids
• Ground states of atomic Fermi gases in a two-dimensional optical lattice with and without population imbalance
• Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices, Part II: Effects of population imbalance
• Shear Viscosity of Uniform Fermi Gases with Population Imbalance
• Two-dimensional spin-imbalanced Fermi gases at non-zero temperature: Phase separation of a non-condensate
• Statistical mechanics of a Feshbach coupled Bose-Fermi gas in an optical lattice
• Finite Temperature Behaviors of q-deformed Fermi Gases
• Probing the homogeneous spectral function of a strongly interacting superfluid atomic Fermi gas in a trap using phase separation and momentum resolved rf spectroscopy
• Bose condensation of squeezed light