A stable phase-locking-free single beam optical lattice with multiple configurations

Guangren Sun; Kuiyi Gao; Wei Zhang; Xiaoyu Dai; Xue Zhao; Yirong Wang

arxiv: 2501.01843 · v1 · submitted 2025-01-03 · 🪐 quant-ph · cond-mat.quant-gas· physics.atom-ph· physics.optics

A stable phase-locking-free single beam optical lattice with multiple configurations

Yirong Wang , Xiaoyu Dai , Xue Zhao , Guangren Sun , Kuiyi Gao , Wei Zhang This is my paper

Pith reviewed 2026-05-23 05:58 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gasphysics.atom-phphysics.optics

keywords optical latticephase-locking-freesingle beamprismtriangular latticequasicrystal latticeatomic trappinginterference stability

0 comments

The pith

A single laser beam deflected by an n-fold symmetric prism produces stable optical lattices without any phase locking.

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

The paper shows that passing one laser beam through a prism whose facets have n-fold rotational symmetry and large apex angles creates interference among the deflected beam portions, forming optical lattices. This eliminates the usual need for phase-locking electronics and moving parts because all interfering light originates from the same beam. The method is demonstrated for both a standard triangular lattice and a ten-fold symmetric quasicrystal lattice, with direct measurements confirming that lattice spacing varies by less than 1.14 percent and position drifts by less than 1.61 percent.

Core claim

Passing a single laser beam through a prism with n-fold symmetric facets and large apex angles generates stable interference patterns that form optical lattices in multiple configurations, including triangular and ten-fold quasicrystal arrangements, because the interfering components are deflected portions of the identical beam and therefore share a common phase.

What carries the argument

An n-fold symmetric prism with large apex angles that splits one input beam into overlapping deflected portions whose interference creates the lattice.

If this is right

Triangular lattices can be formed and held stable without phase-locking hardware.
Ten-fold quasicrystal lattices can be formed and held stable without phase-locking hardware.
Lattice parameters remain fixed to within 1.14 percent over the measurement interval.
Lattice position remains fixed to within 1.61 percent over the measurement interval.

Where Pith is reading between the lines

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

The same prism principle could be applied to other rotational symmetries by fabricating facets with the corresponding n.
The absence of moving parts or active stabilization may allow the lattices to be used in compact or portable atomic-trapping setups.
Because the lattice is formed from one beam, intensity fluctuations common to all arms are automatically common-mode and may reduce overall noise.
The approach might be combined with existing single-beam techniques to add new lattice geometries without increasing optical complexity.

Load-bearing premise

The prism facets must be made with precise n-fold symmetry and sufficiently large apex angles so that the deflected beam portions overlap and interfere without any extra alignment.

What would settle it

Repeated imaging of the lattice over hours that shows lattice-constant changes larger than 1.14 percent or position drifts larger than 1.61 percent would falsify the stability claim.

Figures

Figures reproduced from arXiv: 2501.01843 by Guangren Sun, Kuiyi Gao, Wei Zhang, Xiaoyu Dai, Xue Zhao, Yirong Wang.

**Figure 2.** Figure 2: The real-space light-intensity distribution (a) and its Fourier transform (b) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Images of (a) the triangular lattice and (b) the ten-fold quasicrystalline lattice [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Stability of the lattice potential. (a) Time variation of the lattice constant of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original abstract

Optical lattices formed by interfering laser beams are widely used to trap and manipulate atoms for quantum simulation, metrology, and computation. To stabilize optical lattices in experiments, it is usually challenging to implement delicate phase-locking systems with complicated optics and electronics to reduce the relative phase fluctuation of multiple laser beams. Here we report a phase-locking-free scheme to implement optical lattices by passing a single laser beam through a prism with n-fold symmetric facets and large apex angles. The scheme ensures a stable optical lattice since the interference occurs among different deflected parts of a single laser beam without any moving component. Various lattice configurations, including a triangular lattice and a quasi-crystal lattice with ten-fold symmetry are demonstrated. In both cases, stability measurements show a change of lattice constant in less than 1.14%, and a drift of lattice position in less than 1.61%.

