Designing Arbitrary One-dimensional Potentials on an Atom Chip

Bernhard Rauer; Federica Cataldini; Frederik S. M{\o}ller; Igor E. Mazets; Jo\~ao Sabino; J\"org Schmiedmayer; Mohammadamin Tajik; Si-Cong Ji; Thomas Schweigler

REVIEW 2 major objections 4 minor 38 references

Designing Arbitrary One-dimensional Potentials on an Atom Chip

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A digital micro-mirror device plus a feedback loop writes arbitrary longitudinal potentials—boxes, barriers, and ramps—onto one-dimensional Bose gases on an atom chip.

desk verdict A genuinely useful methods paper that does what it says with care, but the potential claim rests on density inferred from the same measurement used for optimization. read the letter →

arxiv 1908.01563 v2 pith:DLEEOOCK submitted 2019-08-05 cond-mat.quant-gas physics.optics

Mohammadamin Tajik , Bernhard Rauer , Thomas Schweigler , Federica Cataldini , João Sabino , Frederik S. M{o}ller , Si-Cong Ji , Igor E. Mazets

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Jörg Schmiedmayer

This is my paper · ORCID

classification cond-mat.quant-gasphysics.optics PACS 67.85.-d37.10.Gh

keywords atomchipone-dimensionalBosegasdigitalmicro-mirrordeviceopticaldipolepotentialfeedbackoptimizationboxquantumsimulationThomas-Fermidensity

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 establishes a practical route to arbitrary control of the longitudinal potential of a one-dimensional degenerate Bose gas on an atom chip. The authors add a digital micro-mirror device (DMD) shaped blue-detuned light pattern to the magnetic trap, and an automated feedback loop adjusts the pattern until the measured atomic density matches a target density computed from the desired potential. They demonstrate a 160-micrometre box potential, a box with a central tunable barrier, a box with a sinusoidally modulated bottom, and a linear (V-shaped) confining potential, with density residuals of 4.2 to 5.9 percent over the target region, stable for more than six hours. This matters because homogeneous and precisely shaped one-dimensional systems are the foundation for experiments in quantum thermodynamics, transport, and quantum simulation.

What carries the argument

The load-bearing mechanism is the DMD as a binary intensity modulator imaged onto the atoms with spatial averaging and spatial filtering. Because many micro-mirror pixels contribute to each diffraction-limited spot, switching individual pixels in a column changes the local optical potential in small steps, giving quasi-gray-scale one-dimensional potentials. The optimization loop then uses the Thomas–Fermi relation between the one-dimensional density and the total potential, $V(z)=\mu-\frac{g}{2\pi a_\perp^2}\frac{\rho(z)}{\sqrt{1+2a_s\rho(z)}}-\frac{\hbar\omega_\perp}{2}\left(\sqrt{1+2a_s\rho(z)}+\frac{1}{\sqrt{1+2a_s\rho(z)}}\right)$ (Eq. 2), to translate density deviations into pixel updates: where density is too high, pixels are switched on to raise the potential; where too low, outer pixels are shifted away to lower it. The target density itself comes from the non-polynomial Schrödinger equation for each candidate potential.

What would settle it

Toggle on a single DMD super-pixel column and image the density: if the induced density dip appears at more than one longitudinal position, or if toggling pixels in one region shifts density in a distant region by a comparable amount, the local update rule on which the optimization rests is empirically false.

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Extended reading notes

Core claim

The central claim is that superposing an optical dipole potential, locally shaped by a DMD, on the magnetic confinement of an atom chip yields a robust and versatile method to engineer the longitudinal potential of a one-dimensional Bose gas while preserving the chip's transverse trapping and evaporative cooling. The paper shows that an iterative pattern optimization—comparing the measured one-dimensional density with a target density obtained by solving the one-dimensional non-polynomial Schrödinger equation—converges to target potentials without requiring a precise model of the optical setup. In the demonstrated examples, the final density profiles agree with the target to 4.2–5.9% normalized root-mean-square deviation in the target region, and the achieved patterns stay stable for over six hours. The measured potentials match the target potentials once those targets are broadened by the DMD imaging system.

Load-bearing premise

The update rule assumes that turning DMD pixels on or off changes the potential locally and monotonically lowers or raises the local density, per the Thomas–Fermi relation, with negligible coupling to neighbouring positions.

