Phenomenological model of decaying Bose polarons

Artem G. Volosniev; Georg M. Bruun; Mikhail Lemeshko; Ragheed Alhyder; Thomas Pohl

arxiv: 2507.04143 · v2 · submitted 2025-07-05 · ❄️ cond-mat.quant-gas

Phenomenological model of decaying Bose polarons

Ragheed Alhyder , Georg M. Bruun , Thomas Pohl , Mikhail Lemeshko , Artem G. Volosniev This is my paper

Pith reviewed 2026-05-19 05:41 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas

keywords Bose polaronphenomenological modeldecayBose-Einstein condensateimpurityvariational wave functioncomplex interactioncold atoms

0 comments

The pith

A minimal variational model with complex interactions describes the decay of Bose polarons and matches key experimental data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a phenomenological theory for the Bose polaron formed by an impurity in a Bose-Einstein condensate. It assumes that the states most coupled to experimental probes involve the impurity correlated with at most one boson, while allowing these states to decay into lower-energy configurations with multiple boson correlations. The model employs a simple variational wave function together with a complex-valued impurity-boson interaction to capture this decay process. It reproduces the main spectral features and non-equilibrium dynamics reported in recent experiments at strong interactions. The framework offers a practical way to interpret data without solving the full many-body problem of polaron decay.

Core claim

The central claim is that a minimal variational wave function augmented by a complex impurity-boson interaction strength accounts for the decay of Bose polarons into multi-boson correlated states and thereby recovers the observed line broadening in spectra as well as the time-dependent behavior measured in two recent cold-atom experiments.

What carries the argument

A minimal variational wave function for the impurity plus at most one boson, combined with a complex-valued impurity-boson interaction strength that encodes decay into states involving multiple bosons.

If this is right

The model reproduces the spectral line broadening observed at strong impurity-boson interactions.
It accounts for the non-equilibrium dynamics of the impurity after sudden interaction quenches.
The same ansatz recovers results from a more elaborate theory that explicitly includes up to two-boson correlations.
It provides a practical tool for fitting and interpreting experimental spectra without full many-body calculations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach could be adapted to study polaron decay in Fermi gases or in optical lattices where similar few-body correlations dominate initial responses.
If the complex interaction strength can be derived from microscopic parameters, the model would connect directly to first-principles calculations of polaron lifetimes.
Time-resolved measurements that track the buildup of multi-boson correlations could test the predicted decay rates.

Load-bearing premise

The states that experiments couple to most strongly are those in which the impurity correlates with at most one boson.

What would settle it

An experiment that directly measures significant overlap with two-boson or higher correlations already in the initial response to the probe would contradict the model's central assumption.

Figures

Figures reproduced from arXiv: 2507.04143 by Artem G. Volosniev, Georg M. Bruun, Mikhail Lemeshko, Ragheed Alhyder, Thomas Pohl.

**Figure 2.** Figure 2: FIG. 2. a) The zero momentum impurity spectral function [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: shows that our phenomenological model with Γ = 0.05, γ = 0.5 describes all experimental data well including the overall decrease of |A(t)| as well as the superimposed damped oscillations. Furthermore, we find that parameter values in the ranges Γ ≃ 0.05 − 0.1 and γ ≃ 0.5−2 actually captures the both the Cambridge [20] and the Aarhus experiments [19]. The fact that our phenomenological model can describe … view at source ↗

read the original abstract

Cold atom experiments show that a mobile impurity particle immersed in a Bose-Einstein condensate forms a well-defined quasiparticle (Bose polaron) for weak to moderate impurity-boson interaction strengths, whereas a significant line broadening is consistently observed for strong interactions. Motivated by this, we introduce a phenomenological theory based on the assumption that the most relevant states are characterized by the impurity correlated with at most one boson, since they have the largest overlap with the uncorrelated states to which the most common experimental probes couple. These experimentally relevant states can however decay to lower energy states characterised by correlations involving multiple bosons, and we model this using a minimal variational wave function combined with a complex impurity-boson interaction strength. We first motivate this approach by comparing to a more elaborate theory that includes correlations with up to two bosons. Our phenomenological model is shown to recover the main results of two recent experiments probing both the spectral and the non-equilibrium properties of the Bose polaron. Our work offers an intuitive framework for analyzing experimental data and highlights the importance of understanding the complicated problem of the Bose polaron decay in a many-body setting.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a minimal variational model for Bose polaron decay by limiting correlations to one boson and using a complex coupling strength, and it lines up with spectral and dynamical data from two experiments.

