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arxiv: 2410.22032 · v2 · pith:7BUATHJ2new · submitted 2024-10-29 · 🪐 quant-ph · cond-mat.quant-gas

From spin squeezing to fast state discrimination

Michael R. Geller This is my paper

Pith reviewed 2026-05-23 18:47 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gas
keywords spin squeezingBose-Einstein condensatesquantum state discriminationnonlinear dynamicsBloch sphereGross-Pitaevskii equationViviani curvelarge N limit
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The pith

The large-N limit of spin squeezing leaves a nonlinear qubit evolution that solves single-input quantum state discrimination via a Viviani curve.

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

The paper examines spin-squeezed states of N two-level atoms in the limit where N grows very large. The initial coherent-state width shrinks to zero and pairwise entanglement is suppressed by monogamy, yet the twisting motion from atomic interactions survives and drives the center of the state. This center follows a two-state Gross-Pitaevskii equation whose nonlinearity supplies a resource for single-input quantum state discrimination, an operation forbidden in ordinary linear quantum mechanics. The paper gives an explicit solution in the form of a Viviani curve traced on the Bloch sphere. It also treats an open-system version in which dissipation creates two basins of attraction whose shared boundary supports autonomous discrimination.

Core claim

In the N to infinity limit the one-axis twist torsion persists while the coherent-state center evolves as a nonlinear qubit under a two-state Gross-Pitaevskii equation. This nonlinearity implements single-input quantum state discrimination, solved by a Viviani curve on the Bloch sphere. An open-system variant containing both torsion and dissipation produces two basins of attraction with a shared boundary usable for autonomous discrimination. The two-component condensate is therefore presented as a platform for nonlinear quantum gates.

What carries the argument

The one-axis twist torsion that survives the large-N limit and generates the two-state Gross-Pitaevskii dynamics whose solution is the Viviani curve on the Bloch sphere.

If this is right

  • Single-input quantum state discrimination becomes possible through the nonlinearity that remains after the large-N limit is taken.
  • An open-system version with dissipation creates two basins of attraction whose boundary enables autonomous state discrimination.
  • A two-component condensate can realize a nonlinear qubit usable for quantum computation tasks.
  • Spin squeezing in the large-N regime supplies a concrete route to nonlinear quantum gates.

Where Pith is reading between the lines

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

  • The same large-N reduction may simplify experimental tests by removing the need to preserve fragile pairwise entanglement.
  • Similar torsion-driven nonlinearities could appear in other many-body platforms and enable analogous discrimination tasks.
  • The Viviani-curve solution might be adapted to design faster or more robust discrimination protocols in quantum sensing.

Load-bearing premise

That the twisting interaction remains while two-particle entanglement is eliminated by monogamy when the atom number becomes infinite.

What would settle it

Direct observation that the Bloch-vector trajectory of a large-N condensate under one-axis twisting follows a Viviani curve and thereby achieves single-input state discrimination.

Figures

Figures reproduced from arXiv: 2410.22032 by Michael R. Geller.

Figure 1
Figure 1. Figure 1: Efficient reduction of 3SAT to quantum state discrimination (QSD). Here [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Block ball subjected to z-axis torsion. All states in the upper hemisphere are expansive with all states in the lower hemisphere, a powerful quantum information processing resource. The trace norm is physically relevant because the normalized trace distance D(ρa, ρb) := ∥ρa − ρb∥1 2 = max 0⪯E⪯I tr[(ρa−ρb)E], 0 ≤ D(ρa, ρb) ≤ 1, (14) quantifies the distinguishability of (ρa, ρb) by any single (projective or … view at source ↗
Figure 3
Figure 3. Figure 3: Viviani curve mapping |a⟩ 7→ |0⟩ (blue) and |b⟩ 7→ |1⟩ (green). A single-input QSD gate assumes a given set of potential inputs {|a⟩, |b⟩} as initial conditions, and the objective is to send |a⟩ 7→ |0⟩ and |b⟩ 7→ |1⟩. Thus we are faced with a control problem on the Bloch sphere. A unitary can always be used to orient the pair {⃗ra, ⃗rb} anywhere on the Bloch sphere without changing the angle between them. … view at source ↗
Figure 4
Figure 4. Figure 4: Curves show solutions of qubit equations of motion ( [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Expanded view of Figure [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
read the original abstract

