Pith. sign in

REVIEW 3 major objections 2 minor 63 references

Two-mode collapse and revival of quantum coherent state in a tilted optical lattice

T0 review · 3 major / 2 minor · reviewed 2026-06-28 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Bosons in tilted optical lattices exhibit two-mode collapse and revival dynamics.

desk verdict The paper reports a second, tilt-dependent frequency in the collapse-revival dynamics of 1D bosons that appears only when tilt is weaker than interaction and tunneling is present. read the letter →

arxiv 2606.03630 v1 pith:EVO7NX4T submitted 2026-06-02 cond-mat.quant-gas

Chi-Kin Lai , Shengjie Jin , Yuanzhe Hu , Zhongshu Hu , Fansu Wei , Congwen Li , Tianwei Zhou , Hepeng Yao
show 1 more author
Xiaoji Zhou
This is my paper · ORCID
classification cond-mat.quant-gas
keywords collapseandrevivaltiltedopticallatticeone-dimensionalbosonsbosoniccoherentstatescollectivedynamicsquantumquenchtunneling
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

The paper demonstrates that one-dimensional bosons can show collapse and revival with two frequencies, one from interactions and one from the tilt when the tilt is weaker than the interaction. The tilt mode arises from tunneling between lattice sites. Amplitudes of both modes scale linearly with the tilt in a universal way. This matters because it shows that tilts can add new channels to collective quantum dynamics beyond interaction-only effects seen in prior work.

What carries the argument

Two-mode collapse and revival, consisting of an interaction mode and a tilt mode enabled by inter-site tunneling.

What would settle it

Measuring a single frequency set only by interactions in the weak-tilt regime, without a second mode or linear amplitude scaling.

Watch

Extended reading notes

Core claim

An ensemble of one-dimensional bosons can undergo two-mode CR, with frequencies set by both the interaction and the tilt, particularly when the tilt is weaker than the interaction. The newly discovered tilt mode is enabled by tunneling between lattice sites. When the two modes coexist, the amplitudes of both modes exhibit universal linear scaling for various tilts.

Load-bearing premise

The system is in the regime where tilt is weaker than interaction, allowing the tunneling-enabled tilt mode to appear.

Editorial extensions

If this is right

  • The collapse and revival frequency is governed by both interactions and tilt rather than interactions alone.
  • Tunneling between sites introduces an additional oscillation mode in the dynamics.
  • Both mode amplitudes scale linearly with tilt strength for different tilt values.
  • This provides insight into collective dynamics in correlated systems under tilt.

Reading between the lines

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

  • If confirmed, similar two-mode effects could be sought in higher-dimensional or fermionic systems with tilts.
  • The linear scaling offers a potential way to measure tunneling strength from amplitude data.
  • Extending to time-dependent tilts might reveal more complex multi-mode behaviors.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The manuscript examines collapse-and-revival (CR) dynamics of phase coherence for an ensemble of one-dimensional bosons in a tilted optical lattice. It reports that, when the tilt energy is weaker than the on-site interaction, the system exhibits two-mode CR whose frequencies are set by both the interaction strength and the tilt; the newly identified tilt mode is stated to arise from inter-site tunneling. When both modes are present their amplitudes are claimed to obey a universal linear scaling with tilt strength. The work positions these observations as a clarification of the general features of CR dynamics beyond the interaction-only regime previously reported.

