Quantum Gas Microscope for Detecting Single Atoms in a Hubbard-Regime Optical Lattice
Nature, 2009 · paper · Physics
Presents a "quantum gas microscope" that images individual atoms on single sites of a Hubbard-regime optical lattice with near-unity fidelity. The lattice is projected through the high-resolution imaging system, linking bulk ultracold gases with atom-by-atom control.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
3 findings
Reference or label Methods: "This results in tight axial confinement with trap frequencies of typically 900 Hz. The weak axial confinement of 20 Hz is provided by the magnetic trap." The 20 Hz confinement is the in-plane (horizontal) one, so the second "axial" mislabels the direction (radial or in-plane intended).
- p. 7 Methods, Hybrid surface trap
The weak axial confinement of 20 Hz is provided by the magnetic trap.
- p. 7 Methods, Hybrid surface trap, preceding sentence
This results in tight axial confinement with trap frequencies of typically 900 Hz.
- p. 4 main text, 2D quantum gas paragraph
shallow 20 Hz confinement in the horizontal plane
- p. 4 main text, 2D quantum gas paragraph
6 kHz confinement in the vertical direction and shallow 20 Hz confinement in the horizontal plane
Judge's note: Read on the page 7 image: two consecutive sentences call both the tight 900 Hz and the weak 20 Hz confinement "axial", and the next sentence says "In order to increase the axial confinement to the final value, the 2D gas is transferred into a vertical standing wave", so axial means vertical. The main text on page 4 (checked in the extracted text, not the image) says "6 kHz confinement in the vertical direction and shallow 20 Hz confinement in the horizontal plane". Nothing in the paper defines a second axis convention. The 900 Hz versus 6 kHz difference is not a defect: the Methods say the confinement is then increased to its final value.
Second check: another model agreed
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Reference or label Wrong figure pointer: "We measure a typical single atom emission FWHM size 570 and 630 nm along the x and y direction, respectively, which is close to the theoretical minimum value of ~520 nm (Fig. 3)" - the single-atom horizontal and vertical profiles and the 'Minimum Atom Image' curve are in Figure 2(b); Figure 3 is the dense-BEC lattice image with no profile. (Also, the Figure 3 caption prints "640nm" without a space.)
- p. 5 main text, paragraph on fluorescence imaging
close to the theoretical minimum value of ~520 nm (Fig. 3)
- p. 13 Figure 2 caption
(b) Response of a single atom, derived from sparse images: Horizontal (filled dots) and vertical (empty dots) profiles
- p. 14 Figure 3 caption
Figure 3: Site resolved imaging of single atoms on a 640nm period optical lattice, loaded with a high density BEC.
- p. 13 Figure 2 caption
(b) Response of a single atom, derived from sparse images
Judge's note: Opened pages 5, 13 and 14. Figure 2(b) plots the horizontal and vertical single-atom profiles, the Airy function and a blue dashed 'Minimum Atom Image' curve, and its caption describes exactly the minimum the text explains (finite CCD pixel width and extent of the atom's probability distribution). Figure 3 shows only the densely filled lattice with a zoomed inset and a 640 nm marker; it has no profile, FWHM or theoretical curve. The following paragraph on p. 6 introduces Figure 3 afresh ('Figure 3 shows an image obtained by loading a dense condensate'). No statement elsewhere makes Fig. 3 the source of the spot size. The pointer should be Fig. 2 (2b). The '640nm' spacing in the Figure 3 caption is also visible on the page and is a cosmetic point.
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Reference or label Reference 10 is printed as "Jaksch, D. & Zwerger, W., The cold atom Hubbard toolbox, Annals of Physics 315, 52-79 (2005)"; the second author of that article is reportedly P. Zoller, not W. Zwerger.
- p. 10 reference list, ref. 10
Jaksch, D. & Zwerger, W., The cold atom Hubbard toolbox, Annals of Physics 315, 52-79
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that "The cold atom Hubbard toolbox", Annals of Physics 315, 52-79 (2005), was written by D. Jaksch and P. Zoller. The page 10 image prints the entry exactly as quoted, with "Zwerger, W." as second author. The authorship cannot be verified from the files, so this goes to the authors as a query. W. Zwerger does appear in reference 6, which would explain a slip.
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17 minor (typos and the like; most checked by the judge only)
Wording The projected lattice is called "a simple cubic lattice with a lattice constant of 640 nm" (p. 3) and "simple cubic lattice potentials with a periodicity a=640 nm" (p. 4), while the Methods give a two-dimensional potential "V(x,y) = V0(sin2(kx) + sin2(ky))", i.e. a square lattice in the 2D plane.
