The moving Fermi polaron

Technical Summary: The Moving Fermi Polaron

Problem and Motivation
The Fermi polaron, a mobile impurity interacting with a surrounding Fermi sea, serves as a canonical quasiparticle model for quantum many-body systems. While extensive experimental and theoretical work has characterized the polaron at zero momentum ($p=0$), the properties of the polaron at finite momentum remain largely unexplored. Understanding the dispersion relation across a wide range of momenta is crucial for validating the quasiparticle concept, particularly regarding the transition from a low-momentum regime dominated by many-body dressing (effective mass) to a high-momentum regime where the quasiparticle undresses into a bare particle. Previous studies have not systematically mapped the energy shifts and spectral linewidths for both attractive and repulsive interactions over a continuous momentum range, nor have they fully characterized the breakdown of the constant effective mass approximation.

Methodology
The authors combine high-precision experimental measurements with a microscopic diagrammatic T-matrix theory.

• Experimental Platform: The system consists of a dilute gas of $^{41}$K impurity atoms immersed in a deeply degenerate Fermi sea of $^{6}$Li atoms, confined in an optical dipole trap. Interactions are tuned via an interspecies Feshbach resonance near 335 G.
• Momentum Control: A novel, species-selective Raman acceleration scheme is employed to impart well-defined photon momentum kicks to the impurity atoms. This includes a double-pulse scheme combined with trap sloshing to achieve quasi-continuous momentum transfer in the low-momentum regime ($p \lesssim p_F$), and multiple Raman pulses for higher momenta ($p \gg p_F$).
• Spectroscopy: Radio-frequency (RF) injection spectroscopy is used to probe the polaron state. Impurities are transferred from a non-interacting reference state ($K|2\rangle$) to an interacting state ($K|1\rangle$) after momentum transfer. The energy shift ($\Delta E$) and spectral linewidth ($\gamma_{pol}$) of the polaron peak are extracted from the RF spectra.
• Theory: Theoretical predictions are derived using a diagrammatic T-matrix approach at zero temperature, incorporating thermal averaging to account for the finite temperature of the impurity cloud. The theory calculates the impurity self-energy to determine the quasiparticle energy and residue.

Key Contributions and Results
The study systematically maps the dispersion relation and spectral linewidth of Fermi polarons for both attractive and repulsive interactions over a momentum range from $p \approx 0$ to $p \approx 16 p_F$.

1. Quantitative Agreement: Experimental data for energy shifts and linewidths show excellent quantitative agreement with the T-matrix theory across all momentum regimes and for both interaction signs.
2. Low-Momentum Regime ($p \ll p_F$):
   • The attractive polaron exhibits a parabolic dispersion consistent with a constant effective mass ($m^*_\downarrow > m_\downarrow$), resulting in an initial increase in the magnitude of the negative energy shift.
   • The repulsive polaron also follows a parabolic dispersion but shows a monotonic decrease in the positive energy shift.
   • Thermal averaging is shown to be significant, smoothing the spectral features and reducing the contrast of the low-momentum effective mass signature.
3. Intermediate to High-Momentum Regime:
   • Attractive Polaron: The energy shift displays a distinct non-monotonic behavior. After the initial increase in magnitude, the shift decreases, crosses zero, and becomes positive at high momenta. This is accompanied by a sudden, significant increase in spectral linewidth.
   • Repulsive Polaron: The energy shift decreases monotonically with increasing momentum, and the linewidth remains relatively small compared to the attractive case.
   • High-Momentum Limit ($p \gg p_F$): Both branches converge toward the behavior of a weakly interacting bare particle, with energy shifts scaling as $1/p^2$ and positive signs, consistent with unitarity-limited two-body scattering.
4. Motion-Induced Polaron-Molecule Transition:
   • The abrupt increase in linewidth and the non-monotonic energy shift of the attractive polaron are identified as signatures of a transition where the polaron enters the molecule-hole continuum.
   • At a critical momentum (near $p_F$), the attractive polaron ceases to be the ground state, becoming an excited state above the molecule-hole continuum. This opens new decay channels, leading to the observed broadening.
   • The repulsive polaron, being a metastable state above the continuum, does not exhibit this sharp transition and evolves more smoothly.

Significance
The paper establishes a comprehensive understanding of the moving Fermi polaron, bridging the gap between the low-momentum Fermi liquid picture and the high-momentum two-body scattering regime. The primary significance lies in the experimental observation and theoretical confirmation of the motion-induced polaron-molecule transition. This phenomenon demonstrates that the stability of a quasiparticle is not static but depends on its momentum; specifically, the attractive polaron loses its ground-state character and acquires a finite lifetime as it enters the molecule-hole continuum. The work validates the diagrammatic T-matrix approach as a robust tool for describing quasiparticles across diverse momentum scales and provides a benchmark for future studies on transport properties, finite impurity concentrations, and more complex many-body environments.