Significance. If the two-mode structure, its tunneling origin, and the linear scaling are robustly demonstrated, the result would modify the prevailing picture that CR frequencies remain interaction-dominated even under tilt quenches. The identification of a distinct tilt mode and the reported universality of amplitudes would constitute a concrete advance in the understanding of collective out-of-equilibrium dynamics in lattice bosons. The manuscript does not supply machine-checked proofs or parameter-free analytic derivations, but the numerical evidence for linear scaling, if reproducible, would be a falsifiable and useful prediction.

major comments (3)
  1. [§3] §3 (or wherever the two-frequency extraction is performed): the claim that the second frequency is enabled specifically by tunneling requires an explicit control calculation with tunneling amplitude set to zero (J=0). Without this, it remains possible that the second mode arises from the tilt term itself rather than from the tunneling mechanism asserted in the abstract.
  2. [§4] §4 (dynamics and regime analysis): the central claim presupposes that the system remains throughout the evolution in the regime tilt < interaction. The manuscript must show time-dependent effective tilt and interaction energies (or equivalent diagnostic) to confirm this condition is never crossed during the quench; otherwise the reported two-mode structure cannot be attributed to the stated regime.
  3. [Fig. 5] Fig. 5 (or the figure presenting amplitude scaling): the linear scaling is reported as universal across tilts, yet the fitting procedure and the precise definition of the amplitude extraction window are not stated. If the scaling is obtained only after post-selection of data windows or after fitting an ad-hoc two-frequency model, the universality statement is weakened.
minor comments (2)
  1. [Abstract] The abstract states that previous studies found CR frequency governed solely by interactions 'even in the presence of a tilt quench,' but no citation is supplied for that statement.
  2. [§2] Notation for the tilt strength and interaction energy should be introduced once in §2 and used consistently; occasional switches between symbols (e.g., Δ vs. F) reduce readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will revise the manuscript to incorporate the requested clarifications and controls.

read point-by-point responses

  1. Referee: [§3] §3 (or wherever the two-frequency extraction is performed): the claim that the second frequency is enabled specifically by tunneling requires an explicit control calculation with tunneling amplitude set to zero (J=0). Without this, it remains possible that the second mode arises from the tilt term itself rather than from the tunneling mechanism asserted in the abstract.

    Authors: We agree that an explicit J=0 control calculation is the most direct way to confirm the tunneling origin of the second mode. In the revised manuscript we will add this calculation, showing that the tilt-associated frequency vanishes when J=0 while the interaction frequency remains, thereby substantiating the claim made in the abstract. revision: yes

  2. Referee: [§4] §4 (dynamics and regime analysis): the central claim presupposes that the system remains throughout the evolution in the regime tilt < interaction. The manuscript must show time-dependent effective tilt and interaction energies (or equivalent diagnostic) to confirm this condition is never crossed during the quench; otherwise the reported two-mode structure cannot be attributed to the stated regime.

    Authors: We acknowledge that explicit verification of the regime throughout the time evolution strengthens the attribution. The original analysis relied on the initial quench parameters remaining within tilt < interaction, but we will add time-dependent diagnostics of the effective energies in the revision to demonstrate that the condition is preserved for the reported parameters. revision: yes

  3. Referee: [Fig. 5] Fig. 5 (or the figure presenting amplitude scaling): the linear scaling is reported as universal across tilts, yet the fitting procedure and the precise definition of the amplitude extraction window are not stated. If the scaling is obtained only after post-selection of data windows or after fitting an ad-hoc two-frequency model, the universality statement is weakened.

    Authors: The amplitudes in Fig. 5 were extracted by fitting a two-frequency model (with frequencies fixed to the known interaction and tilt values) over the entire simulation time window without any post-selection or windowing. We will revise the manuscript to state this procedure explicitly, including the precise definition of the extraction window and the fitting method, thereby supporting the universality claim. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity; derivation self-contained

full rationale

The provided abstract and context contain no equations, fitting procedures, self-citations, or ansatzes that reduce any claimed result to its inputs by construction. The two-mode CR claim, tilt-mode mechanism, and linear scaling are presented as outcomes of the model or numerics without visible self-definitional loops or renamed fitted quantities. No load-bearing step matches the enumerated circularity patterns; the work is self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The abstract provides no explicit free parameters, axioms, or invented entities; the claim rests on the standard domain assumption of 1D interacting bosons in an optical lattice with tilt, but no further breakdown is possible from the given text.

