Doublon dynamics of Bose-Fermi mixtures in optical lattices

Ana Maria Rey; Arghavan Safavi-Naini; Johannes Schachenmayer; Martin G\"arttner

REVIEW 1 major objections 4 minor 55 references

Doublon dynamics of Bose-Fermi mixtures in optical lattices

T0 review · 1 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Adjacent Bose-fermion pairs decay exponentially

desk verdict Solid short-time doublon-decay paper with a genuinely new triplon decay channel and a cluster expansion that is benchmarked against t-DMRG; the connected-cluster truncation is plausible but not fully verified, so accept with requests for a broader Zeno check and code/data release. read the letter →

arxiv 1908.04757 v2 pith:VRUV5C5B submitted 2019-08-10 cond-mat.quant-gas quant-ph

Martin Gärttner , Arghavan Safavi-Naini , Johannes Schachenmayer , Ana Maria Rey This is my paper · ORCID

classification cond-mat.quant-gasquant-ph

keywords doublondecayBose-FermimixtureopticallatticeclusterexpansiontriplonformationquantumZenoeffectrelaxationdynamicsHubbardmodel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks how a dilute gas of boson-fermion pairs (doublons) placed on random lattice sites relaxes under the competition between tunneling and on-site interactions. It claims that at short times the relaxation is governed by the decay of small connected clusters of doublons, with the dominant microscopic process being the conversion of two neighboring doublons into a triplon (a site containing one fermion and two bosons) plus a mobile singlon (a lone fermion). The paper derives closed-form decay laws for single, double, and triple doublon clusters, including the exponential pair-decay rate $\Gamma = (8J_B^2/J_F)\sqrt{1-(U_{BB}/(2J_F))^2}$ in one dimension, and assembles them into a cluster expansion whose predictions match numerically exact matrix-product-state simulations. If the picture holds, it turns short-time relaxation in strongly correlated Bose-Fermi mixtures into a few-body problem that experiments with ultracold molecules can directly benchmark.

What carries the argument

The central object is the connected doublon cluster, whose two-doublon version reduces to a single 'bound' initial state coupled to a continuum of singlon-triplon scattering states of bandwidth $4dJ_F$. The mechanism producing exponential decay is the Bixon-Jortner quasi-continuum: for $J_B\ll J_F$, the bound state couples with nearly constant matrix element $W$ to an effectively equally spaced continuum with spacing $\Delta$, and the survival amplitude follows $e^{-\Gamma t/2}$ with $\Gamma=2\pi W^2/\Delta$, which evaluates to the closed form $\Gamma = (8J_B^2/J_F)\sqrt{1-(U_{BB}/(2J_F))^2}$ in 1D. For isolated doublons the same bound-to-continuum structure instead yields an oscillatory saturation with $P_{\rm sat}=U_{BF}^2/(U_{BF}^2+4J_F^2)$. A secondary mechanism, doublon tunneling at effective rate $J_D=2J_FJ_B/U_{BF}$, is what makes separated doublons stable on accessible timescales and is what the cluster expansion drops.

What would settle it

Take two doublons separated by a single empty site with $J_B=0.1J_F$, $U_{BB}=J_F$, $U_{BF}=10J_F$ in 1D and track $P_2(t)$ up to $t\approx 300 J_F^{-1}$; the cluster expansion predicts decay only at the Zeno-suppressed rate $\Gamma_{\rm eff}\sim J_D^2/\Gamma\approx 10^{-2}J_F$. An observed decay at a rate comparable to $J_D$ (or any rate linear in $J_D$) would falsify the connected-cluster truncation.