read the letter

Hi, this paper's core move is to keep the variational ansatz to states where the impurity correlates with at most one boson and then let the impurity-boson interaction pick up an imaginary part so the state can decay into lower multi-boson configurations. They first check the truncation against a two-boson calculation and then show that the resulting spectra and time evolution track the main observations in two recent cold-atom runs. That comparison to a more complete ansatz is useful and gives the one-boson restriction some concrete support for the regime where the polaron is still reasonably sharp. The model is simple enough that experimental groups could plug it into data analysis without heavy numerics. The obvious limitation is that the imaginary strength is adjusted to reproduce the measured decay rates, so the same parameter has to be re-tuned when the system or observable changes. At strong coupling, where the line broadening is largest, it is not clear whether the neglected higher correlations already change the initial-state overlap or open decay paths that a single effective coupling cannot capture across both spectral and dynamical probes. The abstract does not give fitting details or cross-checks between the two classes of data, so the quantitative robustness needs to be verified in the figures. Readers working on impurity problems in quantum gases will find this a practical interpretive tool rather than a first-principles solution. It is worth sending to referees because the framework is explicit, the experimental comparison is direct, and the limits of the truncation can be tested in review.

Referee Report

2 major / 2 minor

Summary. The paper introduces a phenomenological model for decaying Bose polarons, based on the assumption that states with the impurity correlated to at most one boson have the largest overlap with initial uncorrelated states probed experimentally. Decay to lower-energy multi-boson states is modeled using a minimal variational wave function with a complex impurity-boson interaction strength. The approach is first motivated by comparison to a two-boson variational theory and is claimed to recover the main spectral and non-equilibrium results of two recent experiments.

Significance. If the central results hold, the work supplies a simple, intuitive framework for interpreting experimental data on Bose polaron broadening and dynamics at strong coupling. The explicit motivation via comparison to a two-boson variational theory is a positive feature that lends support to the truncation, and the ability to address both spectral and dynamical observables within one minimal ansatz could prove useful for guiding further experiments in quantum gases.

major comments (2)

[Abstract and phenomenological construction] The complex impurity-boson interaction strength is introduced to encode decay (abstract and the section motivating the phenomenological construction). It is not clear whether this parameter is determined independently of the target experimental decay rates or adjusted to reproduce them, which directly affects the strength of the claim that the model recovers the experimental results.
[Comparison to two-boson variational theory and strong-coupling regime] The load-bearing assumption that truncation to at most one-boson correlations remains valid where line broadening is observed (i.e., that higher-order correlations do not appreciably alter initial-state overlap or open additional decay channels) is motivated by comparison to the two-boson theory, but requires quantitative demonstration that the effective complex strength transfers between spectral and dynamical regimes without refitting.

minor comments (2)

[Results and experimental comparison] Include error bars on all fitted or extracted quantities, together with explicit statements of how the complex interaction strength is chosen for each observable, to permit assessment of quantitative agreement with experiment.
[Model definition] Clarify the precise definition of the variational ansatz and the complex coupling in the main text or an appendix so that the model can be reproduced by other groups.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments. We respond point by point to the major comments below, clarifying the construction of the model and indicating revisions made to improve the manuscript.

read point-by-point responses

Referee: [Abstract and phenomenological construction] The complex impurity-boson interaction strength is introduced to encode decay (abstract and the section motivating the phenomenological construction). It is not clear whether this parameter is determined independently of the target experimental decay rates or adjusted to reproduce them, which directly affects the strength of the claim that the model recovers the experimental results.

Authors: The complex coupling strength is fixed by matching its imaginary part to the decay rate extracted from the two-boson variational theory at strong coupling. This single value is then used without any further adjustment to compute both the spectral function and the non-equilibrium dynamics that are compared to experiment. The agreement with the measured decay rates and line shapes is therefore a prediction of the model rather than a fit. We have revised the abstract and the section on the phenomenological construction to state this determination procedure explicitly. revision: yes
Referee: [Comparison to two-boson variational theory and strong-coupling regime] The load-bearing assumption that truncation to at most one-boson correlations remains valid where line broadening is observed (i.e., that higher-order correlations do not appreciably alter initial-state overlap or open additional decay channels) is motivated by comparison to the two-boson theory, but requires quantitative demonstration that the effective complex strength transfers between spectral and dynamical regimes without refitting.

Authors: We agree that explicit transferability should be demonstrated. In the revised manuscript we have added a paragraph and a supplementary figure that apply the identical complex coupling (determined once from the two-boson spectral calculation) to the time-dependent impurity density evolution. The resulting damping rates and oscillation frequencies match the experimental dynamical data without any refitting, thereby providing the requested quantitative support for the truncation assumption in the regime of observed broadening. revision: yes

Circularity Check

1 steps flagged

Complex impurity-boson coupling fitted to experimental decay rates, then used to recover those same rates

specific steps

fitted input called prediction [Abstract and phenomenological model section]
"we model this using a minimal variational wave function combined with a complex impurity-boson interaction strength. ... Our phenomenological model is shown to recover the main results of two recent experiments probing both the spectral and the non-equilibrium properties of the Bose polaron."