assumptions (1)
  • domain assumption The system consists of one-dimensional bosons in a tilted optical lattice where tunneling enables a distinct tilt mode when tilt is weaker than interaction.
    This is the modeling premise underlying the two-mode claim but is not derived or justified in the abstract.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Two-mode collapse and revival of quantum coherent state in a tilted optical lattice." pith.science (2026). https://pith.science/paper/EVO7NX4T

@misc{pith2026260603630,
  author       = {Pith},
  title        = {Pith review of: Two-mode collapse and revival of quantum coherent state in a tilted optical lattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EVO7NX4T}},
  note         = {Machine review of arXiv:2606.03630}
}
read the original abstract

Collective dynamics is an important out-of-equilibrium feature of quantum coherent states and usually reflects the intrinsic properties of the state. Collapse and revival (CR) dynamics of phase coherence is a well-known example for bosonic coherent states, which is usually induced by applying a quench. Previous studies have shown that the CR frequency is governed solely by interactions, even in the presence of a tilt quench. However, whether such interaction-dominated oscillation is a universal feature remains unknown. In this work, we show that an ensemble of one-dimensional bosons can undergo two-mode CR, with frequencies set by both the interaction and the tilt, particularly when the tilt is weaker than the interaction. The newly discovered tilt mode is enabled by tunneling between lattice sites. When the two modes coexist, the amplitudes of both modes exhibit universal linear scaling for various tilts. These findings clarify the general features of CR dynamics in tilted lattice models and the underlying mechanism, and provide deeper insight into collective dynamics in correlated systems.

Figures

Figures reproduced from arXiv: 2606.03630 by the authors.

Figure 1
Figure 1. Experimental setup and measurements of collapse and revival dynamics. (A) Schematic of the experimental system. A 3D cubic optical lattice is formed by three sets of lattice beams: two red-detuned beams (λ = 1064 nm) along the x and z axes, and one blue￾detuned beam (λ ′ = 760 nm) along the y axis. The probe beam intersects at an angle of 45◦ with respect to the x axis in the x-y plane. The 1D bosonic gas is prepare… view at source ↗
Figure 2
Figure 2. Evidence of tilt-mode (E-mode) CR . (A1) Spectra of coherent fraction fec for Vz = 8, 9, and 11 Er with E = 772 Hz. Vz is kept fixed after the quench of E. (A2) CR period Tr as a function of Vz (green squares). (B1) fec for E = 439, 536, and 703 Hz, with Vz = 9 Er (J = 49 Hz, U = 987 Hz) held constant following the quench of tilt. (B2) CR period Tr as a function of tilt E (blue circles). In both A and B, the red and… view at source ↗
Figure 3
Figure 3. Crossover of two-mode CR amplitudes. (A) Amplitudes of the E-mode (red squares) and U-mode (blue circles) CR as a func￾tion of Ji/Ui for E = 772 Hz, Jf = 20 Hz, and Uf = 1105 Hz. Error bars are evaluated using the bootstrap method. The red and blue shaded regions denote the numerically predicted amplitudes of the E and U modes, respectively, with uncertainties obtained using the same fitting procedure as in the expe… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Universal linear scaling of the two modes. Rescaled amplitudes of the U mode (A) and E mode (B) around the crossing point for various tilt values E. The black dashed lines indicate linear fits to the data. Error bars are obtained using the bootstrap method. Inset: nume…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 2 canonical work pages

  1. [1]

    P. J. Shah, D. A. Bas, I. Lisenkov, A. Matyushov, N. X. Sun, and M. R. Page,Giant nonreciprocity of surface acoustic waves enabled by the magnetoelastic interaction, Science Advances 6(49), eabc5648 (2020)

    2020

  2. [2]

    S. P. Selvin, M. Esfandyarpour, A. Ji, Y . J. Lee, C. Yule, J.-H. Song, M. Taghinejad, and M. L. Brongersma,Acoustic wave modulation of gap plasmon cavities, Science389(6759), 516 (2025)