Editorial extensions

If this is right

Homogeneous box-like one-dimensional gases remove density inhomogeneity that otherwise masks intrinsic many-body dynamics, enabling cleaner studies of recurrence, thermalization, and transport.
Barriers inside a box allow longitudinal splitting and tunable tunneling between homogeneous segments, extending the double-well physics already available via radio-frequency dressed states.
Because DMD patterns can be changed faster than the axial dynamics, the same setup can implement time-dependent potentials and quenches, for example exciting a chosen mode by imprinting its density modulation.
The autonomous optimization means no detailed optical model is needed: any target potential can be reached from a black screen or from a previous pattern, limited mainly by imaging noise and resolution.

Reading between the lines

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

Possible extension: the same density-feedback loop could be ported to other atomic species or to two-dimensional optical potentials, but the Thomas–Fermi locality assumption would degrade and would need stronger spatial filtering or a more global update rule.
Possible extension: because the DMD refresh rate (17–50 kHz) is far above the axial trap frequencies, stroboscopic or time-averaged patterns could synthesize effective Floquet potentials on the same chip; fast switching is mentioned in the paper but no Floquet experiment is reported.
Possible consequence: pushing the measurement noise down, for example with higher-resolution imaging, should drive the converged density residuals below the 4–6% level, since the paper's own termination criterion is set by the standard error of the mean density.

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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

This is a solid experimental methods paper. The authors combine a DMD-generated optical dipole potential with an atom chip magnetic trap, and they demonstrate an autonomous density-feedback optimization routine that produces box, barrier, sinusoidally modulated, and V-shaped longitudinal potentials for 1D Bose gases. The measured density residuals of 4.2–5.9% and the six-hour stability data are credible. The writing is direct, the calibration procedure is described in enough detail to be reproduced, and the citation practice is honest: prior DMD beam shaping work (Gauthier, Zupancic) is properly acknowledged, so the novelty is correctly framed as integration and optimization rather than inventing the technique.

The soft spot is real but not fatal. The potential itself is never measured independently. Equation (2) reconstructs the potential from the Thomas-Fermi inversion of the same density profile that the optimizer was trying to match, so a density match almost guarantees an apparent potential match. The green broadened target potentials in Fig. 7 are just convolutions of the target, not an independent check. An atom-number scaling test—does the density match at a different atom number if the optical potential is correct?—would have settled this cleanly. The authors do acknowledge this limitation in passing ("quantitative comparison is instructive," Section 5), which counts in their favor.

I do not see this as a load-bearing flaw. For most applications the density profile is the operational quantity, and the paper's claim of 'arbitrary one-dimensional potentials' is honestly hedged by the demonstrated examples. Still, I would have liked one direct potential probe, or at least a more explicit sentence saying the potential plots are model-dependent.

This paper will be useful to experimental groups working on atom chips, 1D quantum gases, and quantum thermodynamics. It deserves a serious referee and could be accepted after minor revision, mostly to add the caveat about indirect potential verification. No data or code are shared, which is a small downside in 2020.

All in all, worth publishing. I would cite it and would bring it to a reading group as a good example of feedback optimization in cold atoms.

Referee Report

2 major / 4 minor

Summary. The paper reports an experimental method for shaping the longitudinal potential of a 1D Bose gas on an atom chip by superposing a DMD-shaped, blue-detuned optical dipole potential on the magnetic chip trap. The central technical contribution is an iterative feedback procedure: starting from a measured density profile, the DMD pattern is updated locally so that the measured longitudinal density approaches the NPSE ground-state density of a desired target potential. The authors demonstrate four potentials—a 160 µm box, a double box with a barrier, a box with sinusoidal modulation, and a V-shaped potential—with final density residuals between 4.2% and 5.9%, and they report stability of a box potential for more than six hours. They argue that the method provides flexible and autonomous control of longitudinal confinement for experiments in quantum thermodynamics and quantum simulation.

Significance. If the central claim holds, this is a useful technical advance: it combines the advantages of atom-chip magnetic trapping (fast evaporative cooling, RF dressed-state capabilities) with the flexibility of DMD-shaped optical potentials, and the optimization loop is described in sufficient detail to be reproduced. The paper is honest in reporting convergence curves, error bars, and a stability measurement, and it explicitly describes the calibration and update rules. However, the verification of the central claim is weakened by a circularity: the optimization acts on the density, and the reported potentials are reconstructed from that same density via the Thomas-Fermi relation. The demonstrated density control is convincing, but the claim of arbitrary potential control would be strengthened by an independent cross-check of the realized potential.

major comments (2)

