On August 14, 2020, Scott Jensen successfully defended his thesis , “Lattice Auxiliary-Field Quantum Monte Carlo Studies of the Unitary Fermi Gas” (Advisor Yoram Alhassid).
Jensen explained “The unitary Fermi gas describes the limit of strongest possible short-range correlations for a two-species quantum gas. Being a well-defined paradigm of strongly correlated systems, it is of interest to physicists across different disciplines, and has been realized experimentally with ultracold atomic gases. The unitary gas is a superfluid at low temperatures but becomes a normal fluid above a certain critical temperature. A controversy has developed during the last decade regarding the existence and extent of a so-called pseudogap regime, in which pairing correlations (which are responsible for superfluidity) persist above the critical temperature when the system is no longer a superfluid. In collaboration with a former group member Chris Gilbreth, we have developed novel quantum Monte Carlo methods to accurately calculate properties of the unitary gas and have shown that a pseudogap regime, if it exists, is significantly narrower than previously believed.
A fundamental property of quantum many-body systems with short-range interactions is the contact, which measures the probability of two atoms being close to each other and is important for understanding various properties of these systems. The determination of its temperature dependence in the unitary gas has been a major challenge in the last decade for both theorists and experimentalists, with widely different results obtained by different groups, even on a qualitative level. My quantum Monte Carlo calculations of the contact are in remarkable agreement with recent precision measurements by two leading experimental groups (MIT and Swinburne), and provide the best quantitative agreement with these experiments compared with all previous theoretical models.”
Jensen is starting a postdoctoral associate position at the University of Illinois at Urbana-Champaign.
Thesis Abstract: The Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover has been experimentally realized using Feshbach resonance techniques with ultracold atomic Fermi gases of 6Li and 40K. In the middle of this crossover is the unitary Fermi gas (UFG), in which the s-wave scattering length diverges and interactions are strongest. The UFG has many interesting properties including a particularly high critical temperature for superfluidity Tc ~ 0.15 TF (in units of the Fermi temperature TF) and a nearly perfect fluid behavior approaching the Kovtun-Son-Starinet bound on the ratio of shear viscosity to entropy density. It has applications to dilute neutron matter in the crust of neutron stars and is relevant to QCD plasmas. The UFG serves as a paradigm of strongly correlated Fermi superfluids with a proposed pseudogap regime above Tc and below a pairing temperature scale T*. This regime is characterized by a strong suppression of the single-particle spectral weight near the Fermi surface in the absence of coherent pairing and off-diagonal long-range order. The extent of this pseudogap regime in the UFG has been debated extensively and to date remains an open and controversial topic. A less controversial but similarly significant open problem has been the temperature dependence of Tan’s contact in the UFG. The contact is a fundamental property of systems with short-range interactions, which appears in the tail of the momentum distribution and in the high-energy tail of the shear viscosity. Various theories lead to widely different temperature dependence of the contact. We address the possible existence and extent of a pseudogap regime in the UFG and present results for the temperature dependence of the contact.
The UFG is a strongly correlated system and the understanding of its properties requires non-perturbative methods. We have implemented lattice finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods for the UFG in the canonical ensemble to calculate its thermodynamic properties including an energy-staggering pairing gap, the condensate fraction, heat capacity, spin susceptibility, thermal energy and its associated Bertsch parameter, and the contact. We also present novel AFMC optimizations which have allowed us to perform controlled simulations with large lattices and extrapolate to the continuum limit, thus removing systematic errors associated with the finite lattice spacing. Taking the continuum limit in particular has proven crucial in obtaining the correct temperature dependence of the contact. Our AFMC results for the contact are in remarkable agreement with the latest precision ultracold gas experiments across the superfluid phase transition. To address pairing correlations and pseudogap physics without the need for numerical analytic continuation, we calculate the temperature dependence of a model-independent energy-staggering pairing gap which requires the use of the canonical ensemble. Our work provides the first finite-temperature calculation of this observable for the homogeneous UFG. We do not see significant signatures of a pseudogap above our estimated critical temperature of Tc=0.153(7)TF and find an upper bound on the pairing temperature scale of T*~0.17 TF suggesting a significantly narrower pseudogap regime than previously proposed.