Abstract
We experimentally determined various thermodynamic quantities of interacting two-component fermions at the zero-temperature limit from the Bardeen-Cooper-Schrieffer (BCS) region to the unitarity limit. The obtained results are very accurate in the sense that the systematic error is within 4% around the unitarity limit. Using this advantage, we can compare our data with various many-body theories. We found that an extended ${\it T}$-matrix approximation, which is a strong-coupling theory involving fluctuations in the Cooper channel, well reproduces our experimental results. We also found that the superfluid order parameter ${\it \Delta}$ calculated by solving the ordinary BCS gap equation with the chemical potential of interacting fermions is close to the binding energy of the paired fermions directly observed in a spectroscopic experiment and that obtained using a quantum Monte Carlo method. Since understanding the strong-coupling properties of a superfluid Fermi gas in the BCS-BEC (Bose-Einstein condensation) crossover region is a crucial issue in condensed matter physics and nuclear physics, the results of the present study are expected to be useful in the further development of these fields.
Highlights
A many-body system of fermions interacting with s-wave scattering length a is a fundamental model that extends the ideal Fermi gas model for various interacting Fermi systems
We find that the superfluid order parameter Δ calculated by solving the ordinary BCS gap equation with the chemical potential of interacting fermions is close to the binding energy of the paired fermions directly observed in a spectroscopic experiment and that obtained using a quantum Monte Carlo method
This paper reports experimental determination of thermodynamic quantities for homogeneous fermions interacting with an s-wave scattering length in the zero-temperature limit from the BCS region to the unitarity limit
Summary
A many-body system of fermions interacting with s-wave scattering length a is a fundamental model that extends the ideal Fermi gas model for various interacting Fermi systems. The binding energy of a paired fermion [14], a single-particle excitation spectrum [15,16,17], and internal energy density E [18], which is the ground-state energy per unit volume, have been experimentally determined in the unitary regime Other thermodynamic quantities, such as pressure [18,19], isothermal compressibility [19,20], speed of sound [21], and contact density [17], were measured. We determine the relations among thermodynamic quantities, such as pressure P, number density n, internal energy density E, chemical potential μ, isothermal compressibility κ, and contact density C, for homogeneous spin-1=2 superfluid fermions at the zerotemperature limit from the BCS region to the unitarity limit.
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