Fermi Polaron: Quasiparticle Dynamics

• Fermi polaron is a quasiparticle formed by an impurity immersed in a Fermi sea, characterized by particle–hole dressing and notable energy shifts.
• Theoretical frameworks like the ladder T-matrix and Chevy variational ansatz quantify observables such as the quasiparticle residue, effective mass, and dispersion features.
• Experimental and numerical studies in ultracold gases and neutron matter illustrate transitions between attractive and repulsive branches, molecule formation, and non-equilibrium dynamics.

A Fermi polaron is the quasiparticle formed when a single impurity is immersed in a degenerate Fermi sea and becomes dressed by the bath’s particle–hole excitations. In ultracold gases it is realized as a spin-$\downarrow$ impurity in a homogeneous, non-interacting spin-$\uparrow$ Fermi sea; more broadly it is the paradigmatic mobile-impurity problem in a spin-polarized Fermi medium and a canonical realization of the quasiparticle concept. Its central observables are the polaron energy, quasiparticle residue, effective mass, spectral linewidth, and spectral function, and its phenomenology includes attractive and repulsive branches, molecule formation, finite-momentum instabilities, and non-equilibrium dressing under drive or dissipation (Parish et al., 2023, Ramachandran et al., 2024).

1. Microscopic formulation

In three dimensions, the standard short-range model is a two-component Fermi Hamiltonian with one mobile impurity,

$$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$

with $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$ and a bare contact coupling $g<0$. The zero-range interaction is renormalized through the $s$-wave scattering length $a$,

$$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$

where $m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$ is the reduced mass. In vacuum the on-shell scattering amplitude is

$f(k)\;=\;-\frac{1}{a^{-1}+ik}.$

These relations encode the universal short-range limit used in ladder and variational descriptions (Parish et al., 2023).

In two dimensions, the contact interaction is instead parameterized by the bound-state energy $\uparrow$0 or the scattering length $\uparrow$1,

$\uparrow$2

and the natural interaction parameter is $\uparrow$3. The weakly attractive regime corresponds to $\uparrow$4, whereas strong attraction is reached for $\uparrow$5 (Koschorreck et al., 2012).

A standard many-body description uses either a ladder $\uparrow$6-matrix or the Chevy variational ansatz. In the simplest zero-momentum ansatz one keeps the bare impurity plus one particle–hole excitation,

$\uparrow$7

Equivalently, one introduces the impurity Green’s function and self-energy,

$\uparrow$8

The quasiparticle residue is the pole strength,

$\uparrow$9

and in the variational language it is the bare-impurity overlap $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$0 (Parish et al., 2023).

2. Attractive and repulsive branches

At $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$1 and low temperature, the spectral function displays two sharp $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$2-peaks plus a broad continuum in between: the attractive polaron is the ground-state branch and the repulsive polaron is the metastable upper branch. In weak three-dimensional coupling, $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$3; toward unitarity the residue decreases to a minimum of order $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$4, while the effective mass $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$5 grows from $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$6 to a value slightly above $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$7 near $$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$8 (Parish et al., 2023).

The transition from a fermionic polaron to a dressed molecule is a central organizing feature. For equal masses in three dimensions, the lecture-note summary places the crossing at

$$\hat H \;=\; \sum_{\mathbf{k},\sigma=\uparrow,\downarrow} \epsilon_{\mathbf{k}\sigma}\,\hat c_{\mathbf{k}\sigma}^\dagger \hat c_{\mathbf{k}\sigma} \;+\; \frac{g}{V}\sum_{\mathbf{k},\mathbf{k}',\mathbf{q}} \hat c_{\mathbf{k}+\mathbf{q}\,\uparrow}^\dagger \hat c_{\mathbf{k}'-\mathbf{q}\,\downarrow}^\dagger \hat c_{\mathbf{k}'\,\downarrow} \hat c_{\mathbf{k}\,\uparrow},$$9

while a unified variational ansatz with up to two particle–hole excitations reports

$\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$0

That same V-2ph analysis interprets the transition as a first-order change between a minimum at $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$1 and a minimum at $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$2, with the strong-coupling molecule ansatz emerging as the asymptotic limit of the $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$3 state and with an $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$4 degeneracy in three dimensions and $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$5 in two dimensions (Peng et al., 2021).