There is great interest in generating and controlling entanglement in Bose-Einstein condensates and similar ensembles for use in quantum computation, simulation, and sensing. One class of entangled states useful for enhanced metrology are spin-squeezed states of $N$ two-level atoms. After preparing a spin coherent state of width $1/\sqrt{N}$ centered at coordinates $( \theta, \phi) $ on the Bloch sphere, atomic interactions generate a nonlinear evolution that shears the state's probability density, stretching it to an ellipse and causing squeezing in a direction perpendicular to the major axis. Here we consider the same setup but in the $N \rightarrow \infty $ limit . This shrinks the initial coherent state to zero area. Large $N$ also suppresses two-particle entanglement and squeezing, as required by a monogamy bound. The torsion (1-axis twist) is still present, however, and the center of the large $N$ coherent state evolves as a qubit governed by a two-state Gross-Pitaevskii equation. The resulting nonlinearity is known to be a powerful resource in quantum computation. It can be used to implement single-input quantum state discrimination, an impossibility within linear one-particle quantum mechanics. We obtain a solution to the discrimination problem in terms of a Viviani curve on the Bloch sphere. We also consider an open-system variant containing both Bloch sphere torsion and dissipation. In this case it should be possible to generate two basins of attraction within the Bloch ball, having a shared boundary that can be used for a type of autonomous state discrimination. We explore these and other connections between spin squeezing in the large $N$ limit and nonlinear quantum gates, and argue that a two-component condensate is a promising platform for realizing a nonlinear qubit.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that in the N→∞ limit of spin squeezing for N two-level atoms, the initial coherent state shrinks to zero width and two-particle entanglement is suppressed by monogamy, yet the torsional nonlinearity survives; the Bloch-vector center then obeys a two-state Gross-Pitaevskii equation whose nonlinearity enables single-input quantum state discrimination (impossible in linear QM) via an explicit Viviani-curve trajectory on the Bloch sphere. An open-system extension with dissipation is argued to produce basins of attraction usable for autonomous discrimination, positioning two-component condensates as platforms for nonlinear quantum gates.

Significance. If the reduction to the GP equation and the Viviani-curve solution are shown to hold, the work would furnish a concrete physical route from spin-squeezing metrology to nonlinear computational resources that can perform tasks forbidden in linear one-particle QM. The geometric construction supplies an explicit, falsifiable trajectory that could be tested in condensate experiments.

major comments (3)
  1. [Section presenting the discrimination solution] The central claim that the Viviani curve solves the single-input discrimination problem under the two-state GP dynamics is stated but not derived: no explicit substitution of the curve into the GP vector field, no verification that the resulting flow separates the target states, and no comparison showing an advantage over linear Bloch precession plus projective measurement appear in the text.
  2. [Large-N limit analysis] The reduction from finite-N spin squeezing to the mean-field GP equation for the Bloch-vector center is asserted via the survival of torsion and the monogamy bound, yet the explicit limiting procedure, the form of the GP equation itself, and error estimates for the N→∞ approximation are not supplied.
  3. [Open-system variant discussion] The open-system variant asserts that torsion plus dissipation can create two basins with a usable shared boundary, but no dynamical equations, no location of the separatrix, and no quantitative discrimination error rate are given.
minor comments (2)
  1. [Abstract and introduction] The abstract states that a solution “in terms of a Viviani curve” is obtained; the main text should contain a dedicated subsection that derives or verifies this curve rather than only citing the result.
  2. [Notation and setup] Notation for the Bloch angles (θ, φ) and the explicit form of the torsion term in the GP equation should be defined once and used consistently.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the work's significance, and constructive major comments. We address each point below and will revise the manuscript to incorporate the requested derivations and details.

read point-by-point responses

  1. Referee: [Section presenting the discrimination solution] The central claim that the Viviani curve solves the single-input discrimination problem under the two-state GP dynamics is stated but not derived: no explicit substitution of the curve into the GP vector field, no verification that the resulting flow separates the target states, and no comparison showing an advantage over linear Bloch precession plus projective measurement appear in the text.

    Authors: We agree that the explicit substitution, verification, and comparison were not included in the submitted version. In the revised manuscript we will add a dedicated subsection that parametrizes the Viviani curve, substitutes it directly into the two-state GP vector field, verifies that the resulting flow separates the target states with the claimed discrimination success probability, and provides a side-by-side comparison against the linear Bloch-precession-plus-projection bound. revision: yes

  2. Referee: [Large-N limit analysis] The reduction from finite-N spin squeezing to the mean-field GP equation for the Bloch-vector center is asserted via the survival of torsion and the monogamy bound, yet the explicit limiting procedure, the form of the GP equation itself, and error estimates for the N→∞ approximation are not supplied.