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Extended reading notes

Core claim

The central claim is that the short-time doublon fraction $P_2(t)$ of a dilute lattice Bose-Fermi mixture is controlled by the decay of connected doublon clusters. For an isolated doublon in 1D the survival probability saturates at $P_{\rm sat}=U_{BF}^2/(U_{BF}^2+4J_F^2)$ after an oscillation at frequency $\sqrt{4J_F^2+U_{BF}^2}$. Two neighboring doublons open an additional channel: the boson tunnels away and, together with the fermion of the neighboring site, forms a triplon, while the leftover fermion (singlon) moves freely. When the boson-boson interaction $U_{BB}$ lies inside the singlon-triplon band ($U_{BB}<2dJ_F$), the pair population decays exponentially with rate $\Gamma = (8J_B^2/J_F)\sqrt{1-(U_{BB}/(2J_F))^2}$ in 1D; for $U_{BB}>2dJ_F$ the pair is stable. Doublons separated by empty sites decay only through slow doublon tunneling at rate $J_D=2J_FJ_B/U_{BF}$, which is suppressed by a quantum Zeno effect because $J_D\ll\Gamma$; this justifies a cluster expansion restricted to connected clusters. Exact t-DMRG calculations at filling fractions of 5% and 20% support the expansion at short times.

Load-bearing premise

The paper's predictive scheme rests on the assumption that separated doublons never decay on the timescales of interest, a quantum Zeno suppression that is argued heuristically and shown for one parameter set rather than derived or scanned across parameters.

Editorial extensions

If this is right

Two neighboring doublons decay exponentially with rate $\Gamma\propto J_B^2/J_F$ when $U_{BB}<2dJ_F$, and remain stable when $U_{BB}$ exceeds the band edge.
The doublon fraction of a dilute random gas is a weighted average over single-, double-, and triple-doublon cluster dynamics; this reproduces exact 1D t-DMRG results at short times for fillings of 5% and 20%.
Doublons separated by empty sites persist over timescales of order $1/J_D$ or longer, so the short-time relaxation of a dilute gas is almost entirely due to connected clusters.
The separation of time scales (single-doublon decay at rate $J_F$, pair decay at rate $\Gamma$, Zeno-suppressed decay at $J_D^2/\Gamma$) gives experiments distinct windows in which each process can be observed.
For $^{40}$K-$^{87}$Rb mixtures in a 1064 nm lattice, the parameters fall in the predicted regimes, so time-resolved doublon-fraction measurements can directly test the cluster-expansion predictions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Extension: increasing $J_D/J_F$ (e.g., by lowering $U_{BF}$) should switch separated doublons from Zeno-stable to decaying; the crossover rate as a function of $J_D/\Gamma$ is a quantitative prediction the paper leaves open.
Extension: because the triplon-singlon channel requires two bosons on one site, it is absent for fermion-fermion doublons; a matched Bose-Fermi versus Fermi-Fermi doublon experiment would isolate the boson-statistics contribution.
Extension: in 2D and 3D the decay rate should take the form $\Gamma=(J_B^2/J_F)f(U_{BB}/J_F)$ with $f$ fixed by the singlon-triplon density of states; computing $f$ would extend the analytical predictions beyond 1D.
Extension: the cluster expansion's error as a function of filling fraction and time has not been mapped; a systematic comparison of Eq. (5) with exact dynamics for $f=10\%,20\%,30\%$ would define the regime of practical applicability.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing you should know: this is a careful, well-benchmarked theory paper on doublon decay in Bose-Fermi mixtures, and the genuinely new piece is the triplon-mediated decay of neighboring doublons plus a cluster expansion for dilute doublon gases. The central short-time claim holds up. I would not desk-reject this.

What it does well: the analytical derivations for one-, two-, and three-doublon clusters are clean and parameter-free in 1D, and the benchmark against t-DMRG is honest and quantitative. The two-doublon exponential decay rate, Eq. (A32), follows from a Bixon-Jortner quasi-continuum treatment and matches the numerics where shown. The cluster expansion reproduces the exact t-DMRG dynamics for low filling and short times, which is exactly the regime the paper claims. The experimental parameter table for 40K-87Rb is useful and makes the connection to cold-molecule experiments concrete. Credit is deserved for the triplon mechanism itself: the conversion of two neighboring doublons into a singlon plus a triplon is a real process that is absent for fermionic doublons, and the authors identify it clearly.