[§5, Eq. (2), Fig. 7] The reported potential fidelity is not independently verified. The optimization observable is the longitudinal density ρ(z), and the "measured potentials" in Fig. 7 are reconstructed from the same measured density using the Thomas-Fermi relation, Eq. (2). A density match therefore produces an apparent potential match by construction, up to the accuracy of the TF approximation and the assumed chemical potential. The 4.2–5.9% density residuals do not by themselves establish that the realized V(z) equals the target potential, because a pattern that reproduces the target density at the calibration atom number can in principle produce a different potential at other densities. The green "broadened target potentials" in Fig. 7 are a useful consistency check but are not an independent measurement. I recommend adding a cross-check that does not reuse the optimization density: for example, measure the density for the same final DMD pattern at a substantially different atom number and compare with the NPSE ground state of the target potential; a genuine potential match should reproduce the density at both atom numbers. The text should also state explicitly that the plotted potentials are inferred from density, not directly measured.
[§4, update rule and Fig. 6] The local update rule assumes a monotonic, local relationship between switching DMD pixels and changes in the local density—effectively a diagonally dominant Jacobian with negligible coupling between neighboring 1.05 µm grid points. Given that the imaging PSF has an Airy diameter of 4 µm, neighboring grid points are coupled, and near steep barriers and box edges the local Thomas-Fermi relation itself becomes questionable. The paper shows empirical convergence for four examples, but it does not discuss conditions under which the loop could stall or converge to a density-matching pattern that is not the intended potential. I ask for a brief analysis of this limitation or an additional experimental test: rerun the optimization for the same target starting from different initial patterns and compare the final DMD patterns and density residuals, and comment explicitly on the role of the finite PSF in the update procedure.

minor comments (4)

[Abstract and §6] The word "arbitrary" overstates the demonstrated capability: the experiment uses only blue-detuned repulsive light, so the optical potential can only add repulsive corrections on top of the magnetic potential. Please qualify the claim (e.g., "shaped repulsive potentials" or "a wide class of one-dimensional potentials") in the abstract and conclusion.
[Eq. (1)] The normalization factor in Eq. (1) is written as 1/(j−l), but the sum runs from k=j to k=l, so the number of terms is l−j+1. Please check and correct the notation.
[§3, scattering-rate estimate] The sentence "This leads to only one spontaneous scattering per second for an ensemble of 10^4 atoms" appears inconsistent with the quoted rate of ~2π×0.1 mHz: for 10^4 atoms, this would be on the order of several scattering events per second. Please recheck the numerical estimate.
[Fig. 10] The text says the stability check exceeds six hours, while the horizontal axis of Fig. 10(a) extends to 500 minutes (about 8.3 hours). Please align the stated time span with the plotted data or adjust the axis.

Circularity Check

1 steps flagged · score 2.0 of 10

Measured potentials are reconstructed from the same density used for optimization, so potential agreement is partly self-referential; overall feedback-control demonstration remains largely self-contained.

self definitional [Sec. 5, Eq. (2) and Fig. 7 (cf. Sec. 4 optimization target, Eq. (1))]
"The initial and final potentials, plotted in Fig. 7, are obtained using the NPSE for 1D condensates. In the limit where the kinetic energy of motion in z-direction is neglected (Thomas-Fermi approximation), the solution for the stationary state reads: ... (2). Here, ρ(z) is the measured 1D density ... Although this measured potential is not used in the optimization process, a qualitative comparison between the measured potential and the target potential is instructive."

The optimization cost function (Eq. 1) and the DMD update rule in Sec. 4 operate on the longitudinal density ρ(z_k), driving the measured density to the NPSE target density of the desired potential. The 'measured potentials' shown in Fig. 7 are then obtained by applying Eq. (2) to that same measured density, with the chemical potential only an offset. Hence the potential curves are not an independent measurement of the optical potential; they are a deterministic re-expression of the same density that was already optimized. Up to the validity of the Thomas-Fermi relation, any density match automatically yields an apparent potential match, so the quoted 4.2-5.9% density residuals cannot by themselves certify that the actual optical potential equals the target.