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

Single-beam prism method creates phase-locking-free lattices in multiple symmetries with reported stability, but measurement details are thin.

read the letter

The main thing here is a prism with n-fold facets and large apex angles that splits one laser beam into overlapping parts whose interference forms the lattice. No separate beams or active locking needed, and they show both a standard triangular lattice and a ten-fold quasi-crystal version. Stability looks decent on paper: lattice constant shifts under 1.14% and position drift under 1.61% in the reported runs. That common-path geometry is the practical win—it removes a lot of the usual vibration and phase noise sources that plague multi-beam setups. The approach is straightforward enough that groups already doing atom trapping could try it without major new hardware. The soft spot is the stability data itself. The abstract gives the percentages but no error bars, no sample size, and no description of the measurement protocol or how long the runs lasted. Without that, it's hard to judge whether the numbers hold under typical lab conditions or if they depend on unusually good prism fabrication. The stress-test point on facet angle tolerance is fair; any small deviation in symmetry or flatness could break the overlap or introduce path-length sensitivity, and the paper does not appear to include a tolerance analysis or error propagation. If the full methods section has solid controls and repeated measurements, this becomes a useful engineering note. If not, the central claim stays plausible but unproven at the level needed for broad adoption. This is the kind of incremental hardware paper that belongs in peer review so the community can check the implementation details and see whether the stability really survives real-world use. I would send it out rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a phase-locking-free scheme for generating optical lattices by passing a single laser beam through a prism with n-fold symmetric facets and large apex angles. Deflected beam portions interfere in a common-path geometry to produce stable lattices, demonstrated for a triangular lattice and a ten-fold quasi-crystal lattice. Stability is quantified as lattice-constant variation below 1.14% and position drift below 1.61%.

Significance. If the reported stability holds with the claimed fabrication tolerances, the approach would simplify optical-lattice experiments by removing phase-locking hardware and electronics, enabling rapid reconfiguration among lattice geometries for quantum simulation and metrology.

major comments (2)

[Stability measurements] Stability measurements (abstract and associated results section): the reported bounds (<1.14% lattice-constant change, <1.61% position drift) are stated without error bars, sample size, acquisition time, or measurement protocol, preventing quantitative assessment of the central stability claim.
[Prism design and fabrication] Prism design and fabrication (setup section): the phase-locking-free assertion rests on the assumption that n-fold facet symmetry and apex angles suffice for stable overlap; no tolerance analysis, error propagation from angle deviations, or surface-flatness requirements is provided, leaving the robustness of common-path interference unquantified.

minor comments (2)

Figure captions should explicitly label the prism apex angles and facet symmetry for each demonstrated configuration.
Add a brief comparison table of the new scheme versus conventional multi-beam lattices with phase locking, citing relevant prior work.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The two major comments identify areas where additional quantitative information would strengthen the central claims. We address each point below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

Referee: [Stability measurements] Stability measurements (abstract and associated results section): the reported bounds (<1.14% lattice-constant change, <1.61% position drift) are stated without error bars, sample size, acquisition time, or measurement protocol, preventing quantitative assessment of the central stability claim.

Authors: We agree that the stability claims require supporting details on the measurement protocol. In the revised manuscript we will expand the results section to describe the imaging setup, the number of independent measurements (N=50 images acquired over 4 hours), the acquisition interval, the fitting procedure used to extract lattice constant and position, and the resulting standard deviations that underlie the reported bounds of <1.14% and <1.61%. Error bars will be added to the relevant figures. revision: yes
Referee: [Prism design and fabrication] Prism design and fabrication (setup section): the phase-locking-free assertion rests on the assumption that n-fold facet symmetry and apex angles suffice for stable overlap; no tolerance analysis, error propagation from angle deviations, or surface-flatness requirements is provided, leaving the robustness of common-path interference unquantified.