    Authors: We acknowledge that the explicit limiting procedure and error estimates were omitted. The revision will include an appendix that starts from the finite-N spin-squeezing Hamiltonian, takes the N→∞ limit while invoking the monogamy bound to suppress entanglement, derives the precise two-state GP equation obeyed by the Bloch-vector center, and supplies rigorous error bounds on the approximation for large but finite N. revision: yes

  3. Referee: [Open-system variant discussion] The open-system variant asserts that torsion plus dissipation can create two basins with a usable shared boundary, but no dynamical equations, no location of the separatrix, and no quantitative discrimination error rate are given.

    Authors: We agree that the open-system section lacked the required equations and quantitative analysis. The revised manuscript will present the explicit master equation combining torsional nonlinearity and dissipation, locate the separatrix between the two basins of attraction on the Bloch ball, and provide an estimate of the discrimination error rate as a function of the dissipation parameter. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses standard external mean-field limits and known nonlinear resources

full rationale

The paper's central steps invoke the established two-state Gross-Pitaevskii equation for the N→∞ mean-field evolution of the Bloch-sphere center and monogamy bounds on entanglement, both drawn from prior literature rather than fitted or self-defined within this work. The Viviani-curve solution for state discrimination is presented as an obtained mapping under the GP flow, without reduction to the inputs by construction or self-citation chains. No load-bearing self-definitional steps, fitted predictions, or ansatzes smuggled via author citations appear in the provided derivation chain. The argument remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard assumption that the large-N limit reduces the many-body dynamics to a two-state Gross-Pitaevskii equation while preserving torsion; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption The center of the large-N coherent state evolves as a qubit governed by a two-state Gross-Pitaevskii equation.
    Invoked directly in the abstract as the governing dynamics after entanglement suppression.
  • domain assumption Monogamy bounds suppress two-particle entanglement and squeezing in the large-N limit while leaving torsion intact.
    Stated as a required property of the large-N regime.

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Works this paper leans on

121 extracted references · 121 canonical work pages · cited by 1 Pith paper · 5 internal anchors

  1. [2]

    W., et al., 2019, Science, DOI: 10.1126/sci- ence.aaw5903 Barsdell et al., 2010, MNRAS, 408,

    V. Giovannetti, S. Lloyd, and L. Maccone. Quantum-enhanced measurements: Beating the standard quantum limit. Science, 306:1330, 2004. DOI: 10.1126/sci- ence.1104149

    work page doi:10.1126/sci- 2004

  2. [3]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone. Quantum metrology. Phys. Rev. Lett. , 96:010401, 2006. DOI: 10.1103/PhysRevLett.96.010401

    work page doi:10.1103/physrevlett.96.010401 2006

  3. [4]

    Kitagawa and M

    M. Kitagawa and M. Ueda. Squeezed spin states. Phys. Rev. A, 47:5138, 1993. DOI: 10.1103/PhysRevA.47.5138

    work page doi:10.1103/physreva.47.5138 1993

  4. [5]

    J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik. Spin squeezed atoms: A macroscopic entangled ensemble created by light. Phys. Rev. Lett. , 39:1319, 1999. DOI: 10.1103/PhysRevLett.83.1319

    work page doi:10.1103/physrevlett.83.1319 1999

  5. [6]

    Kuzmich, L

    A. Kuzmich, L. Mandel, and N. P. Bigelow. Generation of spin squeezing via contin- uous quantum nondemolition measurement. Phys. Rev. Lett. , 85:1594, 2000. DOI: 10.1103/PhysRevLett.85.1594

    work page doi:10.1103/physrevlett.85.1594 2000

  6. [9]

    J. Ma, X. Wang, C. P. Sun, and F. Nori. Quantum spin squeezing. Phys. Rep., 509: 89, 2011. DOI: 10.1016/j.physrep.2011.08.003

    work page doi:10.1016/j.physrep.2011.08.003 2011

  7. [10]