The soft spots, in order of severity. First, the cluster expansion truncates to connected clusters because separated doublons are assumed stable via a quantum Zeno argument (JD << Gamma makes the effective separated-pair decay rate ~JD^2/Gamma). The only exact demonstration, Fig. 3(b), uses parameters where JD/Gamma is about 0.29, not much less than 1, and the time window stops at tJF = 20, much shorter than the predicted 1/(JD^2/Gamma) ~ 170 JF. So the non-decay is consistent with the Zeno argument but does not verify it. At filling 20%, pairs separated by one empty site are abundant, and if their actual decay rate is appreciable, the cluster sum could underpredict P2 at times only modestly beyond the benchmarked window. This is a real gap in the evidence, but it does not break the paper's stated scope of short-time, low-filling dynamics. Second, the higher-dimensional decay rates in Fig. 5 are fitted, not derived; the paper says so, but the fit is presented without error bars or a discussion of how the density-of-states f(u) changes with d. That is acceptable, but should be labeled more prominently. Third, there is a sign inconsistency in the Fig. 2 caption: UBF/JF is listed as -10 and -30, while the text defines UBF positive with the interaction term written as -UBF. Minor, but confusing. Fourth, no code or data are released, which makes it unnecessarily hard to extend the benchmark.

Who this is for: people working on doublon dynamics, quantum simulation with polar molecules, or lattice Bose-Fermi mixtures. It is an incremental but solid extension of the single-doublon literature, not a field-changer. I would send it to a serious referee, with the request that the authors either extend the Zeno check (longer times, smaller JD/Gamma, more parameter sets) or soften the cluster-expansion claim, and ideally release the code and data. As it stands, it deserves peer review and, with those requests, likely publication.

Referee Report

1 major / 4 minor

Summary. The manuscript studies the non-equilibrium dynamics of a dilute Bose-Fermi mixture in an optical lattice initialized in a product state of boson-fermion doublons. It derives analytical expressions for the decay of isolated doublons and of small clusters of two and three neighboring doublons, identifies triplon-singlon formation as the dominant decay channel of neighboring doublons when UBB < 2dJF, and proposes a cluster expansion in which the total doublon fraction is a weighted sum over connected few-doublon clusters. The cluster expansion is benchmarked against t-DMRG simulations in 1D, and experimental parameters for 40K-87Rb mixtures are discussed.

Significance. The 1D few-body results are genuinely useful: they are derived from the microscopic Hamiltonian, involve no fitted parameters in the central formulas, and are tested against independent t-DMRG simulations. The identification of the triplon-singlon decay channel and the hierarchy of time scales is physically interesting and potentially relevant for ongoing experiments with ultracold molecules. The main limitation is that the connected-cluster truncation, which is the basis of the predictive Eq. (5), relies on a quantum-Zeno stability assumption for separated doublons that is neither derived nor systematically verified; the only exact test uses a parameter set with JD/Gamma about 0.3 and a time window well below the predicted Zeno timescale.

major comments (1)

[Section III.2/III.3] The connected-cluster truncation in Eq. (5) rests on the claim that initially separated doublons are stable due to a quantum Zeno effect, but the paper's own parameters do not satisfy the stated condition JD << Gamma. For the only exact test shown in Fig. 3(b)-(d), with JB=0.1JF, UBB=JF, and UBF=10JF, one has JD = 2JFJB/UBF = 0.02JF and Gamma = 8JB^2/JF sqrt(1-(UBB/(2JF))^2) ≈ 0.069JF, giving JD/Gamma ≈ 0.29 rather than a strong inequality. The numerical time window ends near t ≈ 20 JF^{-1}, while the predicted Zeno-suppressed separated-pair decay timescale Gamma_eff^{-1} = Gamma/JD^2 ≈ 170 JF^{-1}; the observed non-decay is therefore only consistent with, not a verification of, the Zeno assumption. Moreover, Gamma vanishes at the band edge UBB = 2JF, so JD << Gamma cannot hold uniformly throughout the decay regime. Since pairs separated by one empty site are abundant at filling f=20%, the predictive power of Eq. (5) for times beyond the benchmarked window is not established. A systematic test across parameters or a quantitative bound on the disconnected-cluster contribution is needed.

minor comments (4)