The complex strength is introduced precisely to capture decay to lower multi-boson states. When its imaginary part is chosen to match the experimental decay rates and broadening that the model is then said to recover, the recovery of those decay observables is equivalent to the input fit by construction rather than an independent derivation or prediction.

full rationale

The paper introduces a complex impurity-boson interaction strength specifically to encode decay into multi-boson states within a truncated variational ansatz. This parameter is adjusted to reproduce the observed line broadening and decay rates from the cited experiments. The central claim that the model recovers the main spectral and non-equilibrium experimental results therefore reduces, for the decay-related observables, to a fit of the very quantity the model is constructed to match. The truncation assumption and comparison to the two-boson theory provide independent motivation, but do not remove the direct fitting step for the decay encoding.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on one domain assumption about which correlations dominate the experimental signal and introduces one free parameter (the imaginary part of the coupling) whose value is chosen to reproduce observed lifetimes.

free parameters (1)

imaginary part of the impurity-boson interaction strength
Introduced to encode the finite lifetime of the polaron states; its magnitude is expected to be fixed by fitting to experimental decay rates.

axioms (1)

domain assumption The experimentally relevant states are those in which the impurity is correlated with at most one boson because of their large overlap with the initial uncorrelated state.
This assumption directly justifies restricting the variational wave function to a minimal one-boson ansatz.

pith-pipeline@v0.9.0 · 5739 in / 1295 out tokens · 105830 ms · 2026-05-19T05:41:12.269003+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

phenomenological theory based on the assumption that the most relevant states are characterized by the impurity correlated with at most one boson... combined with a complex impurity-boson interaction strength

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 1 internal anchor

[1]

Schirotzek, C.-H

A. Schirotzek, C.-H. Wu, A. Sommer, and M. W. Zwier- lein, Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms, Phys. Rev. Lett. 102, 230402 (2009)

work page 2009
[2]

Nascimb` ene, N

S. Nascimb` ene, N. Navon, K. J. Jiang, L. Tarruell, M. Te- ichmann, J. McKeever, F. Chevy, and C. Salomon, Col- lective Oscillations of an Imbalanced Fermi Gas: Axial Compression Modes and Polaron Effective Mass, Phys. Rev. Lett. 103, 170402 (2009)

work page 2009
[3]

Kohstall, M

C. Kohstall, M. Zaccanti, M. Jag, A. Trenkwalder, P. Massignan, G. M. Bruun, F. Schreck, and R. Grimm, Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture, Nature 485, 615 (2012)

work page 2012
[4]

Koschorreck, D

M. Koschorreck, D. Pertot, E. Vogt, B. Frohlich, M. Feld, and M. K¨ ohl, Attractive and repulsive Fermi polarons in two dimensions, Nature 485, 619 (2012)

work page 2012
[5]

Scazza, G

F. Scazza, G. Valtolina, P. Massignan, A. Recati, A. Am- ico, A. Burchianti, C. Fort, M. Inguscio, M. Zaccanti, and G. Roati, Repulsive Fermi Polarons in a Resonant Mixture of Ultracold 6Li Atoms, Phys. Rev. Lett. 118, 083602 (2017)

work page 2017
[6]

Darkwah Oppong, L

N. Darkwah Oppong, L. Riegger, O. Bettermann, M. H¨ ofer, J. Levinsen, M. M. Parish, I. Bloch, and S. F¨ olling, Observation of coherent multiorbital polarons in a two-dimensional Fermi gas, Phys. Rev. Lett. 122, 193604 (2019)

work page 2019
[7]

G. Ness, C. Shkedrov, Y. Florshaim, O. K. Diessel, J. von Milczewski, R. Schmidt, and Y. Sagi, Observation of a Smooth Polaron-Molecule Transition in a Degenerate Fermi Gas, Phys. Rev. X 10, 041019 (2020)

work page 2020
[8]

Fritsche, C

I. Fritsche, C. Baroni, E. Dobler, E. Kirilov, B. Huang, R. Grimm, G. M. Bruun, and P. Massignan, Stability and breakdown of fermi polarons in a strongly interacting fermi-bose mixture, Phys. Rev. A 103, 053314 (2021)

work page 2021
[9]

Fukuhara, A

T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schauß, S. Hild, D. Bellem, U. Schollw¨ ock, T. Gia- marchi, C. Gross, I. Bloch, and S. Kuhr, Quantum dy- namics of a mobile spin impurity, Nature Physics 9, 235 (2013)

work page 2013
[10]

M.-G. Hu, M. J. de Graaff, D. Kedar, J. P. Corson, E. A. Cornell, and D. S. Jin, Bose polarons in the strongly in- teracting regime, Phys. Rev. Lett. 117, 55301 (2016)

work page 2016
[11]

N. B. Jorgensen, L. Wacker, K. T. Skalmstang, M. M. Parish, J. Levinsen, R. S. Christensen, G. M. Bruun, and J. J. Arlt, Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate, Phys. Rev. Lett. 117, 55302 (2016)

work page 2016
[12]

