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Physical Review A

Methods for studying Tan's contact in the BCS-BEC crossover

Manuel Jäger, Johannes Hecker Denschlag

Published Jun 25, 2024• 6 citations
Publisher

Abstract

In a parallel publication [Phys. Rev. Lett. 132, 263401 (2024)] we demonstrate that photoinduced two-body loss can be used to measure Tan's contact with high precision in a two-component Fermi gas. Here, in the present companion paper, we provide relevant background information on this work and describe in detail the methodology for both the experiments and the data analysis. We first review various theoretical approaches for calculating the contact and identify areas in phase space of the spin-balanced Fermi gas where Tan's contact has not yet been determined. Next, we provide detailed information on our experimental methods, in particular, explaining the measurement and calibration procedures to achieve a high-precision results for the contact. Afterwards, we study the variation of the decay laws of two-body loss in a Fermi gas in the crossover from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein-condensate (BEC) regime, verifying previous predictions. Finally, we determine the closed-channel fraction of the Fermi gas and compare it to previous measurements and theoretical calculations.

DOI
10.1103/physreva.109.063330

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In a parallel publication [Phys. Rev. Lett. 132, 263401 (2024)] we demonstrate that photoinduced two-body loss can be used to measure Tan's contact with high precision in a two-component Fermi gas. Here, in the present companion paper, we provide relevant background information on this work and describe in detail the methodology for both the experiments and the data analysis. We first review various theoretical approaches for calculating the contact and identify areas in phase space of the spin-balanced Fermi gas where Tan's contact has not yet been determined. Next, we provide detailed information on our experimental methods, in particular, explaining the measurement and calibration procedures to achieve a high-precision results for the contact. Afterwards, we study the variation of the decay laws of two-body loss in a Fermi gas in the crossover from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein-condensate (BEC) regime, verifying previous predictions. Finally, we determine the closed-channel fraction of the Fermi gas and compare it to previous measurements and theoretical calculations.
We study two-body correlations in a spin-balanced ultracold harmonically trapped Fermi gas of ^{6}Li atoms in the crossover from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein-Condensate (BEC) regime. For this, we precisely measure Tan's contact using a novel method based on photoexcitation of atomic pairs, which was recently proposed by Wang et al. [Photoexcitation measurement of Tan's contact for a strongly interacting Fermi gas, Phys. Rev. A 104, 063309 (2021).PLRAAN2469-992610.1103/PhysRevA.104.063309]. We map out the contact in the entire phase diagram of the BCS-BEC crossover for various temperatures and interaction strengths, probing regions in phase space that have not been investigated yet. Our measurements reach an uncertainty of ≈2% at the lowest temperatures and thus represent a precise quantitative benchmark. By comparison to our data, we localize the regions in phase space where theoretical predictions and interpolations give valid results. In regions where the contact is already well known we find excellent agreement with our measurements. Thus, our results demonstrate that photoinduced loss is a precise probe to measure quantum correlations in a strongly interacting Fermi gas.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T=0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover.
The crossover from weak-coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that have realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. Although our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport, and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics—quark-gluon plasmas, gauge-gravity duality, and high-temperature superconductivity—and conclude with open questions about strongly interacting Fermi gases.
Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform T=0T=0T=0 ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.
The nature of the normal phase of an ultracold Fermi gas in the BCS-BEC crossover regime is an interesting and unresolved question. As interactions increase, while the many-body ground state remains a condensate of paired fermions, the normal state must evolve from a Fermi liquid to a Bose gas of molecules. In this thesis, I present a technique to spatially select a homogeneous sample from the center of a trapped gas to explore this crossover. Combining this technique with RF spectroscopy, we locally measure Tan's contact as a function of temperature and compare to various many-body theories. In another experiment, we measure the distribution of single-particle energies and momenta for a normal gas across the BCS-BEC crossover. We find that the data fit well to a two-part function that includes a peak corresponding to fermionic quasiparticles and an "incoherent background" that is modeled using the dispersion of thermal molecules. I also describe the construction of a new-generation Fermi gas apparatus.
We derive the universal high momentum factorization of the fermion self-energy in the BCS-BEC crossover of ultracold atoms using nonperturbative quantum field theoretical methods. This property is then employed to compute the Tan contact as a function of interaction strength, temperature, and chemical potential or density. We clarify the mechanism of the factorization from an analysis of the self-consistent Schwinger--Dyson equation for the fermion propagator and compute the perturbative contact on the BCS and Bose--Einstein condensate (BEC) sides within this framework. A functional renormalization group approach is then put forward, which makes it possible to determine the contact over the whole crossover and, in particular, for the unitary Fermi gas. We present numerical results from an implementation of the renormalization group equations within a basic truncation scheme.