We theoretically investigate the specific heat
CV at constant volume in the normal state of a
p-wave interacting Fermi gas. Including fluctuations in the
p-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how
CV as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime,
CV is shown to be enhanced by
p-wave pairing fluctuations, near the superfluid phase transition temperature
Tc. Similar enhancement of
CV(T≃Tc) is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of
p-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the
p-wave molecular Bose gas regime, and (3) the region between the two, where
p-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a
p-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above
Tc.
Motivated by recent experimental progress, we make an investigation of
p- and
d-wave resonant Bose gas. An explanation of the Nozi\`eres and Schmitt-Rink (NSR) scheme in terms of two-channel model is provided. Different from the
s-wave case, high-partial-wave interaction supports a quasibound state in the weak-coupling regime. Within the NSR approximation, we study the equation of state, critical temperature, and particle population distributions. We clarify the effect of the quasibound state on the phase diagram and the dimer production. A multicritical point where normal phase, atomic superfluid phase, and molecular superfluid phase meet is predicted within the phase diagram. We also show the occurrence of a resonant conversion between solitary atoms and dimers when temperature
kBT approximates the quasibound energy.
We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length,
aF, and the effective range parameter,
re. In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances. By matching two-body scattering properties near a Feshbach resonance to a simple renormalized model potential, a broad resonance is characterized by a small effective range and the gas displays a universal BCS-BEC crossover behavior. On the other hand, for a narrow resonance thermodynamic quantities depend the effective range which may be large and negative at resonance. For increasing values of
−re we find the transition temperature to be suppressed in the crossover region. We furthermore argue for existence of a lower bound of
Tc at fixed coupling for increasing
−re in the crossover region.
We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.
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.
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.