    C. L. Degen, F. Reinhard, and P. Cappellaro. Quantum sensing. Rev. Mod. Phys., 89:035002, 2017. DOI: 10.1103/RevModPhys.89.035002

    work page internal anchor Pith review doi:10.1103/revmodphys.89.035002 2017

  8. [11]

    Est` eve, C

    J. Est` eve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler. Squeezing and entanglement in a Bose–Einstein condensate. Nature, 455:1216, 2008. DOI: 10.1038/nature07332

    work page doi:10.1038/nature07332 2008

  9. [12]

    Pezz` e, A

    L. Pezz` e, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys., 90:035005,

    work page

  10. [13]

    DOI: 10.1103/RevModPhys.90.035005

    work page internal anchor Pith review doi:10.1103/revmodphys.90.035005

  11. [14]

    X. Chai, D. Lao, K. Fujimoto, R. Hamazaki, M. Ueda, and C. Raman. Magnetic solitons in a spin-1 Bose-Einstein condensate. Phys. Rev. Lett. , 125:030402, 2020. DOI: 10.1103/PhysRevLett.125.030402

    work page doi:10.1103/physrevlett.125.030402 2020

  12. [15]

    L. Xin, M. S. Chapman, and T. A. B. Kennedy. Fast generation of time-stationary spin-1 squeezed states by nonadiabatic control. PRX Quantum , 3:010328, 2022. DOI: 10.1103/PRXQuantum.3.010328

    work page doi:10.1103/prxquantum.3.010328 2022

  13. [16]

    L. Xin, M. Barrios, J. T. Cohen, and M. S. Chapman. Long-lived squeezed ground states in a quantum spin ensemble. Phys. Rev. Lett. , 131:133402., 2023. DOI: 10.1103/PhysRevLett.131.133402

    work page doi:10.1103/physrevlett.131.133402 2023

  14. [17]

    Barberena, A

    D. Barberena, A. Chu, J. K. Thompson, and A. M. Rey. Trade-offs between unitary and measurement induced spin squeezing in cavity QED. arXiv: 2309.15353

    work page arXiv

  15. [18]

    C. Luo, H. Zhang, A. Chu, C. Maruko, A. M. Rey, and J. K. Thompson. Hamilto- nian engineering of collective XYZ spin models in an optical cavity: From one-axis twisting to two-axis counter twisting models. arXiv: 2402.19429

    work page arXiv

  16. [19]

    J. M. Radcliffe. Some properties of coherent spin states. J. Phys. A: Gen. Phys. , 4: 313, 1971. DOI: 10.1088/0305-4470/4/3/009. 23

    work page doi:10.1088/0305-4470/4/3/009 1971

  17. [22]

    Byrnes, D

    T. Byrnes, D. Rosseau, M. Khosla, A. Pyrkov, A. Thomasen, T. Mukai, S. Koyama, A. Abdelrahman, and E. Ilo-Okeke. Macroscopic quantum information process- ing using spin coherent states. Optics Communications , 337:102, 2015. DOI: 10.1016/j.optcom.2014.08.017

    work page doi:10.1016/j.optcom.2014.08.017 2015

  18. [23]

    D. S. Abrams and S. Lloyd. Nonlinear quantum mechanics implies polynomial-time solution for NP-Complete and #P problems. Phys. Rev. Lett. , 81:3992, Nov 1998. DOI: 10.1103/PhysRevLett.81.3992. URL https://link.aps.org/doi/10.1103/ PhysRevLett.81.3992

    work page doi:10.1103/physrevlett.81.3992 1998

  19. [24]

    A. M. Childs and J. Young. Optimal state discrimination and unstruc- tured search in nonlinear quantum mechanics. Phys. Rev. A , 93:022314, 2016. DOI: 10.1103/PhysRevA.93.022314. URL https://link.aps.org/doi/10.1103/ PhysRevA.93.022314

    work page doi:10.1103/physreva.93.022314 2016

  20. [25]

    Bechmann-Pasquinucci, B

    H. Bechmann-Pasquinucci, B. Huttner, and N. Gisin. Nonlinear quantum state transformation of spin-1/2. Phys. Lett. A , 242:198, 1998

    work page 1998

  21. [26]

    M. Czachor. Notes on nonlinear quantum algorithms. Acta Phys. Slov. , 48:157, 1998

    work page 1998

  22. [27]

    M. Czachor. Local modification of the Abrams-Lloyd nonlinear algorithm. quant- ph/9803019

    work page arXiv

  23. [28]