A different variational reinterpretation emphasizes coexistence. In that description the dispersion $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$6 evolves from a single minimum at $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$7 to two local minima at $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$8 and $\epsilon_{\mathbf{k}\sigma}=k^2/(2m_\sigma)$9, then to a single minimum at $g<0$0; the transition criterion is

$g<0$1

numerically at

$g<0$2

with a coexistence window

$g<0$3

This suggests that the precise transition location is sensitive to the variational space and to whether the emphasis is on a strict single-impurity crossing or on finite-momentum coexistence at low but finite density (Cui, 2020).

In two dimensions, the attractive-polaron to dimer crossing is also experimentally accessible. Theory summarized from Parish (2011) predicts a crossing at $g<0$4, while momentum-resolved photoemission measurements give

$g<0$5

identified through vanishing quasiparticle weight and a divergence of the fitted effective mass on the attractive branch. The same experiments observe metastable repulsive polarons with lifetimes from a few$g<0$6 to $g<0$7 (Koschorreck et al., 2012).

The two-dimensional spectral theory has also been placed on a rigorous operator-theoretic footing: for a Fermi polaron in a two-dimensional box, a Birman–Schwinger-type variational principle links low-lying eigenvalues to zero-modes of an auxiliary operator and shows that the polaron and molecule energies computed in the physics literature are upper bounds to the ground-state energy (Griesemer et al., 2018).

3. Dispersion, finite momentum, and motion-induced instabilities

Beyond the $g<0$8 problem, the moving Fermi polaron is characterized by a momentum-dependent pole of the impurity Green’s function,

$g<0$9

At low momentum $s$0, the dispersion has the Fermi-liquid form

$s$1

with $s$2. The measured interaction-induced shift

$s$3

then follows

$s$4

so its initial curvature is opposite for attractive and repulsive branches (Hennebichler et al., 19 Jun 2026).

At high momentum $s$5, the bath acts as a uniform background of density $s$6 and Fermi blocking becomes negligible. In that limit,

$s$7

so $s$8 and the linewidth crosses over to the unitarity-limited two-body collision rate (Hennebichler et al., 19 Jun 2026).

Experimentally, a Raman acceleration scheme combined with high-precision rf injection spectroscopy has mapped $s$9 and $a$0 over $a$1 in a dilute cloud of $a$2 impurities in a $a$3 Fermi sea near a $a$4 interspecies Feshbach resonance. At low momentum the dispersion follows $a$5 with $a$6 at $a$7; at high momentum both attractive and repulsive branches converge to the same repulsive shift $a$8 and weak broadening $a$9 (Hennebichler et al., 19 Jun 2026).

The intermediate regime is branch-dependent. The repulsive polaron connects smoothly between the low- and high-momentum limits and exhibits a monotonic change of the energy shift. The attractive branch is non-monotonic: its energy deviates from the constant-effective-mass form, its broadening rises abruptly, and the experiment identifies a zero crossing at $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$0. Theory attributes this kink-plus-broadening feature to the attractive polaron entering a molecule–hole continuum at a critical momentum $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$1, a motion-induced polaron–molecule transition (Hennebichler et al., 19 Jun 2026).

Dimensional confinement modifies even the zero-momentum phase structure. In quasi-two-dimensional gases described by an effective two-channel model, the critical coupling of the polaron–molecule transition is non-universal and depends on density, or equivalently on $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$2; for equal masses and $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$3, one finds

$$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$4

The same non-universality affects the excited repulsive polaron branch (Shi et al., 2021).

4. Finite temperature, finite impurity concentration, and thermodynamics

At nonzero temperature and finite impurity concentration $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$5, the single-impurity description is replaced by a self-consistent many-body $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$6-matrix theory. In the extended $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$7-matrix approximation,

$$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$8

with $$\frac{1}{g(\Lambda)} \;=\; \frac{m_r}{2\pi\,a} \;-\;\frac{1}{V}\sum_{|\mathbf{k}|<\Lambda}\frac{1}{2\epsilon_{\mathbf{k}}},$$9. In the $m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$0 limit this reduces to the standard non-self-consistent $m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$1-matrix theory, whereas at finite $m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$2 the feedback through $m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$3 generates an induced polaron–polaron interaction (Tajima et al., 2018).

