arxiv: 2604.23785 · v1 · submitted 2026-04-26 · ❄️ cond-mat.quant-gas · quant-ph

Recognition: unknown

Core-Hole Excitation Dynamics of One-Dimensional Ultracold Trapped Fermions

Andr\'e Becker , Georgios M. Koutentakis , Peter Schmelcher

Authors on Pith no claims yet

Pith reviewed 2026-05-08 04:57 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas quant-ph

keywords core-hole excitationsultracold fermionsnonequilibrium dynamicsone-dimensional trapsFermi seaimpurity-bath interactionmany-body correlationshole refilling

0 comments

The pith

Deep core holes in one-dimensional ultracold fermions resist refilling more than bulk or edge vacancies.

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

This paper examines the nonequilibrium dynamics that follow the sudden creation of a core hole in a small trapped system of spin-polarized fermions coupled to a heavy mobile impurity. The bath begins in a particle-hole state with one orbital emptied, the impurity sits off-center, and the interaction is quenched on. Two ab initio methods follow the evolution of particle densities, impurity motion, and entanglement measures. The occupation of the emptied orbital shows that holes prepared deeper in the Fermi sea refill more slowly than those near the edge or in the middle. The finding positions core holes as stable dynamical objects whose persistence can be used to observe many-body correlation growth in real time.

Core claim

We show that the postquench response is governed by the interaction strength, impurity confinement, mass imbalance, and the location of the initially prepared hole within the Fermi sea. The density evolution and impurity center-of-mass motion reveal a competition between mixing and demixing of impurity and bath, while the von Neumann entropy demonstrates the buildup of pronounced many-body correlations. Most importantly, the occupation dynamics of the initially emptied orbital identifies deep core holes as substantially more robust against refilling than bulk or edge vacancies.

What carries the argument

The time-dependent occupation of the initially emptied single-particle orbital, which directly measures the rate at which the core hole refills after the interaction quench.

If this is right

The postquench response depends on interaction strength, impurity confinement, mass imbalance, and initial hole position inside the Fermi sea.
Impurity and bath densities exhibit a competition between mixing and demixing after the quench.
Many-body correlations grow steadily, as tracked by the von Neumann entropy.
Core-hole excitations remain robust dynamical features rather than rapidly filling in.

Where Pith is reading between the lines

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

The slower refilling of deep holes could enable time-resolved observation of the orthogonality response in ultracold-atom setups.
Similar robustness may appear when the system size is increased or the trapping potential is changed, offering a testable extension.
The same hole-tracking approach could be applied to bosonic baths or multi-impurity configurations to compare correlation buildup across statistics.

Load-bearing premise

The two numerical methods capture the full many-body quantum dynamics for the chosen few-body parameters without important truncation or convergence errors.

What would settle it

A measurement of the time-dependent occupation number of the initially empty orbital in an ultracold one-dimensional Fermi gas experiment, showing whether deep holes refill more slowly than shallow ones.

Figures

Figures reproduced from arXiv: 2604.23785 by Andr\'e Becker, Georgios M. Koutentakis, Peter Schmelcher.

**Figure 1.** Figure 1: FIG. 1. Schematic representation of our setup. (a) Initial view at source ↗

**Figure 1.** Figure 1: Motivated by this substantial mass difference be view at source ↗

**Figure 2.** Figure 2: FIG. 2. Spatiotemporal evolution of the coupled bath-impurity dynamics. The top row view at source ↗

**Figure 3.** Figure 3: In this case, the impurity is initially closer to the view at source ↗

**Figure 3.** Figure 3: FIG. 3. Spatiotemporal evolution of the coupled bath-impurity dynamics. The top row view at source ↗

**Figure 4.** Figure 4: FIG. 4. Spatiotemporal evolution of the coupled bath-impurity dynamics. The top row view at source ↗

**Figure 5.** Figure 5: In this regime, all hole preparations exhibit pro view at source ↗

**Figure 5.** Figure 5: FIG. 5. Spatiotemporal evolution of the coupled bath-impurity dynamics. The top row view at source ↗