    D. R. Terno. Nonlinear operations in quantum-information theory. Phys. Rev. A , 59:3320, 1999. DOI: 10.1103/PhysRevA.59.3320

    work page doi:10.1103/physreva.59.3320 1999

  24. [29]

    D. Bacon. Quantum computational complexity in the presence of closed timelike curves. Phys. Rev. A , 70:032309, Sep 2004. DOI: 10.1103/PhysRevA.70.032309. URL https://link.aps.org/doi/10.1103/PhysRevA.70.032309

    work page doi:10.1103/physreva.70.032309 2004

  25. [30]

    NP-complete Problems and Physical Reality

    S. Aaronson. NP-complete problems and physical reality. arXiv: quant-ph/0502072

    work page internal anchor Pith review Pith/arXiv arXiv

  26. [31]

    T. A. Brun, J. Harrington, and M. M. Wilde. Localized closed timelike curves can perfectly distinguish quantum states. Phys. Rev. Lett. , 102:210402, 2009. DOI: 10.1103/PhysRevLett.102.210402. URL https://link.aps.org/doi/10. 1103/PhysRevLett.102.210402

    work page doi:10.1103/physrevlett.102.210402 2009

  27. [33]

    M. E. Kahou and D. L. Feder. Quantum search with interacting Bose-Einstein condensates. Phys. Rev. A , 88:032310, 2013. DOI: 10.1103/PhysRevA.88.032310. URL https://link.aps.org/doi/10.1103/PhysRevA.88.032310

    work page doi:10.1103/physreva.88.032310 2013

  28. [34]

    D. A. Meyer and T. G. Wong. Nonlinear quantum search using the Gross-Pitaevskii equation. New J. Phys. , 15:063014, 2013

    work page 2013

  29. [35]

    D. A. Meyer and T. G. Wong. Quantum search with general nonlinearities. Phys. Rev. A, 89:012312, 2014. DOI: doi:10.1088/1367-2630/15/6/063014

    work page doi:10.1088/1367-2630/15/6/063014 2014

  30. [36]

    Di Molfetta and B

    G. Di Molfetta and B. Herzog. Searching via nonlinear quantum walk on the 2D-grid. arXiv: 2009.07800

    work page arXiv 2009

  31. [37]

    S. Deffner. Nonlinear speed-ups in ultracold quantum gases. Europhys. Lett., 140: 48001, 2022. DOI: 10.1209/0295-5075/ac9fed. 24

    work page doi:10.1209/0295-5075/ac9fed 2022

  32. [39]

    M. R. Geller. Fast quantum state discrimination with nonlinear PTP channels. Adv. Quantum Technol., page 2200156, 2023. DOI: 10.1002/qute.202200156. arXiv: 2111.05977

    work page doi:10.1002/qute.202200156 2023

  33. [40]

    M. R. Geller. Protocol for nonlinear state discrimination in rotating condensate. Adv. Quantum Technol., page 202300431, 2024. DOI: 10.1002/qute.202300431. arXiv: 2404.16288

    work page doi:10.1002/qute.202300431 2024

  34. [41]

    Großardt

    A. Großardt. Nonlinear-ancilla aided quantum algorithm for nonlinear Schr¨ odinger equations. arXiv: 2403.10102

    work page arXiv

  35. [42]

    S. M. Barnet and S. Croke. Quantum state discrimination. arXiv: 0810.1970

    work page internal anchor Pith review Pith/arXiv arXiv 1970

  36. [44]

    Bae and L.-C

    J. Bae and L.-C. Kwek. Quantum state discrimination and its applications. J. Phys. A: Math. Theor. , 48:083001, 2015. DOI: 10.1088/1751-8113/48/8/083001

    work page doi:10.1088/1751-8113/48/8/083001 2015

  37. [45]

    Rouhbakhsh and S

    M. Rouhbakhsh and S. A. Ghoreishi. Minimum-error discrimination of qubit states revisited. arXiv: 2108.12299

    work page arXiv

  38. [46]

    Arora and B

    S. Arora and B. Barak. Computational Complexity: A Modern Approach. Cambridge University Press, 2009

    work page 2009

  39. [47]

    C. G. Shull, D. K. Atwood, J. Arthur, and M. A. Horne. Search for a nonlinear variant of the Schr¨ odinger equation by neutron interferometry.Phys. Rev. Lett., 44: 765, 1980. DOI: 10.1103/PhysRevLett.44.765

    work page doi:10.1103/physrevlett.44.765 1980

  40. [48]