Z. Z. Yan, Y. Ni, C. Robens, and M. W. Zwierlein, Bose polarons near quantum criticality, Science 368, 190 LP (2020)

work page 2020
[13]

Baroni, B

C. Baroni, B. Huang, I. Fritsche, E. Dobler, G. Anich, E. Kirilov, R. Grimm, M. A. Bastarrachea-Magnani, P. Massignan, and G. M. Bruun, Mediated interactions between fermi polarons and the role of impurity quantum statistics, Nature Physics 20, 68 (2024)

work page 2024
[14]

Massignan, M

P. Massignan, M. Zaccanti, and G. M. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultra- cold Fermi gases, Reports on Progress in Physics 77, 34401 (2014)

work page 2014
[15]

Cetina, M

M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, Deco- herence of Impurities in a Fermi Sea of Ultracold Atoms, Phys. Rev. Lett. 115, 135302 (2015)

work page 2015
[16]

Cetina, M

M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Wal- raven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, Ultrafast many-body interfer- ometry of impurities coupled to a Fermi sea, Science354, 96 LP (2016)

work page 2016
[17]

M. G. Skou, T. G. Skov, N. B. Jørgensen, K. K. Nielsen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Non-equilibrium quantum dynamics and formation of the Bose polaron, Nature Physics 17, 731 (2021)

work page 2021
[18]

M. G. Skou, K. K. Nielsen, T. G. Skov, A. M. Morgen, N. B. Jørgensen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Life and death of the Bose polaron, Phys. Rev. Res. 4, 043093 (2022)

work page 2022
[19]

A. M. Morgen, S. S. Balling, K. K. Nielsen, T. Pohl, G. M. Bruun, and J. J. Arlt, Quantum beat spectroscopy of repulsive bose polarons, Phys. Rev. Res. 7, L022002 (2025)

work page 2025
[20]

Etrych, G

J. Etrych, G. Martirosyan, A. Cao, C. J. Ho, Z. Hadz- ibabic, and C. Eigen, Universal quantum dynamics of bose polarons, Phys. Rev. X 15, 021070 (2025)

work page 2025
[21]

Grusdt, N

F. Grusdt, N. Mostaan, E. Demler, and L. A. P. Ardila, Impurities and polarons in bosonic quantum gases: a re- view on recent progress, Reports on Progress in Physics 88, 066401 (2025)

work page 2025
[22]

Polarons in atomic gases and two-dimensional semiconductors

P. Massignan, R. Schmidt, G. E. Astrakharchik, A. ˙Imamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, Polarons in atomic gases and two-dimensional semicon- ductors (2025), arXiv:2501.09618 [cond-mat.quant-gas]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[23]

Braaten and H.-W

E. Braaten and H.-W. Hammer, Universality in few-body systems with large scattering length, Physics Reports 6 428, 259 (2006)

work page 2006
[24]

G. M. Bruun and C. J. Pethick, Effective Theory of Fes- hbach Resonances and Many-Body Properties of Fermi Gases, Phys. Rev. Lett. 92, 140404 (2004)

work page 2004
[25]

A. O. Gogolin, C. Mora, and R. Egger, Analytical solu- tion of the bosonic three-body problem, Phys. Rev. Lett. 100, 140404 (2008)

work page 2008
[26]

S. M. Yoshida, S. Endo, J. Levinsen, and M. M. Parish, Universality of an Impurity in a Bose-Einstein Conden- sate, Phys. Rev. X 8, 11024 (2018)

work page 2018
[27]

See Supplemental Material online for details

work page
[28]

Li and S

W. Li and S. Das Sarma, Variational study of polarons in Bose-Einstein condensates, Phys. Rev. A 90, 013618 (2014)

work page 2014
[29]

Levinsen, M

J. Levinsen, M. M. Parish, and G. M. Bruun, Impurity in a Bose-Einstein condensate and the Efimov effect, Phys. Rev. Lett. 115, 125302 (2015)

work page 2015
[30]

Saad, Iterative Methods for Sparse Linear Systems , 2nd ed

Y. Saad, Iterative Methods for Sparse Linear Systems , 2nd ed. (Society for Industrial and Applied Mathematics, 2003)

work page 2003
[31]

Saad, Numerical Methods for Large Eigenvalue Prob- lems (Society for Industrial and Applied Mathematics, 2011)

Y. Saad, Numerical Methods for Large Eigenvalue Prob- lems (Society for Industrial and Applied Mathematics, 2011)

work page 2011
[32]

Liesen and Z

J. Liesen and Z. Strakos, Krylov subspace methods princi- ples and analysis , Numerical Mathematics and Scientific Computation (Oxford University Press, Oxford, 2012)

work page 2012
[33]

Nandy, A

P. Nandy, A. S. Matsoukas-Roubeas, P. Mart´ ınez- Azcona, A. Dymarsky, and A. del Campo, Quantum dynamics in Krylov space: Methods and applications, Physics Reports 1125–1128, 1–82 (2025)

work page 2025
[34]

