We calculate the momentum distribution n(k) of the Unitary Fermi Gas using Quantum Monte Carlo calculations at finite temperature T/ε_F as well as in the ground state. At large momenta k/k_F, we find that n(k) falls off as C/k^4, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/ε_F and present a comparison with theory. At low T/ε_F, we find that C increases with temperature, and we tentatively identify a maximum around T/ε_F \simeq 0.4. Our calculations are performed on lattices of spatial extent up to N_x = 14 with a particle number per unit volume of \simeq 0.03 - 0.07.
We calculate the one-body temperature Green's (Matsubara) function of the unitary Fermi gas via Quantum Monte Carlo, and extract the spectral weight function $A(p,ω)$ using the methods of maximum entropy and singular value decomposition. From $A(p,ω)$ we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass $m^*$, a mean-field potential $U$, and a gap $Δ$. Below the critical temperature $T_c=0.15\varepsilon_F$ the results for $m^*$, $U$ and $Δ$ can be accurately reproduced using an independent quasiparticle model. We fin…
We investigate the superfluid transition of the Unitary Fermi Gas by means of the Functional Renormalization Group, aiming at quantitative precision. We extract $T_{\rm c}/μ=0.38(2)$ and $Δ/μ=1.04(15)$ for the critical temperature and the superfluid gap at zero temperature, respectively, within a systematic improvement of the truncation for the effective average action. The key new ingredient in comparison to previous approaches consists in the use of regulators which cut off both frequencies and momenta. We incorporate renormalization effects on both the bosonic and the fermionic propagator, …
We propose a phenomenological approach for the equation of state of a unitary Fermi gas. The universal equation of state is parametrised in terms of Fermi-Dirac integrals. This reproduces the experimental data over the accessible range of fugacity and normalised temperature, but cannot describe the superfluid phase transition found in the MIT experiment \cite{ku}. The most sensitive data for compressibility and specific heat at phase transition can, however, befitted by introducing into the grand partition function a pair of complex conjugate zeros lying in the complex fugacity plane slightly …
在局域密度近似下计算了谐波阱中超冷费米气体的热力学性质，使用由Haussmann等人[Phys. Rev. A 75，023610（2007）]开发的BCS到BEC交叉问题的守恒多体形式。我们关注于费什巴赫共振附近的幺正区域，并确定了局域密度和熵分布以及作为总能量E的函数的全局熵S（E）。我们的结果与实验数据和以前的酉费米气体的热力学分析和数值计算结果符合得很好。然而，在T=0和超流转变温度的伯奇参数的值，略有不同。我们表明，以及在超流制度，云边缘附近的原子的去除，使冷却远低于温度已经达到目前为止。
The density of states of a quantum system can be calculated from its definition but, in some cases, this approach is quite cumbersome. Alternatively, the density of states can be deduced from the microcanonical entropy or from the canonical partition function. After discussing the relationship among these procedures, we suggest a simple numerical method, which is equivalent in the thermodynamic limit to perform a Legendre transformation, to obtain the density of states from the Helmholtz free energy. We apply this method to determine the many-body density of states of the unitary Fermi gas, a …
We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures $T$. In this regime, we observe a characteristic $T^2$ dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high $T$, the spectral width decreases again towards the scattering rate of t…