full rationale

The paper is primarily an experimental feedback-control demonstration: a DMD pattern is iteratively updated until the measured 1D density matches the NPSE ground-state density of a desired potential. That loop is self-contained and uses fresh experimental data at each iteration, so the density residuals (4.2-5.9%) are a meaningful demonstration of density control. The principal circular strand is the potential verification: the "measured potentials" in Fig. 7 are obtained from Eq. (2), which inverts the very density that the optimization was designed to match. Consequently, the apparent agreement between measured and target potentials is partly built into the density agreement and does not independently confirm that the optical potential itself equals the target. The paper explicitly notes that this reconstructed potential is not used in the optimization and calls the comparison qualitative, which mitigates the issue but does not remove it. There is no load-bearing self-citation: references to the authors' prior work concern atom-chip apparatus, absorption imaging, and recurrence experiments, all background techniques rather than premises that force the conclusion. No uniqueness theorem is imported, and no ansatz is smuggled in via citation. The weakness is an independent-validation gap: a quantitative cross-check that does not reuse the optimization density (e.g., atom-number scaling or a direct potential probe) would settle whether the potential claim is fully verified. This warrants a moderate-low circularity score of 2, not a higher score, because the central control demonstration has independent content and the circular element is confined to the potential-reconstruction evidence.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No new physical entities, forces, or conserved quantities are introduced. The central claim rests on standard atom-light interaction, the quasi-1D mean-field description of the condensate, local Thomas-Fermi monotonicity for the feedback update, and short-TOF imaging fidelity. The target potential shapes are user specifications, not fitted parameters. The quantitative settings of the imaging PSF used for broadening the target curves are only partially reported.

assumptions (6)

domain assumption V_dip(r) proportional to sgn(omega - omega_0) I(r) for a far-detuned optical field.
Section 2 Basic design. This standard atom-light dipole potential justifies using DMD intensity patterns to create arbitrary potentials.
domain assumption The 1D Bose gas is described by the non-polynomial Schrödinger equation; Eq. (2) inverts the Thomas-Fermi density to obtain the longitudinal potential.
Used in Secs. 4 and 5 to compute target densities from target potentials and to infer the realized potential from measured density. Requires quasi-1D mean-field validity.
domain assumption Local monotonic Thomas-Fermi relation: increasing the local potential decreases the local 1D density.
Sec. 4 update procedure. The pixel-update logic depends on this one-to-one local relationship; a broad or non-local point-spread function would weaken it.
domain assumption DMD time averaging faster than atomic dynamics creates an effective time-averaged potential.
Sec. 2 with refs [28,29]. The DMD refresh rate is assumed fast enough for the atoms to see only the average intensity.
domain assumption The longitudinal density profile is preserved during 1-3 ms time-of-flight imaging.
Sec. 3. The weak longitudinal confinement is assumed to keep expansion negligible; otherwise the imaged density would differ from the in-trap profile used for optimization.
domain assumption The DMD imaging system acts as a linear, shift-invariant system with a 4 micron Airy diameter point-spread function.
Sec. 3 and the green broadened target curves in Fig. 7. The exact PSF used for broadening is not fully specified in the text.

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Pith. "Pith review of Designing Arbitrary One-dimensional Potentials on an Atom Chip." pith.science (2026). https://pith.science/paper/DLEEOOCK

@misc{pith2026190801563,
  author       = {Pith},
  title        = {Pith review of: Designing Arbitrary One-dimensional Potentials on an Atom Chip},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DLEEOOCK}},
  note         = {Machine review of arXiv:1908.01563}
}

abstract

We use laser light shaped by a digital micro-mirror device to realize arbitrary optical dipole potentials for one-dimensional (1D) degenerate Bose gases of 87Rb trapped on an atom chip. Superposing optical and magnetic potentials combines the high flexibility of optical dipole traps with the advantages of magnetic trapping, such as effective evaporative cooling and the application of radio-frequency dressed state potentials. As applications, we present a 160 ${\mu}$m long box-like potential with a central tuneable barrier, a box-like potential with a sinusoidally modulated bottom and a linear confining potential. These potentials provide new tools to investigate the dynamics of 1D quantum systems and will allow us to address exciting questions in quantum thermodynamics and quantum simulations.

Figures

Figures reproduced from arXiv: 1908.01563 by the authors.

**Figure 2.** Creating a box-like potential (green) by superposing blue- or red-detuned light fields [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Expanding the dynamical range of intensity using the concept of spatial averaging [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Integration of the optical setup for DMD shaped dipole potentials into the absorption [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: An example of data used for (a) horizontal (longitudinal) calibration and (b) vertical [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Updating the DMD pattern based on the comparison between the averaged measured [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Results of pattern optimization process for four different cases: (a) a box-like potential [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: Realization of a L = 160 µm long box-like potential with different barrier heights, VB, from 0 to 1 kHz. Density profiles and potentials are shown with different colors. Thin red curves represent the target densities for each case. The figure suggests that the widths o…

**Figure 9.** Figure 9: Evolution of RMS for three different cases (lines are guides to the eye): a box-like potential with length L = 160 µm (black), two box-like potentials separated by a barrier (brown), a box-like potential with a sinusoidally modulated bottom (green) and a V-shaped pote…