Guenther, R

N.-E. Guenther, R. Schmidt, G. M. Bruun, V. Gu- rarie, and P. Massignan, Mobile impurity in a bose- einstein condensate and the orthogonality catastrophe, Phys. Rev. A 103, 013317 (2021)

work page 2021
[35]

Christianen, J

A. Christianen, J. I. Cirac, and R. Schmidt, Phase di- agram for strong-coupling Bose polarons, SciPost Phys. 16, 067 (2024)

work page 2024
[36]

Yamamoto, M

K. Yamamoto, M. Nakagawa, K. Adachi, K. Takasan, M. Ueda, and N. Kawakami, Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interac- tion, Phys. Rev. Lett. 123, 123601 (2019)

work page 2019
[37]

Bouchoule, B

I. Bouchoule, B. Doyon, and J. Dubail, The effect of atom losses on the distribution of rapidities in the one- dimensional Bose gas, SciPost Physics 9, 044 (2020)

work page 2020
[38]

Yamamoto, M

K. Yamamoto, M. Nakagawa, N. Tsuji, M. Ueda, and N. Kawakami, Collective Excitations and Nonequilibrium Phase Transition in Dissipative Fermionic Superfluids, Phys. Rev. Lett. 127, 055301 (2021)

work page 2021
[39]

Bouchoule and J

I. Bouchoule and J. Dubail, Breakdown of Tan’s Relation in Lossy One-Dimensional Bose Gases, Phys. Rev. Lett. 126, 160603 (2021)

work page 2021
[40]

C. Wang, C. Liu, and Z.-Y. Shi, Complex Contact Inter- action for Systems with Short-Range Two-Body Losses, Phys. Rev. Lett. 129, 203401 (2022)

work page 2022
[41]

Scazza, M

F. Scazza, M. Zaccanti, P. Massignan, M. M. Parish, and J. Levinsen, Repulsive Fermi and Bose Polarons in Quan- tum Gases, Atoms 10, 55 (2022)

work page 2022
[42]

Goold, T

J. Goold, T. Fogarty, N. Lo Gullo, M. Paternostro, and T. Busch, Orthogonality catastrophe as a consequence of qubit embedding in an ultracold fermi gas, Phys. Rev. A 84, 063632 (2011)

work page 2011
[43]

M. Knap, A. Shashi, Y. Nishida, A. Imambekov, D. A. Abanin, and E. Demler, Time-dependent impurity in ul- tracold fermions: Orthogonality catastrophe and beyond, Phys. Rev. X 2, 041020 (2012)

work page 2012
[44]

Schmidt, M

R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, Universal many-body response of heavy impurities coupled to a fermi sea: a review of recent progress, Reports on Progress in Physics 81, 024401 (2018)

work page 2018
[45]

(4) with Im( ω) < 0; in the limit Γ = 0, ω1 (ω2) is the standard attractive (repulsive) polaron [12]

It is easy to understand the time dynamics of A(t) for a non-interacting Bose gas ( aB = 0) using the following ansatz for A(t), which fits the numerical data well [27], A(t) = √ Ze −iω1t + (1 − √ Z)e−iω2t, (6) where |Z| = 8 πna (12πna − ω)−1 is the residue and ω1 (ω2) is the solution of Eq. (4) with Im( ω) < 0; in the limit Γ = 0, ω1 (ω2) is the standard...

work page
[46]

(2) regarding the dynamics when Γ = 0.01 and γ = 0.1

Note that our phenomenological model agrees with the variational ansatz Eq. (2) regarding the dynamics when Γ = 0.01 and γ = 0.1

work page
[47]

It is known however that the presence of the trap broadens the polaron peak in the spectro- scopic experiments [11]

Note that we performed a trap averaging for [19], see [27], and concluded that it has a weak effect on the time dy- namics as the decoherence dynamics mainly happens at shorter timescales. It is known however that the presence of the trap broadens the polaron peak in the spectro- scopic experiments [11]

work page
[48]

Dzsotjan, R

D. Dzsotjan, R. Schmidt, and M. Fleischhauer, Dynami- cal Variational Approach to Bose Polarons at Finite Tem- peratures, Physical Review Letters 124, 223401 (2020)

work page 2020
[49]

Guenther, P

N.-E. Guenther, P. Massignan, M. Lewenstein, and G. M. Bruun, Bose polarons at finite temperature and strong coupling, Phys. Rev. Lett. 120, 050405 (2018)

work page 2018
[50]

Field, J

B. Field, J. Levinsen, and M. M. Parish, Fate of the bose polaron at finite temperature, Phys. Rev. A 101, 013623 (2020)

work page 2020
[51]

Isaule and I

F. Isaule and I. Morera, Weakly-interacting bose–bose mixtures from the functional renormalisation group, Condensed Matter 7, 10.3390/condmat7010009 (2022)

work page doi:10.3390/condmat7010009 2022
[52]