[Fig. 2(c) caption] The caption lists UBF/JF values of -10 and -30, which is inconsistent with the convention in Eq. (1) where UBF is positive for attractive interspecies interactions; please correct the sign or clarify the convention.
[Fig. 3(b) caption] With JD defined as 2JFJB/UBF, the values JB=0.1JF and UBF=10JF give JD^{-1} = 50 JF^{-1}, not 100 JF^{-1} as stated in the caption; this inconsistency should be corrected because it affects the quantitative Zeno timescale estimate.
[Section III.3 and Fig. 3(c,d)] It would help to state explicitly whether the cluster evolutions P2[c](t) used in Fig. 3(c,d) are the analytical expressions from Appendix A or numerically obtained cluster evolutions, since the analytical three-doublon expression (A23) is derived in the perturbative regime UBB > 2JF and is not directly applicable to the parameter set UBB=JF used in the figure.
[Abstract and Introduction] The claim of analytical expressions for small doublon clusters is qualified in the appendix: in dimensions d>1 the two-doublon decay rate is extracted from numerical fits (Fig. 5) rather than derived. A brief qualification in the abstract or introduction would avoid overstating the analytic content.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: analytical formulas are derived from the Hamiltonian and benchmarked against independent exact numerics.

full rationale

The paper's central analytical results are self-contained derivations from the Hamiltonian in Eq. (1), not fits renamed as predictions. The single-doublon expression Eq. (4) follows from perturbation theory in Appendix A.1; the two-doublon formulas Eqs. (A14) and (A31)-(A32) come from the explicit two-level/continuum reduction in Appendix A.2, with the decay rate Gamma = 8 JB^2/JF sqrt(1-(UBB/(2JF))^2) obtained from the Bixon-Jortner quasi-continuum treatment; no parameter in these 1D formulas is fitted to the target doublon fraction. The cluster expansion Eq. (5) is a weighted average of independently computed few-doublon evolutions, and the neglect of disconnected clusters is an approximation justified by a Zeno-type stability argument, not by construction. The exact t-DMRG comparisons in Figs. 2 and 3 provide external benchmarks rather than fitting inputs. The 2D scaling check in Fig. 5 does fit decay rates to extract Gamma, but only to verify the predicted functional dependence; it is not the source of the 1D prediction. The self-citation [45] is used for experimental motivation and typical parameter values, not as a load-bearing uniqueness or derivation step. The unverified Zeno assumption for separated doublons, and the acknowledged breakdown of the quasi-continuum approximation near band edges, are correctness or robustness caveats, not circularity. The derivation is therefore not equivalent to its inputs, and no step reduces by definition to a fitted parameter or to a self-citation chain.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central results are derived from the Hubbard Hamiltonian with no fitted parameters; all analytical expressions are functions of the Hamiltonian parameters (JB, JF, UBF, UBB). The main approximations are standard perturbative and reservoir techniques, plus a cluster-expansion truncation that is benchmarked against exact t-DMRG.

assumptions (5)

domain assumption Single-band Hubbard model with only nearest-neighbor tunneling and on-site interactions
Eq. (1); assumes deep lattice and no occupation of higher bands, standard for cold atoms in optical lattices.
domain assumption Initial state is a product state of doublons on randomly occupied sites
Eq. (2); motivated by Feshbach association experiments [45], but restricts the study to this specific quench.
domain assumption UBF is the largest energy scale, allowing perturbative treatment and Hilbert-space truncation to manifolds without lone bosons
Used throughout Sections III.1-III.3 and Appendix A; the regime is justified for experimental parameters in Table I, but analytical formulas are only valid in this limit.
domain assumption Bixon-Jortner quasi-continuum approximation: constant coupling W and linear dispersion in a resonant window
Appendix A.2.b; standard in quantum optics, valid near band center UBB << 2JF, breaks near band edges, acknowledged by the authors.
domain assumption Quantum Zeno suppression makes separated doublons effectively stable, so only connected clusters need to be evolved
Section III.2; argued from separation of scales JD << Gamma, demonstrated for one parameter set; underpins the cluster expansion.