    G¨ ahler, A

    R. G¨ ahler, A. G. Klein, and A. Zeilinger. Neutron optical tests of nonlinear wave mechanics. Phys. Rev. A , 23:1611, 1981. DOI: 10.1103/PhysRevA.23.1611

    work page doi:10.1103/physreva.23.1611 1981

  41. [49]

    Weinberg

    S. Weinberg. Precision tests of quantum mechanics. Phys. Rev. Lett. , 62:485,

    work page

  42. [50]

    URL https://link.aps.org/doi/10

    DOI: 10.1103/PhysRevLett.62.485. URL https://link.aps.org/doi/10. 1103/PhysRevLett.62.485

    work page doi:10.1103/physrevlett.62.485

  43. [51]

    J. J. Bollinger, D. J. Heinzen, W. M. Itano, S. L. Gilbert, and D. J. Wineland. Test of the linearity of quantum mechanics by rf spectroscopy of the 9Be+ ground state. Phys. Rev. Lett. , 63:1031, 1989. DOI: 10.1103/PhysRevLett.63.1031. URL https://link.aps.org/doi/10.1103/PhysRevLett.63.1031

    work page doi:10.1103/physrevlett.63.1031 1989

  44. [53]

    R. L. Walsworth, I. F. Silvera, E. M. Mattison, and R. F. C. Vessot. Test of the linearity of quantum mechanics in an atomic system with a hydrogen maser. Phys. Rev. Lett., 64:2599, 1990. DOI: 10.1103/PhysRevLett.64.2599. URL https://link. aps.org/doi/10.1103/PhysRevLett.64.2599

    work page doi:10.1103/physrevlett.64.2599 1990

  45. [54]

    P. K. Majumder, B. J. Venema, S. K. Lamoreaux, B. R. Heckel, and E. N. Fortson. Test of the linearity of quantum mechanics in optically pumped 201Hg. Phys. Rev. Lett., 65:2931, 1990. DOI: 10.1103/PhysRevLett.65.2931. URL https://link.aps. org/doi/10.1103/PhysRevLett.65.2931

    work page doi:10.1103/physrevlett.65.2931 1990

  46. [55]

    Forstner, M

    S. Forstner, M. Zych, S. Basiri-Esfahani, K. E. Khosla, and W. P. Bowen. Nanome- chanical test of quantum linearity. Optica, 7:1427, 2020. DOI: 10.1364/OP- TICA.391671

    work page doi:10.1364/op- 2020

  47. [56]

    I. J. Arnquist, F. T. Avignone, A. S. Barabash, C. J. Barton, K. H. Bhimani, E. Blalock, B. Bos, M. Busch, M. Buuck, T. S. Caldwell, Y-D. Chan, C. D. Christof- 25 ferson, P.-H. Chu, M. L. Clark, C. Cuesta, J. A. Detwiler, Yu. Efremenko, H. Ejiri, S. R. Elliott, G. K. Giovanetti, M. P. Green, J. Gruszko, I. S. Guinn, V. E. Guiseppe, C. R. Haufe, R. Henning...

    work page doi:10.1103/physrevlett.129.080401 2022

  48. [57]

    Polkovnikov, A

    M. Polkovnikov, A. V. Gramolin, D. E. Kaplan, S. Rajendran, and A. O. Sushkov. Experimental limit on nonlinear state-dependent terms in quantum theory. Phys. Rev. Lett., 130:040202, 2023. DOI: 10.1103/PhysRevLett.130.040202

    work page doi:10.1103/physrevlett.130.040202 2023

  49. [58]

    J. Broz, B. You, S. Khan, H. H¨ affner, D. E. Kaplan, and S. Rajendran. Test of causal nonlinear quantum mechanics by Ramsey interferometry with a trapped ion. Phys. Rev. Lett., 130:200201, 2023. DOI: 10.1103/PhysRevLett.130.200201

    work page doi:10.1103/physrevlett.130.200201 2023

  50. [59]

    C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. Strengths and weaknesses of quantum computing. SIAM J. Comput. , 26:1510, 1997. DOI: 10.1137/S0097539796300933

    work page doi:10.1137/s0097539796300933 1997

  51. [60]