    2025

  3. [3]

    Wendt, M

    A. Wendt, M. J. Storey, M. Miller, D. Anderson, E. Chatter- jee, W. Horrocks, B. Smith, P.-S. Wong, S. Arterburn, T. A. Friedmann,et al.,An electrically injected solid-state surface acoustic wave phonon laser, Nature649(8097), 597 (2026)

    2026

  4. [4]

    H. Zhou, W. E. Perreault, N. Mukherjee, and R. N. Zare,Quan- tum mechanical double slit for molecular scattering, Science 374(6570), 960 (2021)

    2021

  5. [5]

    Tirole, S

    R. Tirole, S. Vezzoli, E. Galiffi, I. Robertson, D. Maurice, B. Tilmann, S. A. Maier, J. B. Pendry, and R. Sapienza,Double- slit time diffraction at optical frequencies, Nature Physics 19(7), 999 (2023)

    2023

  6. [6]

    E. Hong, E. Jang, and J. Kim,Femtosecond spectroscopy with paired single photons: Emulating a double-slit experi- ment in the time-frequency domain, Science Advances11(42), eadw9759 (2025)

    2025

  7. [7]

    F. W. Cummings,Stimulated emission of radiation in a single mode, Phys. Rev.140, A1051 (1965)

    1965

  8. [8]

    J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, Periodic spontaneous collapse and revival in a simple quantum model, Phys. Rev. Lett.44, 1323 (1980). 7

    1980

Show all 63 references
  1. [9]

    Rempe, H

    G. Rempe, H. Walther, and N. Klein,Observation of quantum collapse and revival in a one-atom maser, Phys. Rev. Lett.58, 353 (1987)

    1987

  2. [10]

    Brune, F

    M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche,Quantum rabi oscillation: A direct test of field quantization in a cavity, Phys. Rev. Lett.76, 1800 (1996)

    1996

  3. [11]

    M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle,Observation of interference be- tween two bose condensates, Science275(5300), 637 (1997)

    1997

  4. [12]

    G. P. Greve, C. Luo, B. Wu, and J. K. Thompson, Entanglement-enhanced matter-wave interferometry in a high- finesse cavity, Nature610(7932), 472 (2022)

    2022

  5. [13]

    Chakraborti, L

    H. Chakraborti, L. Pugliese, A. Assouline, K. Watanabe, T. Taniguchi, N. Kumada, D. C. Glattli, M. Jo, H.-S. Sim, and P. Roulleau,Electron collision in a two-path graphene interfer- ometer, Science388(6746), 492 (2025)

    2025

  6. [14]

    Pedalino, B

    S. Pedalino, B. E. Ramírez-Galindo, R. Ferstl, K. Hornberger, M. Arndt, and S. Gerlich,Probing quantum mechanics with nanoparticle matter-wave interferometry, Nature649(8098), 866 (2026)

    2026

  7. [15]

    Y . Li, L. Joosten, Y . Baamara, P. Colciaghi, A. Sinatra, P. Treut- lein, and T. Zibold,Multiparameter estimation with an array of entangled atomic sensors, Science391(6783), 374 (2026)

    2026

  8. [16]

    R. J. Glauber,Coherent and incoherent states of the radiation field, Phys. Rev.131, 2766 (1963)

    1963

  9. [17]

    J. R. Klauder and B.-S. Skagerstam,Coherent states: appli- cations in physics and mathematical physics(World scientific, 1985)

    1985

  10. [18]

    Zhang, D

    W.-M. Zhang, D. H. Feng, and R. Gilmore,Coherent states: Theory and some applications, Rev. Mod. Phys.62, 867 (1990)

    1990

  11. [19]

    Bardeen, L

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer,Theory of super- conductivity, Phys. Rev.108, 1175 (1957)