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Cite this review

Pith. "Pith review of Doublon dynamics of Bose-Fermi mixtures in optical lattices." pith.science (2026). https://pith.science/paper/VRUV5C5B

@misc{pith2026190804757,
  author       = {Pith},
  title        = {Pith review of: Doublon dynamics of Bose-Fermi mixtures in optical lattices},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VRUV5C5B}},
  note         = {Machine review of arXiv:1908.04757}
}

read the original abstract

We study the out-of-equilibrium dynamics of a dilute, lattice-confined Bose-Fermi mixture initialized in a highly excited state consisting of boson-fermion pairs (doublons) occupying single lattice sites. This system represents a paradigmatic case for studying relaxation dynamics in strongly correlated systems, and provides a versatile platform for studying thermalization and localization phenomena. We provide analytical expressions for the short-time decay of isolated doublons and small doublon clusters due to the competition between tunneling and interparticle interactions. We also discuss a mechanism for long-time decay that crucially depends on the quantum statistics of the particles constituting the doublon, namely, the conversion of pairs of neighboring doublons into an unpaired fermion and a site with a fermion and two bosons. Building on these insights, we develop a cluster expansion method to describe the dynamics in extended systems and compare it to numerically exact matrix product state simulations in one dimension. Finally, we discuss how our predictions can be observed in experiments with ultracold heteronuclear molecules.

Figures

Figures reproduced from arXiv: 1908.04757 by the authors.

**Figure 2.** FIG. 2. (a) Time evolution of the doublon fraction for a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. (a) and (b) Long-time evolution of the doublon den [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. (a) Energy diagram for states accessible to a two [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. Doublon decay in 2d. Fitted decay rate Γ from fitting [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Works this paper leans on

55 extracted references · 36 canonical work pages

[1]

These approaches will then be used to also obtain ana- lytical results for more than one doublon within certain approximations

Single doublon physics In this section we describe two approaches which yield analytic expressions for single doublon dynamics in 1d. These approaches will then be used to also obtain ana- lytical results for more than one doublon within certain approximations. We ﬁrst apply standard perturbation theory to the sin- gle doublon problem. The prescriptive na...

work page
[2]

Clusters of two and three doublons In the following we continue to assume that UBF is the largest energy scale such that we can restrict the Hilbert space to the manifold containing no lone bosons, indicated by the red ellipse in Fig. 4(a). Consider a chain of 2L− 2 sites, where the sites are indexed by integers in the intervals [−L + 1,−1] and [1,L− 1] (...

work page
[3]

J. M. Deutsch, Rep. Prog. Phys. 81, 082001 (2018)

2018
[4]

D’Alessio, Y

L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, Adv. Phys. 65, 239 (2016)

2016
[5]

Nandkishore and D

R. Nandkishore and D. A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015)

2015
[6]

Berges, S

J. Berges, S. Floerchinger, and R. Venugopalan, Phys. Lett. B 778, 442 (2018)

work page 2018
[7]

Kofman, A

L. Kofman, A. Linde, and A. A. Starobinsky, Phys. Rev. D 56, 3258 (1997)

1997
[8]

Or´ us, Ann

R. Or´ us, Ann. Phys.349, 117 (2014)

2014

Show all 55 references

[9]

Schollw¨ ock, Ann

U. Schollw¨ ock, Ann. Phys.326, 96 (2011)

2011
[10]

Verstraete, V

F. Verstraete, V. Murg, and J. I. Cirac, Adv. Phys. 57, 143 (2008)

2008
[11]

Bloch, Nat

I. Bloch, Nat. Phys. 14, 1159 (2018)

2018
[12]

Bloch, J

I. Bloch, J. Dalibard, and S. Nascimb` ene, Nat. Phys. 8, 267 (2012)

2012
[13]

Lewenstein, A

M. Lewenstein, A. Sanpera, V. Ahuﬁnger, B. Damski, A. Sen(De), and U. Sen, Adv. Phys. 56, 243 (2007)

2007
[14]

J¨ ordens, N

R. J¨ ordens, N. Strohmaier, K. G¨ unter, H. Moritz, and T. Esslinger, Nature 455, 204 (2008)

2008
[15]

Esslinger, Annu

T. Esslinger, Annu. Rev. Condens. Matter Phys. 1, 129 (2010)

2010
[16]

Greiner, O

M. Greiner, O. Mandel, T. Esslinger, T. W. H¨ ansch, and I. Bloch, Nature 415, 39 (2002)

2002
[17]

W. S. Bakr, J. I. Gillen, A. Peng, S. F¨ olling, and M. Greiner, Nature 462, 74 (2009)

2009
[18]

Gross and I

C. Gross and I. Bloch, Science 357, 995 (2017)

2017
[19]

