Ultracold atomic gases with short-range interactions are characterized by a number of universal species-independent relations. Many of these relations involve the two-body Tan contact. Employing the canonical ensemble, we determine the Tan contact for small harmonically trapped two-component Fermi gases at unitarity over a wide range of temperatures, including the zero and high-temperature regimes. A cluster expansion that describes the properties of the
N-particle system in terms of those of smaller subsystems is introduced and shown to provide an accurate description of the contact in the high-temperature regime. Finite-range corrections are quantified and the role of the Fermi statistics is elucidated by comparing results for Fermi, Bose, and Boltzmann statistics.
The recently discovered universal thermodynamic behavior of dilute, strongly interacting Fermi gases also implies a universal structure in the many-body pair-correlation function at short distances, as quantified by the contact . Here, we theoretically calculate the temperature dependence of this universal contact for a Fermi gas in free space and in a harmonic trap. At high temperatures above the Fermi degeneracy temperature, T ≳ T F , we obtain a reliable non-perturbative quantum virial expansion up to third order. At low temperatures, we compare different approximate strong-coupling theories. These make different predictions, which need to be tested either by future experiments or by advanced quantum Monte Carlo simulations. We conjecture that in the universal unitarity limit, the contact or correlation decreases monotonically with increasing temperature, unless the temperature is significantly lower than the critical temperature, T ≪ T c ∼0.2 T F . We also discuss briefly how to measure the universal contact in either homogeneous or harmonically trapped Fermi gases.
A quantity known as the contact is a fundamental thermodynamic property of quantum many-body systems with short-range interactions. Determination of the temperature dependence of the contact for the unitary Fermi gas of infinite scattering length has been a major challenge, with different calculations yielding qualitatively different results. Here we use finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods on the lattice within the canonical ensemble to calculate the temperature dependence of the contact for the homogeneous spin-balanced unitary Fermi gas. We extrapolate to the continuum limit for 40, 66, and 114 particles, eliminating systematic errors due to finite-range effects. We observe a dramatic decrease in the contact as the superfluid critical temperature is approached from below, followed by a gradual weak decrease as the temperature increases in the normal phase. Our theoretical results are in excellent agreement with the most recent precision ultracold atomic gas experiments. We also present results for the energy as a function of temperature in the continuum limit.
We investigate the superfluid properties of a one-component Fermi gas with a uniaxially anisotropic
p-wave pairing interaction,
Ux>Uy=Uz [where
Ui(i=x,y,z) is a
pi-wave pairing interaction]. This type of interaction is considered to be realized in a
40K Fermi gas. Including pairing fluctuations within a strong-coupling
T-matrix theory, we determine the
px-wave superfluid phase transition temperature
Tcpx, as well as the other phase transition temperature
Tcpx+ipy(<Tcpx), below which the superfluid order parameter has the
px+ipy-wave symmetry. In the normal state near
Tcpx,px-wave pairing fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a dip structure in the angle-resolved density of states around $\ensuremath{\omega}=0$ is the most remarkable in the
px direction. In the
px-wave superfluid phase $({T}_{\mathrm{c}}^{{p}_{x}+i{p}_{y}}<T\ensuremath{\le}{T}_{\mathrm{c}}^{{p}_{x}})$, while the pseudogap in the
px direction continuously changes to the superfluid gap, the pseudogap in the perpendicular direction to the
px axis is found to continue developing because of enhanced
py-wave and
pz-wave pairing fluctuations around the node of the
px-wave superfluid order parameter. Since pairing fluctuations are always suppressed in the isotropic
s-wave superfluid state, this phenomenon is peculiar to an unconventional Fermi superfluid with a nodal superfluid order parameter. Since the
p-wave Fermi superfluid is the most promising non-
s-wave pairing state in an ultracold Fermi gas, our results would contribute to understanding how the anisotropic pairing fluctuations, as well as the existence of plural superfluid phases, affect many-body properties of this unconventional Fermi superfluid.
We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined
T-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature
Tc, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures
T∗ and
T∗∗ at which the pseudogap structures in these quantities completely disappear. Determining
T∗ and
T∗∗ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by the JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal-state properties of this strongly interacting Fermi system.
The contact I, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter 1/(k(F)a), where k(F) is the Fermi wave vector and a is the s-wave scattering length, and the temperature T/T(F), where T(F) is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.