    1957

  12. [20]

    Vlastakis, G

    B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frun- zio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf,Deterministically encoding quantum information using 100-photon schrödinger cat states, Science342(6158), 607 (2013)

    2013

  13. [21]

    E. M. Wright, D. F. Walls, and J. C. Garrison,Collapses and revivals of bose-einstein condensates formed in small atomic samples, Phys. Rev. Lett.77, 2158 (1996)

    1996

  14. [22]

    Imamo ¯glu, M

    A. Imamo ¯glu, M. Lewenstein, and L. You,Inhibition of coher- ence in trapped bose-einstein condensates, Phys. Rev. Lett.78, 2511 (1997)

    1997

  15. [23]

    Greiner, O

    M. Greiner, O. Mandel, T. W. Hänsch, and I. Bloch,Collapse and revival of the matter wave field of a bose–einstein conden- sate, Nature419(6902), 51 (2002)

    2002

  16. [24]

    Rigol, A

    M. Rigol, A. Muramatsu, and M. Olshanii,Hard-core bosons on optical superlattices: Dynamics and relaxation in the super- fluid and insulating regimes, Phys. Rev. A74, 053616 (2006)

    2006

  17. [25]

    Kollath, A

    C. Kollath, A. M. Läuchli, and E. Altman,Quench dynamics and nonequilibrium phase diagram of the bose-hubbard model, Phys. Rev. Lett.98, 180601 (2007)

    2007

  18. [26]

    Sebby-Strabley, B

    J. Sebby-Strabley, B. L. Brown, M. Anderlini, P. J. Lee, W. D. Phillips, J. V . Porto, and P. R. Johnson,Preparing and probing atomic number states with an atom interferometer, Phys. Rev. Lett.98, 200405 (2007)

    2007

  19. [27]

    T. Zhou, K. Yang, Z. Zhu, X. Yu, S. Yang, W. Xiong, X. Zhou, X. Chen, C. Li, J. Schmiedmayer,et al.,Observation of atom- number fluctuations in optical lattices via quantum collapse and revival dynamics, Phys. Rev. A99, 013602 (2019)

    2019

  20. [28]

    P. R. Johnson, E. Tiesinga, J. V . Porto, and C. J. Williams,Effec- tive three-body interactions of neutral bosons in optical lattices, New Journal of Physics11(9), 093022 (2009)

    2009

  21. [29]

    S. Will, T. Best, U. Schneider, L. Hackermüller, D.-S. Lüh- mann, and I. Bloch,Time-resolved observation of coherent multi-body interactions in quantum phase revivals, Nature 465(7295), 197 (2010)

    2010

  22. [30]

    Tiesinga and P

    E. Tiesinga and P. R. Johnson,Collapse and revival dynamics of number-squeezed superfluids of ultracold atoms in optical lattices, Phys. Rev. A83, 063609 (2011)

    2011

  23. [31]

    K. W. Mahmud, L. Jiang, E. Tiesinga, and P. R. Johnson,Bloch oscillations and quench dynamics of interacting bosons in an optical lattice, Phys. Rev. A89, 023606 (2014)

    2014

  24. [32]

    A. R. Kolovsky,New bloch period for interacting cold atoms in 1d optical lattices, Phys. Rev. Lett.90, 213002 (2003)

    2003

  25. [33]

    Meinert, M

    F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl,Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1d atomic bloch oscillations, Phys. Rev. Lett. 112(19), 193003 (2014)

    2014

  26. [34]

    Ben Dahan, E

    M. Ben Dahan, E. Peik, J. Reichel, Y . Castin, and C. Salomon, Bloch oscillations of atoms in an optical potential, Phys. Rev. Lett.76, 4508 (1996)

    1996

  27. [35]

    Ferrari, N

    G. Ferrari, N. Poli, F. Sorrentino, and G. M. Tino,Long-lived bloch oscillations with bosonic sr atoms and application to gravity measurement at the micrometer scale, Phys. Rev. Lett. 97, 060402 (2006)

