The moving Fermi polaron

Abstract: The Fermi polaron, formed by an impurity interacting with a surrounding Fermi sea, exemplifies the canonical quasiparticle concept as a cornerstone in our description of quantum many-body systems across a wide range of energy scales. Experiments on atomic quantum gases have provided profound insights into the universal nature of the Fermi polaron. While most previous studies have focused on the case of zero impurity momentum, finite-momentum properties have remained largely uncharted. Here, we investigate the moving Fermi polaron by combining a novel Raman acceleration scheme with high-precision radio-frequency spectroscopy, exploring the quasiparticle dispersion relation over a wide range of momenta. We compare our measurements of energy shifts and spectral linewidths with a microscopic theory and reach quantitative agreement for all momenta. For low momenta, we find the energy of the moving polaron to be fully consistent with the Fermi liquid picture of a dressed particle with a constant effective mass. At high momenta, the polaron approaches the behavior of a weakly interacting bare particle, featuring small energy shifts and weak broadening. For intermediate momenta, broadening is generally larger and, most strikingly, the behavior differs for attractive and repulsive polarons. While the repulsive polaron exhibits a smooth connection between both regimes along with a monotonic change of the energy shift, the attractive case shows a peculiar non-monotonic behavior. With increasing momentum, the attractive polaron enters a regime where its energy deviates from the constant effective mass expression and broadening suddenly increases. By comparing this observation with theory, we show that this abrupt behavior coincides with the attractive polaron entering a molecule-hole continuum, where it is no longer the ground state. We interpret this as a motion-induced polaron-molecule transition.

• The paper demonstrates a detailed mapping of momentum-dependent energy shifts and decay properties of moving Fermi polarons using Raman acceleration and RF spectroscopy.
• It reveals a sharp momentum-driven polaron-to-molecule transition near p_F, with contrasting behaviors in attractive and repulsive branches that match T-matrix theory predictions.
• The methodology provides actionable insights for probing non-equilibrium many-body dynamics and tailoring impurity physics in ultracold atomic systems.

Microscopic Properties of the Moving Fermi Polaron

Introduction and Context

This paper presents a detailed study of the Fermi polaron—a fundamental quasiparticle formed by a mobile impurity interacting with a degenerate Fermi sea—focusing specifically on its finite-momentum properties. While the zero-momentum regime of the Fermi polaron is well established, both experimentally and theoretically, little was known about the full momentum-dependent dispersion and decoherence mechanisms at finite $p$. The authors address this gap by employing a novel Raman acceleration technique and high-precision radio-frequency (RF) spectroscopy to systematically probe the polaron's energy shifts and spectral linewidths across a wide range of impurity momenta. Findings are compared with a diagrammatic $T$-matrix theory, and both attractive and repulsive polaronic branches are examined.

Theoretical Foundation: Dispersion and Effective Mass

The polaron's dispersion at low momentum is described by a simple parabolic form with a constant effective mass, $m^*_\downarrow$, which is typically enhanced relative to the bare impurity mass due to medium-induced dressing. In reduced units, the regime of parabolic behavior is limited to $p/p_F \lesssim 1$, with $p_F$ set by the background Fermi sea. Finite-momentum effects lead to a breakdown of the effective-mass picture when $p$ approaches $p_F$ or exceeds it, as two-body processes dominate, dressing is suppressed, and the polaron approaches the behavior of a bare impurity.

Figure 1: Energies of impurity states in the low-momentum regime, showing the parabolic dispersion associated with constant effective mass and the interaction-induced energy shifts for attractive and repulsive branches.

A crucial contrast is revealed between attractive and repulsive branches: for attractive interactions, the energy shift initially increases in magnitude with small momentum before exhibiting a non-monotonic, downward trend, whereas for the repulsive branch, the shift decreases monotonically. The diagrammatic $T$-matrix theory accurately captures this full crossover between low- and high-momentum regimes.

Figure 2: Momentum-dependent energy shift for the attractive (red) and repulsive (blue) polaronic branches according to various theoretical models, highlighting the crossover from parabolic to non-parabolic dispersion.

Experimental Methods: Raman Acceleration and RF Spectroscopy

The experimental system consists of $^{41}$K impurities in an optically trapped Fermi sea of $^6$Li, with interaction strength tunable via a Feshbach resonance. The authors developed a Raman acceleration protocol, allowing for quasi-continuous momentum transfer to the impurity atoms while maintaining negligible perturbation to the background Fermi sea. Momentum kicks up to $T$0 (with $T$1) are achieved, spanning deeply into the high-momentum regime.

Figure 3: Controlled photon momentum transfer to K impurity atoms, enabling precise tuning of the impurity momentum up to many times $T$2.

