Thermodynamic signatures of the polaron-molecule transition in a Fermi gas

Abstract

We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $\downarrow$ impurities attractively interacting with a sea of $\uparrow$ fermions. In the single-impurity limit at zero temperature, there exists the so-called polaron-molecule transition, where the impurity sharply changes its character by binding a $\uparrow$ fermion at sufficiently strong attraction. Using a recently developed variational approach, we calculate the thermodynamic properties of the impurity, and we show that the transition becomes a smooth crossover at finite temperature due to the thermal occupation of excited states in the impurity spectral function. However, remnants of the single-impurity transition are apparent in the momentum-resolved spectral function, which can in principle be probed with Raman spectroscopy. We furthermore show that the Tan contact exhibits a characteristic non-monotonic dependence on temperature that provides a signature of the zero-temperature polaron-molecule transition. For a finite impurity density, we argue that descriptions purely based on the behavior of the Fermi polaron are invalid near the polaron-molecule transition, since correlations between impurities cannot be ignored. In particular, we show that the spin-imbalanced system undergoes phase separation at low temperatures due to the strong attraction between $\uparrow \downarrow$ molecules induced by the Fermi sea. Thus, we find that the impurity spectrum and the induced impurity-impurity interactions are key to understanding the phase diagram of the spin-imbalanced Fermi gas.

15 pages, 9 figures

References in corpus (22)

• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• Weakly bound dimers of fermionic atoms
• Attractive and repulsive Fermi polarons in two dimensions
• Observation of Phase Separation in a Strongly-Interacting Imbalanced Fermi Gas
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Phase diagram of a two-component Fermi gas with resonant interactions
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Repulsive Fermi polarons in a resonant mixture of ultracold ${}^6$Li atoms
• Many-Body Theory of Trion Absorption Features in Two-Dimensional Semiconductors
• Three-boson problem near a narrow Feshbach resonance
• Ultra-cold Polarized Fermi Gases
• Excitation spectra and rf-response near the polaron-to-molecule transition from the functional renormalization group
• Theory of RF-spectroscopy of strongly interacting Fermions
• Trimers, molecules and polarons in imbalanced atomic Fermi gases
• Polaron-molecule transitions in a two-dimensional Fermi gas
• Highly polarized Fermi gases in two dimensions
• Ground state of a tightly bound composite dimer immersed in a Fermi Sea
• Observation of coherent multiorbital polarons in a two-dimensional Fermi gas
• Polarons and Molecules in a Two-Dimensional Fermi Gas
• Decay of polarons and molecules in a strongly polarized Fermi gas
• Radio frequency spectroscopy of a strongly imbalanced Feshbach-resonant Fermi gas

Cited by in corpus (2)

• Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium
• Fermi polarons at finite temperature: Spectral function and rf-spectroscopy