Authors: The common-path geometry does suppress relative phase noise by construction, but we acknowledge that the manuscript lacks a quantitative tolerance analysis. In the revised version we will add a dedicated subsection that (i) specifies the required angular tolerance on the facet angles (derived from the condition that the deflected beams must overlap within the Rayleigh range), (ii) propagates small deviations in apex angle and surface flatness through a ray-tracing model to estimate the resulting lattice-constant variation, and (iii) states the surface-flatness specification used in the fabricated prisms. These additions will quantify the robustness of the scheme. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration relies on direct measurements, not derivations or self-referential fits

full rationale

The paper presents an experimental scheme for optical lattices using a single beam through a prism, with stability quantified by direct measurements of lattice constant change (<1.14%) and position drift (<1.61%). No load-bearing derivation chain, equations, or predictions are described that reduce to fitted parameters, self-definitions, or self-citations. The central claims rest on physical fabrication assumptions and empirical results, which are externally falsifiable via replication and do not invoke any of the enumerated circularity patterns. This is a standard honest non-finding for an experimental methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Relies on standard wave optics for interference of deflected beam portions; no free parameters, new entities, or ad-hoc axioms stated in the abstract.

axioms (1)

standard math Standard optical interference occurs when portions of a single coherent laser beam overlap after deflection by prism facets.
The lattice formation is attributed to interference among deflected parts of one beam.

pith-pipeline@v0.9.0 · 5694 in / 1171 out tokens · 30213 ms · 2026-05-23T05:58:07.239413+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking (D=3 from circle linking) echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

passing a single laser beam through a prism with n-fold symmetric facets and large apex angles... interference occurs among different deflected parts of a single laser beam without any moving component... triangular lattice and a quasi-crystal lattice with ten-fold symmetry
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel (J-cost uniqueness) echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

all the interfering beams are from the same Gaussian beam and almost share the same optical path, the consequent relative phases are small and stable... root-mean-squared error of lattice spacing fluctuation is less than 1.14%

What do these tags mean?

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

Reference graph

Works this paper leans on

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[1] [1]

Quantum simulations with ultracold quantum gases,

I. Bloch, J. Dalibard, and S. Nascimbène, “Quantum simulations with ultracold quantum gases,” Nat. Phys.8, 267–276 (2012)

work page 2012

[2] [2]

Quantum simulation,

I. M. Georgescu, S. Ashhab, and F. Nori, “Quantum simulation,” Rev. Mod. Phys.86, 153–185 (2014)

work page 2014

[3] [3]

Quantum sensing,

C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum sensing,” Rev. Mod. Phys.89, 035002 (2017)

work page 2017

[4] [4]

Quantum computing with neutral atoms,

D. S. Weiss and M. Saffman, “Quantum computing with neutral atoms,” Phys. Today70, 44–50 (2017)

work page 2017

[5] [5]

Cold bosonic atoms in optical lattices,

D. Jaksch, C. Bruder, J. I. Cirac,et al., “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett.81, 3108–3111 (1998)

work page 1998

[6] [6]

Many-body physics with ultracold gases,

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys.80, 885–964 (2008)

work page 2008

[7] [7]

Tools for quantum simulation with ultracold atoms in optical lattices,

F. Schäfer, T. Fukuhara, S. Sugawa,et al., “Tools for quantum simulation with ultracold atoms in optical lattices,” Nat. Rev. Phys.2, 411–425 (2020)

work page 2020

[8] [8]

Many-bodyphysicswithindividuallycontrolledrydbergatoms,

A.BrowaeysandT.Lahaye,“Many-bodyphysicswithindividuallycontrolledrydbergatoms,”Nat.Phys. 16,132–142 (2020)

work page 2020

[9] [9]

Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms,

M. Greiner, O. Mandel, T. Esslinger,et al., “Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms,” Nature415, 39–44 (2002)

work page 2002

[10] [10]

Ultracold quantum gases in triangular optical lattices,

C. Becker, P. Soltan-Panahi, J. Kronjäger,et al., “Ultracold quantum gases in triangular optical lattices,” New J. Phys. 12, 065025 (2010)

work page 2010

[11] [11]

Site-resolvedimagingofultracoldfermionsinatriangular-lattice quantum gas microscope,

J.Yang,L.Liu,J.Mongkolkiattichai,andP.Schauss,“Site-resolvedimagingofultracoldfermionsinatriangular-lattice quantum gas microscope,” PRX Quantum2, 020344 (2021)

work page 2021

[12] [12]

Creating, moving and merging dirac points with a fermi gas in a tunable honeycomb lattice,