Impurity energy shifts and spectral line broadenings are then measured via RF injection spectroscopy by driving transitions between a non-interacting reference state and a strongly interacting polaron state. This protocol enables direct extraction of the quasiparticle energy and decoherence effects as a function of the impurity momentum.

Results: Energy Shifts and Spectral Broadening

Momentum-Dependent Energy Shifts

Experimental data reveal a non-monotonic energy shift $T$3 for the attractive polaron: the magnitude initially increases with $T$4, reaches a minimum in the vicinity of $T$5, and then reverses direction as $T$6 increases further. For the repulsive polaron, the energy shift exhibits a smooth, monotonic decrease with increasing momentum.

Figure 4: Effect of photon momentum transfer on the RF spectral peak for the attractive polaron, demonstrating non-monotonic energy shift behavior.

Figure 5: Extracted polaron peak shift as a function of impurity momentum, showing characteristic non-monotonicity for the attractive branch.

These results quantitatively match predictions from the $T$7-matrix theory, with universal scaling in reduced units observed across independent datasets.

Figure 6: Universal representation of measured and theoretical momentum-dependent energy shifts for both attractive and repulsive polarons.

Spectral Linewidths

The linewidth of the polaron spectral peak provides information about quasiparticle decay. For the attractive branch, the linewidth is small at $T$8 but increases rapidly at intermediate $T$9, reaching a maximum before decreasing at higher $m^*_\downarrow$0. This pronounced growth in linewidth coincides with the polaron entering the molecule-hole continuum, where it ceases to be a well-defined ground state and mixes with molecular excitations. For the repulsive polaron, linewidths remain significantly smaller throughout, consistent with the absence of such continuum coupling.

Figure 7: Momentum-dependent linewidths for attractive and repulsive polarons, with the attractive branch exhibiting strong growth at intermediate momenta due to decay into the molecule-hole continuum.

The high-momentum asymptote is well modeled by two-body scattering theory and exhibits universal behavior determined by the effective range of the Feshbach resonance.

Motion-Induced Polaron-Molecule Transition

One of the central findings is the observation of a sharp, motion-induced polaron-to-molecule transition for the attractive branch. As the impurity's momentum exceeds a threshold near $m^*_\downarrow$1, the polaron energy enters the molecule-hole continuum, leading to enhanced decay and a qualitative change in both the energy dispersion and effective mass tensor. The $m^*_\downarrow$2-matrix calculations naturally account for this transition via the Thouless pole condition and reveal a distinct change in the nature of the lowest-lying excitation of the system.

Figure 8: Full energy spectrum as a function of impurity momentum, showing the crossing of the attractive polaron with the molecule-hole continuum.

The onset and effects of this transition are further evidenced by pronounced kinks in the momentum-resolved energy shift and linewidth.

Figure 9: Fine structure of the attractive polaron’s energy shift and linewidth at low momentum, marking the polaron-molecule transition.

Effective-Mass Tensor and Universality

The effective mass tensor, including longitudinal and transverse components, is extracted from the dispersion. For the attractive polaron, both masses are enhanced near $m^*_\downarrow$3, but drop and become anomalously lighter than the bare mass once the polaron is no longer the ground state, reflecting the drastic change in quasiparticle character as it merges with the continuum.

Figure 10: Longitudinal and transverse effective masses for attractive and repulsive polarons as functions of momentum, emphasizing nontrivial behavior across the transition.

Implications and Outlook

These results provide a comprehensive quantitative test of diagrammatic $m^*_\downarrow$4-matrix theory for Fermi polarons spanning low- to high-momentum regimes, verifying its accuracy for both energy and decay properties. The identification and control of the motion-induced polaron-molecule transition open new opportunities for exploring dynamical many-body physics and non-equilibrium phenomena in impurity systems.

Practically, the Raman acceleration and precise spectroscopic toolbox demonstrated here can be generalized to probe polaronic dispersion in a wide class of ultracold atomic mixtures, including extreme mass ratio systems, dipolar gases, or media with spin-orbit coupling, enabling tailored studies of Fermi- and Bose-polaron transport, decoherence, and emergent collective phenomena. The methodology is extensible to dynamical and time-resolved protocols, with implications for quantum simulation of nonequilibrium quasiparticle physics, Anderson orthogonality, and strongly correlated transport.

Conclusion

This work achieves a detailed mapping of the moving Fermi polaron's dispersion relation and spectral properties over a broad range of momenta, confirming the validity of many-body $m^*_\downarrow$5-matrix theory and uncovering distinctive contrasts between attractive and repulsive branches. The discovery of a momentum-driven polaron-to-molecule transition and associated spectral broadening illustrates the richness of finite-momentum impurity physics in Fermi gases. The experimental and theoretical frameworks developed provide a foundation for future investigations into quasiparticle dynamics, emergent transport, and novel quantum phases in ultracold atomic mixtures.