    E. P. Gross. Structure of a quantized vortex in boson systems. Nuovo Cimento, 20: 454, 1961. DOI: 10.1007/BF02731494

    work page doi:10.1007/bf02731494 1961

  52. [61]

    L. P. Pitaevskii. Vortex lines in an imperfect Bose gas. Sov. Phys. JETP , 13:451, 1961

    work page 1961

  53. [62]

    Erd˝ os and B

    L. Erd˝ os and B. Schlein. Quantum dynamics with mean field interactions: A new approach. J. Stat. Phys. , 134:859, 2009. DOI: 10.1007/s10955-008-9570-7

    work page doi:10.1007/s10955-008-9570-7 2009

  54. [64]

    E. H. Lieb and D. W. Robinson. The finite group velocity of quantum spin systems. Comm. Math. Phys. , 28:251, 1972. DOI: 10.1007/BF01645779

    work page doi:10.1007/bf01645779 1972

  55. [65]

    Idziaszek, T

    Z. Idziaszek, T. Calarco, and P. Zoller. Controlled collisions of a single atom and an ion guided by movable trapping potentials. Phys. Rev. A, 76:033409, 2007. DOI: 10.1103/PhysRevA.76.033409

    work page doi:10.1103/physreva.76.033409 2007

  56. [66]

    Tomza, K

    M. Tomza, K. Jachymski, R. Gerritsma, A. Negretti, T. Calarco, Z. Idziaszek, and P. S. Julienne. Cold hybrid ion-atom systems. Rev. Mod. Phys. , 91:035001, 2019. DOI: 10.1103/RevModPhys.91.035001

    work page doi:10.1103/revmodphys.91.035001 2019

  57. [67]

    Jyothi, K

    S. Jyothi, K. N. Egodapitiya, B. Bondurant, Z. Jia, E. Pretzsch, P. Chiappina, G. Shu, and K. R. Brown. A hybrid ion-atom trap with integrated high resolution mass spectrometer. Rev.. Sci.. Instrum. , 90:103201, 2019. DOI: 10.1063/1.5121431

    work page doi:10.1063/1.5121431 2019

  58. [68]

    L. Karpa. Interactions of ions and ultracold neutral atom ensembles in composite optical dipole traps: Developments and perspectives. Atoms, 9:39, 2021. DOI: 10.3390/atoms9030039

    work page doi:10.3390/atoms9030039 2021

  59. [69]

    R. S. Lous and R. Gerritsma. Ultracold ion-atom experiments: cooling, chemistry, and quantum effects. Advances in Atomic, Molecular, and Optical Physics , 71:65,

    work page

  60. [70]

    DOI: 10.1016/bs.aamop.2022.05.002

    work page doi:10.1016/bs.aamop.2022.05.002 2022

  61. [71]

    Zipkes, S

    C. Zipkes, S. Palzer, C. Sias, and M. Kohl. A trapped single ion inside a Bose–Einstein condensate. Nature, 464:388, 2010. DOI: 10.1038/nature08865

    work page doi:10.1038/nature08865 2010

  62. [72]

    Schmidt, P

    J. Schmidt, P. Weckesser, F. Thielemann, T. Schaetz, and L. Karpa. Optical traps for sympathetic cooling of ions with ultracold neutral atoms. Phys. Rev. Lett., 124: 053402, 2020. DOI: 10.1103/PhysRevLett.124.053402. 26

    work page doi:10.1103/physrevlett.124.053402 2020

  63. [73]

    Gerritsma, A

    R. Gerritsma, A. Negretti, H. Doerk, Z. Idziaszek, T. Calarco, and F. Schmidt-Kaler. Bosonic Josephson junction controlled by a single trapped ion. Phys. Rev. Lett., 109: 080402, 2012. DOI: 10.1103/PhysRevLett.109.080402

    work page doi:10.1103/physrevlett.109.080402 2012

  64. [74]

    Joger, A

    J. Joger, A. Negretti, and R. Gerritsma. Quantum dynamics of an atomic double- well system interacting with a trapped ion. Phys. Rev. A , 89:063621, 2014. DOI: 10.1103/PhysRevA.89.063621

    work page doi:10.1103/physreva.89.063621 2014

  65. [75]

    M. R. Ebgha, S. Saeidian, P. Schmelcher, and A. Negretti. Compound atom-ion Josephson junction: Effects of finite temperature and ion motion. Phys. Rev. A , 100:033616, 2019. DOI: 10.1103/PhysRevA.100.033616

    work page doi:10.1103/physreva.100.033616 2019

  66. [76]