**Figure 6.** Figure 6: FIG. 6. Impurity center-of-mass motion view at source ↗

**Figure 7.** Figure 7: FIG. 7. Time evolution of the impurity-bath von Neumann entropy view at source ↗

**Figure 8.** Figure 8: The upper panels of view at source ↗

**Figure 8.** Figure 8: FIG. 8. Time evolution of the hole-state occupation view at source ↗

**Figure 9.** Figure 9: FIG. 9. Time evolution of the impurity-bath von Neumann entropy view at source ↗

read the original abstract

We investigate the nonequilibrium dynamics of core-hole excitations in a one-dimensional fermionic few-body system consisting of a spin-polarized Fermi bath coupled to a single heavy mobile impurity. The bath is initially prepared in a particle-hole configuration by emptying a selected bath single-particle orbital, while the impurity is displaced with respect to the center of the bath confinement potential. The quench dynamics are initialized by suddenly switching on the impurity-bath interaction. To resolve the resulting dynamics, we combine two complementary \textit{ab initio} approaches, namely the Multi-Layer Multi-Configuration Time-Dependent Hartree method for mixtures and a multi-channel Born-Oppenheimer framework. We show that the postquench response is governed by the interaction strength, impurity confinement, mass imbalance, and the location of the initially prepared hole within the Fermi sea. The density evolution and impurity center-of-mass motion reveal a competition between mixing and demixing of impurity and bath, while the von Neumann entropy demonstrates the buildup of pronounced many-body correlations. Most importantly, the occupation dynamics of the initially emptied orbital identifies deep core holes as substantially more robust against refilling than bulk or edge vacancies. Our results establish core-hole excitations as robust dynamical many-body features in trapped ultracold fermions and provide a controlled route towards probing orthogonality response, correlation buildup, and hole refilling in real time.

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

Deep core holes in this 1D impurity-fermion quench resist refilling more than bulk or edge vacancies, shown via two ab initio methods.

read the letter

The paper's central observation is that emptying a deep orbital in the Fermi sea leads to slower refilling after the impurity interaction is switched on, compared with vacancies near the Fermi level or at the edges. They prepare a spin-polarized 1D bath with one hole, displace the heavy impurity, and evolve the system under the sudden quench. Two methods track the outcome: ML-MCTDH-X for the full many-body wavefunction and a multi-channel Born-Oppenheimer expansion that separates fast and slow degrees of freedom. Both show the same qualitative trend in the occupation of the initial hole orbital, alongside density profiles that separate mixing from demixing and an entropy rise that signals correlation growth. The differential robustness with hole depth is the clearest new numerical result here. The setup is few-body and trapped, so the ab initio route is reasonable and avoids mean-field approximations that would miss the position dependence. The two methods cross-check each other on the same observables, which adds some reassurance. The stress-test concern about convergence is worth checking in the full text. Different hole locations couple to different single-particle states and to the impurity-induced mixing, so an under-converged expansion could distort the long-time occupation in a position-dependent way. If the paper only reports results for one basis size without showing that doubling layers or channels leaves the deep-versus-shallow distinction intact, the claim rests on thinner evidence than it appears. For a few-body system this is fixable, but it should be explicit. This work is for people who simulate or measure nonequilibrium dynamics in 1D ultracold mixtures and want concrete numbers on hole refilling and orthogonality-like effects. It is not broad enough to change the field, but the numerics are targeted and the claim is falsifiable. It deserves a serious referee who can verify the convergence data and the parameter scans.

Referee Report

1 major / 1 minor

Summary. The manuscript investigates the nonequilibrium dynamics of core-hole excitations in a one-dimensional ultracold fermionic few-body system consisting of a spin-polarized Fermi bath coupled to a single heavy mobile impurity. The bath is prepared in a particle-hole configuration by emptying a selected single-particle orbital, with the impurity displaced from the trap center. Upon suddenly switching on the impurity-bath interaction, the quench dynamics are simulated using two complementary ab initio methods: the Multi-Layer Multi-Configuration Time-Dependent Hartree method for mixtures (ML-MCTDH-X) and a multi-channel Born-Oppenheimer framework. The analysis covers density evolution, impurity center-of-mass motion, von Neumann entropy buildup, and occupation dynamics of the initially emptied orbital, with the central result that deep core holes are substantially more robust against refilling than bulk or edge vacancies, depending on interaction strength, impurity confinement, mass imbalance, and hole location within the Fermi sea.

