[Paper Review] Fermi polarons and beyond

Meera M. Parish, Jesper Levinsen|arXiv (Cornell University)|Jun 2, 2023

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper provides a pedagogical theoretical framework for the Fermi polaron problem in three-dimensional ultracold atomic gases, focusing on a mobile impurity in a degenerate Fermi sea. Using variational approaches and renormalization techniques, it accurately describes the polaron's ground state, energy spectrum, and coherent dynamics, with strong agreement to experimental data—particularly in predicting the polaron residue and lifetime via Rabi spectroscopy and injection spectroscopy.

ABSTRACT

These lecture notes give a brief introduction to the so-called Fermi-polaron problem, which explores the behaviour of a mobile impurity introduced into an ideal Fermi gas. While this problem has been considered now for more than a decade in ultracold atomic gases, it continues to generate surprises and insights as new quantum mixtures emerge, both in atomic gases and in the solid state. Here we summarise the basic theory for the Fermi polaron with a focus on the three-dimensional case, although the results can be straightforwardly generalised to two dimensions. Our aim is to provide a pedagogical treatment of the subject and we thus cover fundamental topics such as scattering theory and renormalisation. We discuss the ground state of the Fermi polaron and how it is connected to the phase diagram of the spin-imbalanced Fermi gas, and we also give a brief overview of the energy spectrum and non-equilibrium dynamics. Throughout, we highlight how the static and dynamic behaviour of the Fermi polaron is well described using intuitive variational approaches.

Motivation & Objective

• To provide a pedagogical introduction to the Fermi polaron problem in three-dimensional ultracold atomic gases.
• To explain the behavior of a single mobile impurity in a degenerate Fermi sea using scattering theory and renormalization.
• To connect the Fermi polaron to the phase diagram of spin-imbalanced Fermi gases and many-body transitions.
• To describe experimental probes such as injection spectroscopy and Rabi oscillations for measuring polaron properties.
• To explore open questions in polaron-polaron correlations, few-body bound states, and non-equilibrium dynamics in quantum mixtures.

Proposed method

• Formulates the two-component Fermi gas Hamiltonian with contact interactions and momentum-dependent coupling.
• Applies T-matrix and renormalization techniques to handle strong interactions and divergences in scattering amplitudes.
• Uses a variational ansatz with particle-hole excitations to describe the dressed impurity state and derive equations of motion.
• Calculates the polaron residue and energy shift via the overlap between the dressed state and the non-interacting impurity state.
• Models coherent dynamics using Ramsey interferometry and Rabi spectroscopy to extract the polaron residue and lifetime.
• Analyzes the injection spectrum and population dynamics in Rabi-coupled systems to probe the dressing cloud and many-body correlations.

Experimental results

Research questions

• RQ1 How does a single impurity become dressed by a Fermi sea, and what are the resulting quasiparticle properties such as mass and residue?
• RQ2 What is the role of the medium in mediating transitions and inducing non-trivial many-body effects like the orthogonality catastrophe?
• RQ3 How do coherent dynamics such as Rabi oscillations and Ramsey interference reveal the polaron residue and lifetime?
• RQ4 What is the impact of longer-ranged interactions, such as dipolar or three-body forces, on polaronic behavior?
• RQ5 How do correlations between multiple polarons influence quantum phase transitions and thermalization in out-of-equilibrium systems?

Key findings

• The variational approach with one particle-hole excitation accurately predicts the polaron energy and residue, showing excellent agreement with experimental data.
• The polaron residue is extracted from Rabi oscillations, with the oscillation frequency scaling as $\Omega \simeq \sqrt{Z}\Omega_0$, where $Z$ is the residue.
• Damping in Rabi oscillations provides a direct measurement of the inverse polaron lifetime, consistent with theoretical predictions.
• The injection spectrum reveals the polaron's energy and residue, with the first term in the population dynamics dominated by the non-interacting state at early times.
• The second term in the population dynamics involves the dressing cloud and is inaccessible via linear response, offering new insight into many-body correlations.
• Exotic few-body bound states, such as trimers, are predicted to form in systems with large mass imbalance ($m_\uparrow/m_\downarrow \gtrsim 8.2$), with experimental hints already observed in $^{40}$K-$^6$Li mixtures.