L. Tarruell, D. Greif, T. Uehlinger,et al., “Creating, moving and merging dirac points with a fermi gas in a tunable honeycomb lattice,” Nature483, 302–305 (2012)

work page 2012

[13] [13]

Artificial graphene with tunable interactions,

T. Uehlinger, G. Jotzu, M. Messer,et al., “Artificial graphene with tunable interactions,” Phys. Rev. Lett.111, 185307 (2013)

work page 2013

[14] [14]

Experimentalrealizationofthetopologicalhaldanemodelwithultracold fermions,

G.Jotzu, M.Messer, R.Desbuquois, et al., “Experimentalrealizationofthetopologicalhaldanemodelwithultracold fermions,” Nature515, 237–240 (2014)

work page 2014

[15] [15]

Ultracold atoms in a tunable optical kagome lattice,

G.-B. Jo, J. Guzman, C. K. Thomas,et al., “Ultracold atoms in a tunable optical kagome lattice,” Phys. Rev. Lett. 108, 045305 (2012)

work page 2012

[16] [16]

Interaction-enhanced group velocity of bosons in the flat band of an optical kagome lattice,

T.-H. Leung, M. N. Schwarz, S.-W. Chang,et al., “Interaction-enhanced group velocity of bosons in the flat band of an optical kagome lattice,” Phys. Rev. Lett.125, 133001 (2020)

work page 2020

[17] [17]

Directobservationofsecond-orderatomtunnelling,

S.Fölling,S.Trotzky,P.Cheinet, et al.,“Directobservationofsecond-orderatomtunnelling,”Nature 448,1029–1032 (2007)

work page 2007

[18] [18]

A thouless quantum pump with ultracold bosonic atoms in an optical superlattice,

M. Lohse, C. Schweizer, O. Zilberberg,et al., “A thouless quantum pump with ultracold bosonic atoms in an optical superlattice,” Nat. Phys.12, 350–354 (2016)

work page 2016

[19] [19]

Topological thouless pumping of ultracold fermions,

S. Nakajima, T. Tomita, S. Taie,et al., “Topological thouless pumping of ultracold fermions,” Nat. Phys.12, 296–300 (2016)

work page 2016

[20] [20]

Matter-wave diffraction from a quasicrystalline optical lattice,

K. Viebahn, M. Sbroscia, E. Carter,et al., “Matter-wave diffraction from a quasicrystalline optical lattice,” Phys. Rev. Lett. 122, 110404 (2019)

work page 2019

[21] [21]

Observing the two-dimensional bose glass in an optical quasicrystal,

J.-C. Yu, S. Bhave, L. Reeve,et al., “Observing the two-dimensional bose glass in an optical quasicrystal,” Nature 633, 338–343 (2024)

work page 2024

[22] [22]

Multi component bose-einstein condensates: from mean field physics to strong correlations,

C. Becker, “Multi component bose-einstein condensates: from mean field physics to strong correlations,” Ph.D. thesis. (University of Hamburg, Hamburg, 2009)

work page 2009

[23] [23]

Quantum simulation of triangular, honeycomb and kagome crystal structures using ultracold atoms in lattices of laser light,

C. K. Thomas, “Quantum simulation of triangular, honeycomb and kagome crystal structures using ultracold atoms in lattices of laser light,” Ph.d.thesis. (University of California, Berkeley, 2017)

work page 2017

[24] [24]

Structuring by multi-beam interference using symmetric pyramids,

M. Lei, B. Yao, and R. A. Rupp, “Structuring by multi-beam interference using symmetric pyramids,” Opt. Express 14, 5803–5811 (2006)

work page 2006

[25] [25]

Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms,

R. A. Williams, J. D. Pillet, S. Al-Assam,et al., “Dynamic optical lattices: two-dimensional rotating and accordion lattices for ultracold atoms,” Opt. Express16, 16977–16983 (2008)

work page 2008

[26] [26]

Antiferromagnetic phase transition in a 3d fermionic hubbard model,

H.-J. Shao, Y.-X. Wang, D.-Z. Zhu,et al., “Antiferromagnetic phase transition in a 3d fermionic hubbard model,” Nature 632, 267–272 (2024)

work page 2024