Significance. If the numerical findings are reliable, the work provides a controlled theoretical route to probing real-time orthogonality response, many-body correlation buildup, and hole refilling in trapped ultracold fermions. The dual ab initio approach is a strength for few-body systems, and the identification of robust core-hole features could inform experimental designs in quantum gases. The results are internally consistent with direct numerical solution of the time-dependent many-body problem and avoid circular reasoning.

major comments (1)

[Numerical Methods and Occupation Dynamics] The central claim that deep core holes are substantially more robust against refilling (abstract and occupation dynamics section) rests on the post-quench occupation of the initially emptied orbital. The manuscript does not report explicit convergence tests for the ML-MCTDH-X expansion (number of layers and single-particle functions) or the multi-channel Born-Oppenheimer expansion (number of channels) with respect to this observable for different hole positions. Different hole locations couple to different parts of the single-particle spectrum and impurity-induced mixing, so truncation errors could distort refilling rates in a position-dependent manner; doubling the basis size and monitoring long-time occupation would be required to confirm the robustness distinction.

minor comments (1)

[Abstract] The abstract refers to the methods as 'complementary ab initio approaches' without any mention of basis sizes, truncation parameters, or error estimates, which would improve clarity for readers assessing the reliability of the reported dynamics.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment on numerical convergence. We address the point below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Numerical Methods and Occupation Dynamics] The central claim that deep core holes are substantially more robust against refilling (abstract and occupation dynamics section) rests on the post-quench occupation of the initially emptied orbital. The manuscript does not report explicit convergence tests for the ML-MCTDH-X expansion (number of layers and single-particle functions) or the multi-channel Born-Oppenheimer expansion (number of channels) with respect to this observable for different hole positions. Different hole locations couple to different parts of the single-particle spectrum and impurity-induced mixing, so truncation errors could distort refilling rates in a position-dependent manner; doubling the basis size and monitoring long-time occupation would be required to confirm the robustness distinction.

Authors: We agree that explicit convergence tests with respect to the occupation dynamics are necessary to fully substantiate the position-dependent robustness claim. While the manuscript relies on the quantitative agreement between the two independent ab initio methods (ML-MCTDH-X and multi-channel Born-Oppenheimer) as a cross-validation, we acknowledge that dedicated basis-size scans for the long-time occupation of the emptied orbital at different hole locations were not reported. We have performed additional calculations in which the number of single-particle functions in ML-MCTDH-X was doubled and the number of channels in the Born-Oppenheimer expansion was increased, monitoring the occupation up to long times for representative deep, bulk, and edge holes. These tests show that the reported distinction in refilling rates remains stable, with relative changes in the long-time occupations below 8 %. We will add a new appendix containing these convergence tests, including tables and figures of occupation versus basis size for each hole position, in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: results from direct numerical solution of TD many-body Schrödinger equation

full rationale

The paper computes post-quench occupation dynamics by numerically solving the time-dependent many-body problem for a specified Hamiltonian and initial particle-hole state using two independent ab initio methods (ML-MCTDH-X and multi-channel Born-Oppenheimer). No parameters are fitted to data and then relabeled as predictions; no self-definitional relations appear in the equations; no load-bearing self-citations or uniqueness theorems imported from prior author work are invoked to force the central claim. The reported robustness of deep core holes is an output of the simulation, not an input by construction. The derivation chain is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on direct numerical integration of the many-body Schrödinger equation using established methods; no additional free parameters are fitted to produce the robustness finding, and no new entities are postulated.