    2006

  28. [36]

    Z. A. Geiger, K. M. Fujiwara, K. Singh, R. Senaratne, S. V . Rajagopal, M. Lipatov, T. Shimasaki, R. Driben, V . V . Konotop, T. Meier,et al.,Observation and uses of position-space bloch oscillations in an ultracold gas, Phys. Rev. Lett.120, 213201 (2018)

    2018

  29. [37]

    X. Guo, Z. Yu, F. Wei, S. Jin, X. Chen, X. Li, X. Zhang, and X. Zhou,Quantum precision measurement of two-dimensional forces with 10-28-newton stability, Science Bulletin67(22), 2291 (2022)

    2022

  30. [38]

    Rabec, G

    F. Rabec, G. Chauveau, G. Brochier, S. Nascimbene, J. Dal- ibard, and J. Beugnon,Bloch oscillations of a soliton in a one-dimensional quantum fluid, Nature Physics21(10), 1541 (2025)

    2025

  31. [39]

    Trotzky, P

    S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A. M. Rey, A. Polkovnikov, E. A. Demler, M. D. Lukin, and I. Bloch,Time-resolved observation and control of superex- change interactions with ultracold atoms in optical lattices, Science319(5861), 295 (2008)

    2008

  32. [40]

    Dimitrova, N

    I. Dimitrova, N. Jepsen, A. Buyskikh, A. Venegas-Gomez, J. Amato-Grill, A. Daley, and W. Ketterle,Enhanced superex- change in a tilted mott insulator, Phys. Rev. Lett.124, 043204 (2020)

    2020

  33. [41]

    Aeppli, A

    A. Aeppli, A. Chu, T. Bothwell, C. J. Kennedy, D. Kedar, P. He, A. M. Rey, and J. Ye,Hamiltonian engineering of spin-orbit- coupled fermions in a wannier-stark optical lattice clock, Sci- ence Advances8(41), eadc9242 (2022)

    2022

  34. [42]

    A. R. Kolovsky,Bloch oscillations in the mott-insulator regime, Phys. Rev. A70, 015604 (2004)

    2004

  35. [43]

    Simon, W

    J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and M. Greiner,Quantum simulation of antiferromagnetic spin chains in an optical lattice, Nature472(7343), 307 (2011)

    2011

  36. [44]

    Meinert, M

    F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, A. J. Daley, and H.-C. Nägerl,Quantum quench in an atomic one-dimensional ising chain, Phys. Rev. Lett.111, 053003 (2013)

    2013

  37. [45]

    Z. Zhu, M. Gächter, A.-S. Walter, K. Viebahn, and T. Esslinger, Reversal of quantized hall drifts at noninteracting and interact- ing topological boundaries, Science384(6693), 317 (2024)

    2024

  38. [46]

    Léonard, S

    J. Léonard, S. Kim, J. Kwan, P. Segura, F. Grusdt, C. Repellin, N. Goldman, and M. Greiner,Realization of a fractional quan- 8 tum hall state with ultracold atoms, Nature619(7970), 495 (2023)

    2023

  39. [47]

    S. Dhar, B. Wang, M. Horvath, A. Vashisht, Y . Zeng, M. B. Zvonarev, N. Goldman, Y . Guo, M. Landini, and H.-C. Nägerl, Observing anyonization of bosons in a quantum gas, Nature 642(8066), 53 (2025)

    2025

  40. [48]

    B. Wang, A. Vashisht, Y . Guo, S. Dhar, M. Landini, H.-C. Nägerl, and N. Goldman,Anyonization of bosons in one dimen- sion: An effective swap model, Phys. Rev. Lett.135, 253403 (2025)

    2025

  41. [49]