**Figure 10.** Figure 10: Stability measurement: (a) evolution of RMS before and after optimization for a box-like potential with length L = 100 µm. The horizontal axis on the top is the time corresponding to different iterations. The optimization stopped at iteration number 40 (orange line) …

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A. Imambekov, I. E. Mazets, D. S. Petrov, V. Gritsev, S. Manz, S. Hoﬀerberth, T. Schumm, E. Demler, and J. Schmiedmayer, “Density ripples in expanding low-dimensional gases as a probe of correlations,” Phys. Rev. A80, 033604 (2009)

2009
[35]

Two-point density correlations of quasicondensates in free expansion,

S. Manz, R. Bücker, T. Betz, C. Koller, S. Hoﬀerberth, I. E. Mazets, A. Imambekov, E. Demler, A. Perrin, J. Schmiedmayer, and T. Schumm, “Two-point density correlations of quasicondensates in free expansion,” Phys. Rev. A 81, 031610 (2010)

2010
[36]

Projective phase measurements in one-dimensional Bose gases,

Y. D. van Nieuwkerk, J. Schmiedmayer, and F. H. L. Essler, “Projective phase measurements in one-dimensional Bose gases,” SciPost Phys.5, 46 (2018)

2018
[37]

Roughness suppression via rapid current modulation on an atom chip,

J.-B. Trebbia, C. L. Garrido Alzar, R. Cornelussen, C. I. Westbrook, and I. Bouchoule, “Roughness suppression via rapid current modulation on an atom chip,” Phys. Rev. Lett.98, 263201 (2007)

2007
[38]

Eﬀective wave equations for the dynamics of cigar-shaped and disk-shaped bose condensates,

L. Salasnich, A. Parola, and L. Reatto, “Eﬀective wave equations for the dynamics of cigar-shaped and disk-shaped bose condensates,” Phys. Rev. A65, 043614 (2002)

2002
[39]

One-dimensional atomic superﬂuids as a model system for quantum thermodynamics,

J. Schmiedmayer, “One-dimensional atomic superﬂuids as a model system for quantum thermodynamics,” in Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, eds. (Springer International Publi...

2018

Pith tools

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

[1] [1]

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)

2008

[2] [2]

Ultracold atoms out of equilibrium,

T. Langen, R. Geiger, and J. Schmiedmayer, “Ultracold atoms out of equilibrium,” Annu. Rev. Condens. Matter Phys. 6, 201–217 (2015)

work page 2015

[3] [3]

Bose-einstein condensation of atoms in a uniform potential,

A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, “Bose-einstein condensation of atoms in a uniform potential,” Phys. Rev. Lett.110, 200406 (2013)

2013

[4] [4]

Two-Dimensional Homogeneous Fermi Gases,

K. Hueck, N. Luick, L. Sobirey, J. Siegl, T. Lompe, and H. Moritz, “Two-Dimensional Homogeneous Fermi Gases,” Phys. Rev. Lett.120, 060402 (2018)

work page 2018

[5] [5]

Homogeneous Atomic Fermi Gases,

B. Mukherjee, Z. Yan, P. B. Patel, Z. Hadzibabic, T. Yefsah, J. Struck, and M. W. Zwierlein, “Homogeneous Atomic Fermi Gases,” Phys. Rev. Lett.118, 123401 (2017)

work page 2017

[6] [6]

Recurrences in an isolated quantum many-body system,

B. Rauer, S. Erne, T. Schweigler, F. Cataldini, M. Tajik, and J. Schmiedmayer, “Recurrences in an isolated quantum many-body system,” Science360, 307 (2018)

work page 2018

[7] [7]

Sound Propagation in a Uniform Superﬂuid Two-Dimensional Bose Gas,

J. L. Ville, R. Saint-Jalm, É. Le Cerf, M. Aidelsburger, S. Nascimbène, J. Dalibard, and J. Beugnon, “Sound Propagation in a Uniform Superﬂuid Two-Dimensional Bose Gas,” Phys. Rev. Lett.121, 145301 (2018)

work page 2018

[8] [8]

Realization of a Sonic Black Hole Analog in a Bose-Einstein Condensate,

O. Lahav, A. Itah, A. Blumkin, C. Gordon, S. Rinott, A. Zayats, and J. Steinhauer, “Realization of a Sonic Black Hole Analog in a Bose-Einstein Condensate,” Phys. Rev. Lett.105, 240401 (2010)

work page 2010