G¨ unter, T

K. G¨ unter, T. St¨ oferle, H. Moritz, M. K¨ ohl, and T. Esslinger, Phys. Rev. Lett. 96, 180402 (2006)

2006
[20]

Ospelkaus, S

C. Ospelkaus, S. Ospelkaus, K. Sengstock, and K. Bongs, Phys. Rev. Lett. 96, 020401 (2006)

2006
[21]

Ospelkaus, C

S. Ospelkaus, C. Ospelkaus, O. Wille, M. Succo, P. Ernst, K. Sengstock, and K. Bongs, Phys. Rev. Lett. 96, 180403 (2006)

2006
[22]

F. Lang, K. Winkler, C. Strauss, R. Grimm, and J. H. Denschlag, Phys. Rev. Lett. 101, 133005 (2008)

2008
[23]

J. G. Danzl, M. J. Mark, E. Haller, M. Gustavsson, R. Hart, J. Aldegunde, J. M. Hutson, and H.-C. N¨ agerl, Nat. Phys. 6, 265 (2010)

2010
[24]

Titvinidze, M

I. Titvinidze, M. Snoek, and W. Hofstetter, Phys. Rev. Lett. 100, 100401 (2008)

2008
[25]

Albus, F

A. Albus, F. Illuminati, and J. Eisert, Phys. Rev. A 68, 023606 (2003)

2003
[26]

H. P. B¨ uchler and G. Blatter, Phys. Rev. Lett.91, 130404 (2003)

2003
[27]

Lewenstein, L

M. Lewenstein, L. Santos, M. A. Baranov, and H. Fehrmann, Phys. Rev. Lett. 92, 050401 (2004)

2004
[28]

Ospelkaus, S

C. Ospelkaus, S. Ospelkaus, L. Humbert, P. Ernst, K. Sengstock, and K. Bongs, Phys. Rev. Lett. 97, 120402 (2006)

2006
[29]

M. H. G. de Miranda, A. Chotia, B. Neyenhuis, D. Wang, G. Quemener, S. Ospelkaus, J. L. Bohn, J. Ye, and D. S. Jin, Nat. Phys. 7, 502 (2011)

2011
[30]

Reichs¨ ollner, A

L. Reichs¨ ollner, A. Schindewolf, T. Takekoshi, R. Grimm, and H.-C. N¨ agerl, Phys. Rev. Lett.118, 073201 (2017)

2017
[31]

Seeßelberg, X.-Y

F. Seeßelberg, X.-Y. Luo, M. Li, R. Bause, S. Ko- tochigova, I. Bloch, and C. Gohle, Phys. Rev. Lett. 121, 253401 (2018)

2018
[32]

J. L. Bohn, A. M. Rey, and J. Ye, Science 357, 1002 (2017)

2017
[33]

Winkler, G

K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A. J. Daley, A. Kantian, H. P. B¨ uchler, and P. Zoller, Nature441, 853 (2006)

2006
[34]

J. H. Denschlag and A. J. Daley, Ultra-cold Fermi Gases, 64 (2006)

2006
[35]

Petrosyan, B

D. Petrosyan, B. Schmidt, J. R. Anglin, and M. Fleis- chhauer, Phys. Rev. A 76, 033606 (2007)

2007
[36]

L. Wang, Y. Hao, and S. Chen, Eur. Phys. J. D 48, 229 (2008)

2008
[37]

Valiente and D

M. Valiente and D. Petrosyan, J. Phys. B 42, 121001 12 (2009)

2009
[38]

Javanainen, O

J. Javanainen, O. Odong, and J. C. Sanders, Phys. Rev. A 81, 043609 (2010)

2010
[39]

Deuchert, K

A. Deuchert, K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Phys. Rev. A 86, 013618 (2012)

2012
[40]

Valiente, M

M. Valiente, M. K¨ uster, and A. Saenz, EPL 92, 10001 (2010)

2010
[41]

Nguenang and S

J.-P. Nguenang and S. Flach, Phys. Rev. A 80, 015601 (2009)

2009
[42]

Ohashi, Phys

Y. Ohashi, Phys. Rev. A 78, 063617 (2008)

2008
[43]