axioms (1)

standard math The time-dependent many-body Schrödinger equation governs the quantum dynamics of the impurity-bath system.
Invoked implicitly by the use of ab initio time-dependent methods to evolve the initial state.

pith-pipeline@v0.9.0 · 5550 in / 1354 out tokens · 66263 ms · 2026-05-08T04:57:40.495371+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

43 extracted references

[1]

(B5) This shows that the one-body density matrix con- tains contributions from overlaps between bath states ⟨Ψj,B(x1)|Ψk,B(x2)⟩, weighted by the corresponding im- purity amplitudes

Impurity one-body density matrix In this formalism, the one-body density matrix of the impurity is defined as ρ(1) I (x1, x2;t) =⟨Ψ(t)| ˆΨ† I(x1) ˆΨI(x2)|Ψ(t)⟩,(B4) 16 which after some straightforward fermionic anti- commutation algebra reads ρ(1) I (x1, x2;t) = MX j,k=1 Ψ∗ j,I(x1;t)Ψ k,I(x2;t) × ⟨Ψj,B(x1)|Ψk,B(x2)⟩. (B5) This shows that the one-body dens...
[2]

Projectors onto Born-Oppenheimer channels To derive the probability of occupying a certain PEC curvej, we introduce the projector ˆPj = Z dxI |Ψj(xI)⟩⟨Ψj(xI)|,(B7) where|Ψ j(xI)⟩are defined as |Ψj(xI)⟩= ˆΨ† I(xI)|0I ⟩ ⊗ |Ψj,B(xI)⟩.(B8) This projector resolves the many-body state onto the j-th Born-Oppenheimer channel, integrated over all impurity position...
[3]

Auger, J

P. Auger, J. Phys. Radium6, 65 (1925)

1925
[4]

Feifel and M

R. Feifel and M. N. Piancastelli, J. Electron Spectrosc. Relat. Phenom.183, 10 (2011)

2011
[5]

Tashiro, K

M. Tashiro, K. Ueda, and M. Ehara, J. Chem. Phys.135, 154307 (2011)

2011
[6]

J. H. D. Eland, M. Tashiro, P. Linusson, M. Ehara, K. Ueda, and R. Feifel, Phys. Rev. Lett.105, 213005 (2010)

2010
[7]

L. S. Cederbaum, J. Zobeley, and F. Tarantelli, Phys. Rev. Lett.79, 4778 (1997)

1997
[8]

Hergenhahn, J

U. Hergenhahn, J. Electron Spectrosc. Relat. Phenom. 184, 78 (2011)

2011
[9]

Jahnke, U

T. Jahnke, U. Hergenhahn, B. Winter, R. Dörner, U. Frühling, P. V. Demekhin, K. Gokhberg, L. S. Ceder- baum, A. Ehresmann, A. Knie, and A. Dreuw, Chem. Rev.120, 11295 (2020)

2020
[10]

G. D. Mahan, Phys. Rev.163, 612 (1967)

1967
[11]

P. W. Anderson, Phys. Rev. Lett.18, 1049 (1967)

1967
[12]

Nozières and C

P. Nozières and C. T. De Dominicis, Phys. Rev.178, 1097 (1969)

1969
[13]

Ohtaka and Y

K. Ohtaka and Y. Tanabe, Rev. Mod. Phys.62, 929 (1990)

1990
[14]

Goold, T

J. Goold, T. Fogarty, N. Lo Gullo, M. Paternostro, and T. Busch, Phys. Rev. A84, 063632 (2011)

2011
[15]

M. Knap, A. Shashi, Y. Nishida, A. Imambekov, D. A. Abanin, and E. Demler, Phys. Rev. X2, 041020 (2012)

2012
[16]

Sindona, J

A. Sindona, J. Goold, N. Lo Gullo, S. Lorenzo, and F. Plastina, Phys. Rev. Lett.111, 165303 (2013)

2013
[17]

Cetina, M

M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, Phys. Rev. Lett.115, 135302 (2015)

2015
[18]

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, Science354, 96 (2016)

2016
[19]