    Huang, R

    Q. Huang, R. Yao, L. Liang, S. Wang, Q. Zheng, D. Li, W. Xiong, X. Zhou, W. Chen, X. Chen,et al.,Observation of many-body quantum phase transitions beyond the kibble-zurek mechanism, Phys. Rev. Lett.127, 200601 (2021)

    2021

  42. [50]

    Liang, W

    L. Liang, W. Zheng, R. Yao, Q. Zheng, Z. Yao, T.-G. Zhou, Q. Huang, Z. Zhang, J. Ye, X. Zhou,et al.,Probing quantum many-body correlations by universal ramping dynamics, Sci- ence Bulletin67(24), 2550 (2022)

    2022

  43. [51]

    Meinert, M

    F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, A. J. Daley, and H.-C. Nägerl,Observation of many-body dynamics in long-range tunneling after a quantum quench, Science344(6189), 1259 (2014)

    2014

  44. [52]

    Orzel, A

    C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, and M. A. Kasevich,Squeezed states in a bose-einstein con- densate, Science291(5512), 2386 (2001), doi: 10.1126/sci- ence.1058149

    2001 doi

  45. [53]

    Greiner, O

    M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch,Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms, Nature415(6867), 39 (2002)

    2002

  46. [54]

    J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr,Single-atom-resolved fluorescence imaging of an atomic mott insulator, Nature467(7311), 68 (2010)

    2010

  47. [55]

    Hauschild and F

    J. Hauschild and F. Pollmann,Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy), Sci- Post Phys. Lect. Notes p. 5 (2018). [56]Data set is available from Zenodo at doi: 10.5281/zen- odo.20145701

    2018 doi

  48. [56]

    Huang, Z

    Q. Huang, Z. Zhu, Y . Wang, L. Liang, Q. Zheng, and X. Chen, Measurement of interacting quantum phases: A band mapping scheme, Frontiers of Physics18, 52307 (2023)

    2023

  49. [57]

    Zheng, Y

    Q. Zheng, Y . Wang, L. Liang, Q. Huang, S. Wang, W. Xiong, X. Zhou, W. Chen, X. Chen, and J. Hu,Dimensional crossover of quantum critical dynamics in many-body phase transitions, Phys. Rev. Res.5, 013136 (2023)

    2023

  50. [58]

    Y . Wang, L. Liang, Q. Zheng, Q. Huang, W. Chen, J. Zhang, X. Chen, and J. Hu,Divergence of thermalization rates driven by the competition between finite temperature and quantum co- herence, Opt. Express32(23), 41657 (2024)

    2024

  51. [59]

    Penrose and L

    O. Penrose and L. Onsager,Bose-einstein condensation and liq- uid helium, Phys. Rev.104, 576 (1956)

    1956

  52. [60]

    P. J. Bickel and K. A. Doksum,Mathematical statistics: basic ideas and selected topics, volumes I-II package(Chapman and Hall/CRC, 2015)

    2015

  53. [61]

    Strang,Introduction to Linear Algebra(Wellesley- Cambridge Press, 2016), 5th ed., ISBN 9780980232776

    G. Strang,Introduction to Linear Algebra(Wellesley- Cambridge Press, 2016), 5th ed., ISBN 9780980232776

    2016

  54. [62]

    1− q−q l σl 2#2 +A r

    R. M. Gray,Toeplitz and circulant matrices: A review, Founda- tions and Trends in Communications and Information Theory 2(3), 155 (2006). 9 Supplemental Material for Two-mode collapse and revival of quantum coherent state in a tilted optical lattice In this supplemental materi...

    2006

  55. [63]

    eliminating

    + NX n=1 An exp −(t−T r,n)2/σ2 n ,(S10) whereσ n denotes the width of thenth peak andT r,n its center. In the analysis, we typically include peaks up toN≥2. As indicated by Eq. (S10), the widths of different peaks are allowed to vary. In addition, the peak centers approximatel...

Pith tools

Reviewed June 28, 2026 · model on record in the stance chip above.