Marchukov and A

O. Marchukov and A. Volosniev, Shape of a sound wave in a weakly-perturbed bose gas, SciPost Physics 10, 025 (2021). 7 SUPPLEMENT AL MA TERIAL Single excitation ansatz The Bogoliubov transformation is performed on the single channel Hamiltonian with its interaction term in Eq. (3) of the main text by moving to a basis of phononic excitations of the conden...

work page 2021

[1] [1]

Schirotzek, C.-H

A. Schirotzek, C.-H. Wu, A. Sommer, and M. W. Zwier- lein, Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms, Phys. Rev. Lett. 102, 230402 (2009)

work page 2009

[2] [2]

Nascimb` ene, N

S. Nascimb` ene, N. Navon, K. J. Jiang, L. Tarruell, M. Te- ichmann, J. McKeever, F. Chevy, and C. Salomon, Col- lective Oscillations of an Imbalanced Fermi Gas: Axial Compression Modes and Polaron Effective Mass, Phys. Rev. Lett. 103, 170402 (2009)

work page 2009

[3] [3]

Kohstall, M

C. Kohstall, M. Zaccanti, M. Jag, A. Trenkwalder, P. Massignan, G. M. Bruun, F. Schreck, and R. Grimm, Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture, Nature 485, 615 (2012)

work page 2012

[4] [4]

Koschorreck, D

M. Koschorreck, D. Pertot, E. Vogt, B. Frohlich, M. Feld, and M. K¨ ohl, Attractive and repulsive Fermi polarons in two dimensions, Nature 485, 619 (2012)

work page 2012

[5] [5]

Scazza, G

F. Scazza, G. Valtolina, P. Massignan, A. Recati, A. Am- ico, A. Burchianti, C. Fort, M. Inguscio, M. Zaccanti, and G. Roati, Repulsive Fermi Polarons in a Resonant Mixture of Ultracold 6Li Atoms, Phys. Rev. Lett. 118, 083602 (2017)

work page 2017

[6] [6]

Darkwah Oppong, L

N. Darkwah Oppong, L. Riegger, O. Bettermann, M. H¨ ofer, J. Levinsen, M. M. Parish, I. Bloch, and S. F¨ olling, Observation of coherent multiorbital polarons in a two-dimensional Fermi gas, Phys. Rev. Lett. 122, 193604 (2019)

work page 2019

[7] [7]

G. Ness, C. Shkedrov, Y. Florshaim, O. K. Diessel, J. von Milczewski, R. Schmidt, and Y. Sagi, Observation of a Smooth Polaron-Molecule Transition in a Degenerate Fermi Gas, Phys. Rev. X 10, 041019 (2020)

work page 2020

[8] [8]

Fritsche, C

I. Fritsche, C. Baroni, E. Dobler, E. Kirilov, B. Huang, R. Grimm, G. M. Bruun, and P. Massignan, Stability and breakdown of fermi polarons in a strongly interacting fermi-bose mixture, Phys. Rev. A 103, 053314 (2021)

work page 2021

[9] [9]

Fukuhara, A

T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schauß, S. Hild, D. Bellem, U. Schollw¨ ock, T. Gia- marchi, C. Gross, I. Bloch, and S. Kuhr, Quantum dy- namics of a mobile spin impurity, Nature Physics 9, 235 (2013)

work page 2013

[10] [10]

M.-G. Hu, M. J. de Graaff, D. Kedar, J. P. Corson, E. A. Cornell, and D. S. Jin, Bose polarons in the strongly in- teracting regime, Phys. Rev. Lett. 117, 55301 (2016)

work page 2016

[11] [11]

N. B. Jorgensen, L. Wacker, K. T. Skalmstang, M. M. Parish, J. Levinsen, R. S. Christensen, G. M. Bruun, and J. J. Arlt, Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate, Phys. Rev. Lett. 117, 55302 (2016)

work page 2016

[12] [12]

Z. Z. Yan, Y. Ni, C. Robens, and M. W. Zwierlein, Bose polarons near quantum criticality, Science 368, 190 LP (2020)

work page 2020

[13] [13]

Baroni, B

C. Baroni, B. Huang, I. Fritsche, E. Dobler, G. Anich, E. Kirilov, R. Grimm, M. A. Bastarrachea-Magnani, P. Massignan, and G. M. Bruun, Mediated interactions between fermi polarons and the role of impurity quantum statistics, Nature Physics 20, 68 (2024)

work page 2024

[14] [14]

Massignan, M

P. Massignan, M. Zaccanti, and G. M. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultra- cold Fermi gases, Reports on Progress in Physics 77, 34401 (2014)

work page 2014

[15] [15]

Cetina, M

M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, Deco- herence of Impurities in a Fermi Sea of Ultracold Atoms, Phys. Rev. Lett. 115, 135302 (2015)

work page 2015

[16] [16]