Several finite-$m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$4, finite-$m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$5 effects are explicit. The majority chemical potential is shifted below $m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$6 according to

$m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$7

The impurity chemical potential is thermally depleted; from the low-momentum attractive-polaron branch one obtains a Boltzmann-like relation implying

$m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$8

At finite impurity fraction, the attractive branch shows a weak upward shift with increasing $m_r^{-1}=m_\uparrow^{-1}+m_\downarrow^{-1}$9 in the strong-coupling region, interpreted as a repulsive Landau-Fermi-liquid–type residual interaction between dressed polarons, and the effective mass decreases with temperature, indicating weaker dressing (Tajima et al., 2018).

Thermodynamic benchmarks at strong coupling are now available from finite-temperature auxiliary-field quantum Monte Carlo in the canonical ensemble with $f(k)\;=\;-\frac{1}{a^{-1}+ik}.$0 fixed and $f(k)\;=\;-\frac{1}{a^{-1}+ik}.$1. In the regime $f(k)\;=\;-\frac{1}{a^{-1}+ik}.$2 and $f(k)\;=\;-\frac{1}{a^{-1}+ik}.$3, the average sign remains $f(k)\;=\;-\frac{1}{a^{-1}+ik}.$4–$f(k)\;=\;-\frac{1}{a^{-1}+ik}.$5, enabling controlled calculations of Tan’s contact and the thermal energy gap (Ramachandran et al., 2024).

At unitarity, the contact increases with temperature for $f(k)\;=\;-\frac{1}{a^{-1}+ik}.$6: $f(k)\;=\;-\frac{1}{a^{-1}+ik}.$7 The thermal energy gap

$f(k)\;=\;-\frac{1}{a^{-1}+ik}.$8

is a monotonically increasing function of temperature at unitarity, with

$f(k)\;=\;-\frac{1}{a^{-1}+ik}.$9

These data show that heating weakens quasiparticle binding while short-range correlations, as measured by the contact, can increase over a substantial low-temperature interval (Ramachandran et al., 2024).

5. Driven and dissipative Fermi polarons

The driven Fermi polaron introduces coherent coupling between two internal states of the impurity. In a homogeneous $\uparrow$00 Fermi gas, impurities are prepared initially in a weakly interacting state $\uparrow$01, while an rf field of Rabi frequency $\uparrow$02 mixes $\uparrow$03 with a strongly interacting state $\uparrow$04 at unitarity. In the rotating frame, the Hamiltonian contains the internal-state coupling term

$\uparrow$05

in addition to state-dependent contact interactions with the bath (Vivanco et al., 2023).

A steady-state spectroscopy is defined from the impurity magnetization

$\uparrow$06

After a long rf pulse, the measured magnetization collapses onto

$\uparrow$07

so the zero crossing $\uparrow$08 directly yields the driven-polaron energy,

$\uparrow$09

On resonance, $\uparrow$10 exhibits damped Rabi oscillations,

$\uparrow$11

from which one extracts the decay rate $\uparrow$12 and the renormalized Rabi frequency $\uparrow$13. Within the equilibrium-spectral-function picture,

$\uparrow$14

At weak drive, $\uparrow$15, the attractive polaron is recovered with $\uparrow$16 and $\uparrow$17. For $\uparrow$18–$\uparrow$19, however, the extracted residue rises above unity, reaching $\uparrow$20; microscopically the upper dressed-state branch hybridizes and merges with an incoherent continuum, and the usual Taylor expansion of $\uparrow$21 at $\uparrow$22 breaks down (Vivanco et al., 2023).

Dissipative dynamics can also stabilize new impurity branches. In the quantum-Zeno Fermi polaron, a two-dimensional impurity is subjected to momentum-dependent loss,

$\uparrow$23

For $\uparrow$24, the attractive peak broadens and merges into the continuum. In the strongly dissipative limit $\uparrow$25, virtual processes into the dissipative subspace are projected out, the impurity dynamics is confined to $\uparrow$26, and a new long-lived attractive-polaron branch re-emerges for $\uparrow$27. In this Zeno limit the pole equation has the same form as in a lossless medium but with an effective Fermi circle $\uparrow$28; the branch width saturates and becomes independent of $\uparrow$29 (Wasak et al., 2019).