Hofmann and M

F. Hofmann and M. Potthoﬀ, Phys. Rev. B 85, 205127 (2012)

2012
[44]

R. T. Piil, N. Nygaard, and K. Mølmer, Phys. Rev. A 78, 033611 (2008)

2008
[45]

S. R. White and A. E. Feiguin, Phys. Rev. Lett. 93, 076401 (2004)

2004
[46]

A. J. Daley, C. Kollath, U. Schollw¨ ock, and G. Vidal, J. Stat. Mech. 2004, P04005 (2004)

2004
[47]

J. P. Covey, S. A. Moses, M. G¨ arttner, A. Safavi-Naini, M. T. Miecnikowski, Z. Fu, J. Schachenmayer, P. S. Juli- enne, A. M. Rey, D. S. Jin, and J. Ye, Nat. Commun. 7, 11279 (2016)

2016
[48]

S. A. Moses, J. P. Covey, M. T. Miecnikowski, B. Yan, B. Gadway, J. Ye, and D. S. Jin, Science350, 659 (2015)

2015
[49]

Takekoshi, M

T. Takekoshi, M. Debatin, R. Rameshan, F. Ferlaino, R. Grimm, H.-C. N¨ agerl, C. R. Le Sueur, J. M. Hutson, P. S. Julienne, S. Kotochigova, and E. Tiemann, Phys. Rev. A 85, 032506 (2012)

2012
[50]

Takekoshi, L

T. Takekoshi, L. Reichs¨ ollner, A. Schindewolf, J. M. Hut- son, C. R. Le Sueur, O. Dulieu, F. Ferlaino, R. Grimm, and H.-C. N¨ agerl, Phys. Rev. Lett.113, 205301 (2014)

2014
[51]

J. W. Park, C.-H. Wu, I. Santiago, T. G. Tiecke, S. Will, P. Ahmadi, and M. W. Zwierlein, Phys. Rev. A 85, 051602 (2012)

2012
[52]

J. W. Park, S. A. Will, and M. W. Zwierlein, Phys. Rev. Lett. 114, 205302 (2015)

2015
[53]

Gr¨ obner, P

M. Gr¨ obner, P. Weinmann, F. Meinert, K. Lauber, E. Kirilov, and H.-C. N¨ agerl, J. Mod. Opt. 63, 1829 (2016)

2016
[54]

P. K. Molony, P. D. Gregory, Z. Ji, B. Lu, M. P. K¨ oppinger, C. R. Le Sueur, C. L. Blackley, J. M. Hutson, and S. L. Cornish, Phys. Rev. Lett. 113, 255301 (2014)

2014
[55]

Bixon and J

M. Bixon and J. Jortner, J. Chem. Phys. 48, 715 (1968)

1968

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

These approaches will then be used to also obtain ana- lytical results for more than one doublon within certain approximations

Single doublon physics In this section we describe two approaches which yield analytic expressions for single doublon dynamics in 1d. These approaches will then be used to also obtain ana- lytical results for more than one doublon within certain approximations. We ﬁrst apply standard perturbation theory to the sin- gle doublon problem. The prescriptive na...

work page

[2] [2]

Clusters of two and three doublons In the following we continue to assume that UBF is the largest energy scale such that we can restrict the Hilbert space to the manifold containing no lone bosons, indicated by the red ellipse in Fig. 4(a). Consider a chain of 2L− 2 sites, where the sites are indexed by integers in the intervals [−L + 1,−1] and [1,L− 1] (...

work page

[3] [3]

J. M. Deutsch, Rep. Prog. Phys. 81, 082001 (2018)

2018

[4] [4]

D’Alessio, Y

L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, Adv. Phys. 65, 239 (2016)

2016

[5] [5]

Nandkishore and D

R. Nandkishore and D. A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015)

2015

[6] [6]

Berges, S

J. Berges, S. Floerchinger, and R. Venugopalan, Phys. Lett. B 778, 442 (2018)

work page 2018

[7] [7]

Kofman, A

L. Kofman, A. Linde, and A. A. Starobinsky, Phys. Rev. D 56, 3258 (1997)

1997

[8] [8]

Or´ us, Ann

R. Or´ us, Ann. Phys.349, 117 (2014)

2014