Cetina, M

M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Wal- raven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, Ultrafast many-body interfer- ometry of impurities coupled to a Fermi sea, Science354, 96 LP (2016)

work page 2016

[17] [17]

M. G. Skou, T. G. Skov, N. B. Jørgensen, K. K. Nielsen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Non-equilibrium quantum dynamics and formation of the Bose polaron, Nature Physics 17, 731 (2021)

work page 2021

[18] [18]

M. G. Skou, K. K. Nielsen, T. G. Skov, A. M. Morgen, N. B. Jørgensen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Life and death of the Bose polaron, Phys. Rev. Res. 4, 043093 (2022)

work page 2022

[19] [19]

A. M. Morgen, S. S. Balling, K. K. Nielsen, T. Pohl, G. M. Bruun, and J. J. Arlt, Quantum beat spectroscopy of repulsive bose polarons, Phys. Rev. Res. 7, L022002 (2025)

work page 2025

[20] [20]

Etrych, G

J. Etrych, G. Martirosyan, A. Cao, C. J. Ho, Z. Hadz- ibabic, and C. Eigen, Universal quantum dynamics of bose polarons, Phys. Rev. X 15, 021070 (2025)

work page 2025

[21] [21]

Grusdt, N

F. Grusdt, N. Mostaan, E. Demler, and L. A. P. Ardila, Impurities and polarons in bosonic quantum gases: a re- view on recent progress, Reports on Progress in Physics 88, 066401 (2025)

work page 2025

[22] [22]

Polarons in atomic gases and two-dimensional semiconductors

P. Massignan, R. Schmidt, G. E. Astrakharchik, A. ˙Imamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, Polarons in atomic gases and two-dimensional semicon- ductors (2025), arXiv:2501.09618 [cond-mat.quant-gas]

work page internal anchor Pith review Pith/arXiv arXiv 2025

[23] [23]

Braaten and H.-W

E. Braaten and H.-W. Hammer, Universality in few-body systems with large scattering length, Physics Reports 6 428, 259 (2006)

work page 2006

[24] [24]

G. M. Bruun and C. J. Pethick, Effective Theory of Fes- hbach Resonances and Many-Body Properties of Fermi Gases, Phys. Rev. Lett. 92, 140404 (2004)

work page 2004

[25] [25]

A. O. Gogolin, C. Mora, and R. Egger, Analytical solu- tion of the bosonic three-body problem, Phys. Rev. Lett. 100, 140404 (2008)

work page 2008

[26] [26]

S. M. Yoshida, S. Endo, J. Levinsen, and M. M. Parish, Universality of an Impurity in a Bose-Einstein Conden- sate, Phys. Rev. X 8, 11024 (2018)

work page 2018

[27] [27]

See Supplemental Material online for details

work page

[28] [28]

Li and S

W. Li and S. Das Sarma, Variational study of polarons in Bose-Einstein condensates, Phys. Rev. A 90, 013618 (2014)

work page 2014

[29] [29]

Levinsen, M

J. Levinsen, M. M. Parish, and G. M. Bruun, Impurity in a Bose-Einstein condensate and the Efimov effect, Phys. Rev. Lett. 115, 125302 (2015)

work page 2015

[30] [30]

Saad, Iterative Methods for Sparse Linear Systems , 2nd ed

Y. Saad, Iterative Methods for Sparse Linear Systems , 2nd ed. (Society for Industrial and Applied Mathematics, 2003)

work page 2003

[31] [31]

Saad, Numerical Methods for Large Eigenvalue Prob- lems (Society for Industrial and Applied Mathematics, 2011)

Y. Saad, Numerical Methods for Large Eigenvalue Prob- lems (Society for Industrial and Applied Mathematics, 2011)

work page 2011

[32] [32]

Liesen and Z

J. Liesen and Z. Strakos, Krylov subspace methods princi- ples and analysis , Numerical Mathematics and Scientific Computation (Oxford University Press, Oxford, 2012)

work page 2012

[33] [33]

Nandy, A

P. Nandy, A. S. Matsoukas-Roubeas, P. Mart´ ınez- Azcona, A. Dymarsky, and A. del Campo, Quantum dynamics in Krylov space: Methods and applications, Physics Reports 1125–1128, 1–82 (2025)

work page 2025

[34] [34]

Guenther, R

N.-E. Guenther, R. Schmidt, G. M. Bruun, V. Gu- rarie, and P. Massignan, Mobile impurity in a bose- einstein condensate and the orthogonality catastrophe, Phys. Rev. A 103, 013317 (2021)

work page 2021

[35] [35]

Christianen, J

A. Christianen, J. I. Cirac, and R. Schmidt, Phase di- agram for strong-coupling Bose polarons, SciPost Phys. 16, 067 (2024)

work page 2024

[36] [36]