    C. E. Wieman, D. E. Pritchard, and D. J. Wineland. Atom cooling, trapping, and quantum manipulation. Rev. Mod. Phys. , 71:S253, 1999. DOI: 10.1103/RevMod- Phys.71.S253

    work page doi:10.1103/revmod- 1999

  67. [77]

    Dalfovo , author S

    F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari. Theory of Bose- Einstein condensation in trapped gases. Rev. Mod. Phys. , 71:463, 1999. DOI: 10.1103/RevModPhys.71.463

    work page doi:10.1103/revmodphys.71.463 1999

  68. [78]

    A. J. Leggett. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys., 73:307, 2001. DOI: 10.1103/RevModPhys.73.307

    work page doi:10.1103/revmodphys.73.307 2001

  69. [79]

    Morsch and M

    O. Morsch and M. Oberthaler. Dynamics of Bose-Einstein condensates in optical lattices. Rev. Mod. Phys., 78:179, 2006. DOI: 10.1103/RevModPhys.78.179

    work page doi:10.1103/revmodphys.78.179 2006

  70. [80]

    E. H. Lieb, R. Seiringer, and J. Yngvason. Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional. Phys. Rev. A , 61:043602, 2000. DOI: 10.1103/PhysRevA.61.043602

    work page doi:10.1103/physreva.61.043602 2000

  71. [81]

    Bardos, F

    C. Bardos, F. Golse, and N. J. Mauser. Weak coupling limit of the N-particle Schrodinger equation. Methods and Applications of Analysis , 7:275, 2000

    work page 2000

  72. [82]

    C. Gokler. Mean field limit for many-particle interactions. arXiv: 2006.05486

    work page arXiv 2006

  73. [83]

    Fr¨ ohlich, S

    J. Fr¨ ohlich, S. Graffi, and S. Schwarz. Mean-field and classical limit of many- body Schr¨ odinger dynamics for bosons. Comm. Math. Phys. , 271:681, 2007. DOI: 10.1007/s00220-007-0207-5

    work page doi:10.1007/s00220-007-0207-5 2007

  74. [84]

    Erd˝ os, B

    L. Erd˝ os, B. Schlein, and H.-T. Yau. Rigorous derivation of the Gross-Pitaevskii equation. Phys. Rev. Lett., 98:040404, 2007. DOI: 10.1103/PhysRevLett.98.040404

    work page doi:10.1103/physrevlett.98.040404 2007

  75. [85]

    Rodnianski and B

    I. Rodnianski and B. Schlein. Quantum fluctuations and rate of convergence towards mean field dynamics. Comm. Math. Phys. , 291:31, 2009. DOI: 10.1007/s00220-009- 0867-4

    work page doi:10.1007/s00220-009- 2009

  76. [86]

    Knowles and P

    A. Knowles and P. Pickl. Mean-field dynamics: Singular potentials and rate of convergence. Commun. Math. Phys., 298:101, 2010. DOI: 10.1007/s00220-010-1010- 2

    work page doi:10.1007/s00220-010-1010- 2010

  77. [87]

    L. Chen, J. O. Lee, and B. Schlein. Rate of convergence towards Hartree dynamics. J. Stat. Phys. , 144:872, 2011. DOI: 10.1007/s10955-011-0283-y

    work page doi:10.1007/s10955-011-0283-y 2011

  78. [88]

    On the rate of convergence for the mean field approximation of many-body quantum dynamics

    Z. Ammari, M. Falconi, and B. Pawilowski. On the rate of convergence for the mean field approximation of many-body quantum dynamics. arXiv: 1411.6284v1

    work page internal anchor Pith review Pith/arXiv arXiv

  79. [89]

    P. Pickl. Derivation of the time dependent Gross–Pitaevskii equation with external fields. Reviews in Mathematical Physics , 27:1550003, 2015. DOI: 10.1142/S0129055X15500038

    work page doi:10.1142/s0129055x15500038 2015

  80. [90]

    Benedikter, M

    N. Benedikter, M. Porta, and B. Schlein. Effective Evolution Equations from Quan- tum Dynamics. Springer, Berlin, 2016. DOI: 10.1007/978-3-319-24898-1

    work page doi:10.1007/978-3-319-24898-1 2016

Showing first 80 references.