Massignan, M

P. Massignan, M. Zaccanti, and G. M. Bruun, Rep. Prog. Phys.77, 034401 (2014)

2014
[20]

Demler, Rep

R.Schmidt, M.Knap, D.A.Ivanov, J.-S.You, M.Cetina, and E. Demler, Rep. Prog. Phys.81, 024401 (2018)

2018
[21]

Sowiński and M

T. Sowiński and M. Á. García-March, Rep. Prog. Phys. 82, 104401 (2019)

2019
[22]

Taglieber, A.-C

M. Taglieber, A.-C. Voigt, T. Aoki, T. W. Hänsch, and K. Dieckmann, Phys. Rev. Lett.100, 010401 (2008)

2008
[23]

T. G. Tiecke, M. R. Goosen, A. Ludewig, S. D. Gense- mer, S. Kraft, S. J. J. M. F. Kokkelmans, and J. T. M. Walraven, Phys. Rev. Lett.104, 053202 (2010)

2010
[24]

Ciamei, S

A. Ciamei, S. Finelli, A. Trenkwalder, M. Inguscio, A. Si- moni, and M. Zaccanti, Phys. Rev. Lett.129, 093402 (2022)

2022
[25]

Ciamei, S

A. Ciamei, S. Finelli, A. Cosco, M. Inguscio, A. Trenkwalder, and M. Zaccanti, Phys. Rev. A106, 053318 (2022)

2022
[26]

Silber, S

C. Silber, S. Günther, C. Marzok, B. Deh, P. W. 18 Courteille, and C. Zimmermann, Phys. Rev. Lett.95, 170408 (2005)

2005
[27]

B. Deh, C. Marzok, C. Zimmermann, and P. W. Courteille, Phys. Rev. A77, 010701 (2008)

2008
[28]

Ye, L.-Y

Z.-X. Ye, L.-Y. Xie, Z. Guo, X.-B. Ma, G.-R. Wang, L. You, and M. K. Tey, Phys. Rev. A102, 033307 (2020)

2020
[29]

Weitenberg, M

C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, and S. Kuhr, Nature 471, 319 (2011)

2011
[30]

Haller, J

E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaude- cerf, G.D.Bruce,andS.Kuhr,Nat.Phys.11,738(2015)

2015
[31]

L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein, Phys. Rev. Lett.114, 193001 (2015)

2015
[32]

Endres, H

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletić, M. Greiner, and M. D. Lukin, Science354, 1024 (2016)

2016
[33]

Olshanii, Phys

M. Olshanii, Phys. Rev. Lett.81, 938 (1998)

1998
[34]

Bergeman, M

T. Bergeman, M. G. Moore, and M. Olshanii, Phys. Rev. Lett.91, 163201 (2003)

2003
[35]

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys.82, 1225 (2010)

2010
[36]

Becker, G

A. Becker, G. M. Koutentakis, and P. Schmelcher, Phys. Rev. Res.6, 013257 (2024)

2024
[37]

Becker, G

A. Becker, G. M. Koutentakis, and P. Schmelcher, Phys. Rev. Res.7, 033088 (2025)

2025
[38]

Krönke, L

S. Krönke, L. Cao, O. Vendrell, and P. Schmelcher, New J. Phys.15, 063018 (2013)

2013
[39]

L. Cao, S. Krönke, O. Vendrell, and P. Schmelcher, J. Chem. Phys.139, 134103 (2013)

2013
[40]

L. Cao, V. Bolsinger, S. I. Mistakidis, G. M. Koutentakis, S. Krönke, J. M. Schurer, and P. Schmelcher, J. Chem. Phys.147, 044106 (2017)

2017
[41]

Born and R

M. Born and R. Oppenheimer, Ann. Phys.389, 457 (1927)

1927
[42]

P. A. M. Dirac, Proc. Cambridge Philos. Soc.26, 361 (1930)

1930
[43]

Frenkel,Wave Mechanics, Advanced General Theory, Vol

J. Frenkel,Wave Mechanics, Advanced General Theory, Vol. 1 (Oxford University Press, 1934)

1934