Yamamoto, M

K. Yamamoto, M. Nakagawa, K. Adachi, K. Takasan, M. Ueda, and N. Kawakami, Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interac- tion, Phys. Rev. Lett. 123, 123601 (2019)

work page 2019

[37] [37]

Bouchoule, B

I. Bouchoule, B. Doyon, and J. Dubail, The effect of atom losses on the distribution of rapidities in the one- dimensional Bose gas, SciPost Physics 9, 044 (2020)

work page 2020

[38] [38]

Yamamoto, M

K. Yamamoto, M. Nakagawa, N. Tsuji, M. Ueda, and N. Kawakami, Collective Excitations and Nonequilibrium Phase Transition in Dissipative Fermionic Superfluids, Phys. Rev. Lett. 127, 055301 (2021)

work page 2021

[39] [39]

Bouchoule and J

I. Bouchoule and J. Dubail, Breakdown of Tan’s Relation in Lossy One-Dimensional Bose Gases, Phys. Rev. Lett. 126, 160603 (2021)

work page 2021

[40] [40]

C. Wang, C. Liu, and Z.-Y. Shi, Complex Contact Inter- action for Systems with Short-Range Two-Body Losses, Phys. Rev. Lett. 129, 203401 (2022)

work page 2022

[41] [41]

Scazza, M

F. Scazza, M. Zaccanti, P. Massignan, M. M. Parish, and J. Levinsen, Repulsive Fermi and Bose Polarons in Quan- tum Gases, Atoms 10, 55 (2022)

work page 2022

[42] [42]

Goold, T

J. Goold, T. Fogarty, N. Lo Gullo, M. Paternostro, and T. Busch, Orthogonality catastrophe as a consequence of qubit embedding in an ultracold fermi gas, Phys. Rev. A 84, 063632 (2011)

work page 2011

[43] [43]

M. Knap, A. Shashi, Y. Nishida, A. Imambekov, D. A. Abanin, and E. Demler, Time-dependent impurity in ul- tracold fermions: Orthogonality catastrophe and beyond, Phys. Rev. X 2, 041020 (2012)

work page 2012

[44] [44]

Schmidt, M

R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, Universal many-body response of heavy impurities coupled to a fermi sea: a review of recent progress, Reports on Progress in Physics 81, 024401 (2018)

work page 2018

[45] [45]

(4) with Im( ω) < 0; in the limit Γ = 0, ω1 (ω2) is the standard attractive (repulsive) polaron [12]

It is easy to understand the time dynamics of A(t) for a non-interacting Bose gas ( aB = 0) using the following ansatz for A(t), which fits the numerical data well [27], A(t) = √ Ze −iω1t + (1 − √ Z)e−iω2t, (6) where |Z| = 8 πna (12πna − ω)−1 is the residue and ω1 (ω2) is the solution of Eq. (4) with Im( ω) < 0; in the limit Γ = 0, ω1 (ω2) is the standard...

work page

[46] [46]

(2) regarding the dynamics when Γ = 0.01 and γ = 0.1

Note that our phenomenological model agrees with the variational ansatz Eq. (2) regarding the dynamics when Γ = 0.01 and γ = 0.1

work page

[47] [47]

It is known however that the presence of the trap broadens the polaron peak in the spectro- scopic experiments [11]

Note that we performed a trap averaging for [19], see [27], and concluded that it has a weak effect on the time dy- namics as the decoherence dynamics mainly happens at shorter timescales. It is known however that the presence of the trap broadens the polaron peak in the spectro- scopic experiments [11]

work page

[48] [48]

Dzsotjan, R

D. Dzsotjan, R. Schmidt, and M. Fleischhauer, Dynami- cal Variational Approach to Bose Polarons at Finite Tem- peratures, Physical Review Letters 124, 223401 (2020)

work page 2020

[49] [49]

Guenther, P

N.-E. Guenther, P. Massignan, M. Lewenstein, and G. M. Bruun, Bose polarons at finite temperature and strong coupling, Phys. Rev. Lett. 120, 050405 (2018)

work page 2018

[50] [50]

Field, J

B. Field, J. Levinsen, and M. M. Parish, Fate of the bose polaron at finite temperature, Phys. Rev. A 101, 013623 (2020)

work page 2020

[51] [51]

Isaule and I

F. Isaule and I. Morera, Weakly-interacting bose–bose mixtures from the functional renormalisation group, Condensed Matter 7, 10.3390/condmat7010009 (2022)

work page doi:10.3390/condmat7010009 2022

[52] [52]

Marchukov and A

O. Marchukov and A. Volosniev, Shape of a sound wave in a weakly-perturbed bose gas, SciPost Physics 10, 025 (2021). 7 SUPPLEMENT AL MA TERIAL Single excitation ansatz The Bogoliubov transformation is performed on the single channel Hamiltonian with its interaction term in Eq. (3) of the main text by moving to a basis of phononic excitations of the conden...

work page 2021