These driven and dissipative constructions show that the Fermi polaron is not restricted to equilibrium quasiparticle physics. It remains meaningful as a spectroscopic object deep into regimes where $\uparrow$30, linewidths, and even the existence of a narrow Lorentzian pole cease to obey equilibrium expectations (Vivanco et al., 2023, Wasak et al., 2019).

6. Generalizations, alternative platforms, and non-universal extensions

The neutral short-range benchmark is not exhaustive. In atom–ion hybrid systems, the impurity is a mobile ion of mass $\uparrow$31 interacting with a polarized Fermi gas through a regularized long-range polarization potential of Buckingham form,

$\uparrow$32

Zero-temperature fixed-node diffusion Monte Carlo finds large density inhomogeneities around the ion, with $\uparrow$33 at $\uparrow$34 for $\uparrow$35. At strong coupling, the polaron energy becomes much deeper than ladder predictions, the effective mass reaches $\uparrow$36 near $\uparrow$37, and the residue vanishes continuously as $\uparrow$38, yielding a smooth polaron–molecule crossover rather than the first-order crossing familiar from the neutral short-range case (Pessoa et al., 2024).

In low-density spin-polarized neutron matter, a spin-down neutron immersed in a free spin-up Fermi sea exhibits polaron parameters very close to the unitary ultracold-atom problem. For $\uparrow$39, Brueckner–Hartree–Fock calculations with either the Entem–Machleidt N$\uparrow$40LO interaction or Argonne V18 give

$\uparrow$41

These values are compatible with state-of-the-art quantum Monte Carlo for the attractive Fermi polaron in ultracold atomic gases and support a quantitative universality between dilute neutron matter and unitary atomic systems (Vidana, 2021).

The static-impurity limit provides an exactly solvable reference point. For an infinitely heavy impurity, Fumi’s theorem expresses the zero-temperature energy shift in terms of scattering phase shifts,

$\uparrow$42

In the zero-range $\uparrow$43-wave limit, this yields the closed-form result

$\uparrow$44

which reduces to the mean-field shift $\uparrow$45 at weak coupling and gives $\uparrow$46 at unitarity. Finite effective range and higher partial waves enter naturally in this framework and are relevant for ionic and Rydberg polarons, mass-imbalanced mixtures, and impurity-in-tweezer experiments (Yegovtsev, 27 Aug 2025).

Long-range interactions also change the underlying effective theory. In a Thomas–Fermi treatment of a single impurity interacting with a Fermi gas via a bounded slowly varying potential, the two-dimensional problem reduces exactly to a Landau–Pekar functional,

$\uparrow$47

so the Fermi polaron is fully bosonized in two dimensions. In $\uparrow$48, the impurity self-interacts with an infinite number of its own images, producing an infinite series of many-body kernels and a self-trapping transition that is second order in $\uparrow$49 and first order in $\uparrow$50 (Myśliwy et al., 2023).

Solid-state realizations further broaden the concept. In charge-tunable monolayer $\uparrow$51 embedded in a microcavity, cavity spectroscopy reveals strongly bound trion and polaron resonances, with oscillator strength transferred from the higher-energy repulsive-exciton-polaron resonance to the lower-energy attractive-polaron manifold as electron density increases; simultaneous attractive- and repulsive-branch polariton formation realizes an ultra-light-impurity regime not available in cold atoms (Sidler et al., 2016). In strained transition-metal dichalcogenides, the attractive Fermi polaron acquires a fine-structure splitting polarized along the principal strain axes, with the leading scaling

$\uparrow$52

reflecting the combined effect of excitonic splitting and Fermi-sea dressing (Iakovlev et al., 2023).

Taken together, these extensions show that “Fermi polaron” denotes not a single model but a class of impurity quasiparticles whose precise character depends on dimensionality, range, recoil, bath correlations, and external control. The short-range neutral-atom problem remains the benchmark, but current work increasingly uses it as a reference theory for neutron matter, atom–ion hybrids, exciton–electron systems, cavity polaritons, and driven or dissipative many-body media (Pessoa et al., 2024, Vidana, 2021, Yegovtsev, 27 Aug 2025, Myśliwy et al., 2023, Sidler et al., 2016, Iakovlev et al., 2023).