- p. 3 main text
Here we project a simple cubic lattice with a lattice constant of 640 nm
- p. 4 main text
we create blue detuned simple cubic lattice potentials with a periodicity a=640 nm
- p. 8 Methods, Optical lattice projection
V(x,y) = V0(sin2(kx) + sin2(ky))
Judge's note: Checked pages 3, 4 and 8 on the images. The potential given in Methods depends on x and y only and the paper elsewhere speaks of 'a two-dimensional optical lattice' and 'periodic potentials in the 2D plane'. 'Simple cubic' is a three-dimensional lattice type; the term is used loosely here for the square geometry. There is a vertical standing wave, but the atoms occupy one plane and the paper does not describe it as a third lattice axis of period 640 nm. Imprecise terminology, not a contradiction a reader would be misled by; either form could be defended, so kept as an observation.
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Typo Affiliation reads "Harvard-MIT Center for Ultracold Atoms and Dept. Of Physics, Harvard University" with the preposition 'Of' capitalised.
- p. 1 affiliation line
Dept. Of Physics
Judge's note: Viewed the crop of page 1: the affiliation line prints 'Dept. Of Physics' with a capital O. Cosmetic.
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Typo Subject-verb disagreement: "a combination of high fidelity single atom detection and short lattice periods are important, which has not been previously achieved" (singular subject 'a combination' with 'are', then 'has').
- p. 2 main text, third paragraph
a combination of high fidelity single atom detection and short lattice periods are important, which has not been previously achieved
Judge's note: Read on the page 2 image, third paragraph. The sentence is printed as quoted; 'a combination ... is important' is expected. Grammar only.
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Typo Page 2: "such as a solid immersion microscopy for cold atoms" (indefinite article with 'microscopy'); page 3: "(full width, half maximum , FWHM)" has a space before the comma.
- p. 2 main text, second paragraph
such as a solid immersion microscopy for cold atoms
- p. 3 main text
(full width, half maximum , FWHM)
- p. 3 paragraph 'The quantum gas microscope is based on a high aperture optical system'
half maximum , FWHM
Judge's note: Both visible on the page images (p. 2 second paragraph; p. 3 line 'measure an optical resolution of ~ 600 nm (full width, half maximum , FWHM)'). The stray space before the comma is in the rendered page, not only the text layer. Cosmetic.
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Typo Subject-verb disagreement: "A lithographically produced mask and our high resolution optics allows us to generate arbitrary potential landscapes" (compound subject with singular 'allows').
- p. 3 main text, second paragraph
A lithographically produced mask and our high resolution optics allows us
Judge's note: Read on the page 3 image, second paragraph. Printed as quoted; 'allow' is expected. Grammar only.
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Typo The same optical element is named three ways: "a hemispheric lens is placed inside the vacuum" (p. 3), "the hemisphere lens" (p. 4) and "a hemispherical lens" (Figure 1 caption, p. 12).
- p. 3 setup paragraph
a hemispheric lens is placed inside the
- p. 12 Figure 1 caption
hemispherical lens
Judge's note: All three forms seen on the page images / crop. All are understandable and refer unambiguously to the same lens; a wording consistency point only.
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Typo Comma where a full stop is needed: "without changing the lattice geometry, This is important since we strongly increase the lattice depth".
- p. 4 main text, projection-method paragraph
without changing the lattice geometry, This is important
Judge's note: Visible on the page 4 image, last paragraph: a comma is followed by a capitalised 'This' starting a new sentence. Not an extraction artefact.
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Typo Paragraph ends with a comma: "with shot to shot fluctuations of less than 15% rms," followed by a paragraph break.
- p. 5 main text, end of paragraph on drifts
than 15% rms,
- p. 5 paragraph on stability, last line
shot to shot fluctuations of less than 15% rms,
Judge's note: Visible on the page 5 image: the line 'than 15% rms,' is the last of the paragraph and the next paragraph ('Pair densities within multiply occupied lattice sites ...') starts indented after a blank line. Either a full stop is meant or the end of the sentence is missing; the statement itself is complete as it stands, so treated as punctuation.
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Typo Stray comma before a citation superscript: "which is important for single-site addressing ,21."
- p. 5 main text
which is important for single-site addressing ,21.
- p. 5 imaging paragraph
single-site addressing ,21
- p. 5 Results
Figure (2) shows a
- p. 6 Results
no significant hopping occurs. .
Judge's note: Visible on the page 5 image: 'addressing ,' followed by superscript 21 and a full stop. The other items bundled into this cluster ('Figure (2)', the doubled full stop on p. 6, the comma ending the paragraph) are judged under C012, C014 and C010.
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Typo Inconsistent figure-reference style: "Figure (2) shows a typical image" with the number in parentheses and a double space, against "(Fig. 1)", "Figure 3 shows" and "Figure 4 shows" elsewhere.
- p. 5 main text
atom emission FWHM size 570 and 630 nm along the x and y direction
- p. 5 main text
Figure (2) shows a typical image
Judge's note: Visible on the page 5 image ('Figure (2) shows a typical image'); pages 3 and 6 use 'Fig. 1', 'Figure 3', 'Figure 4' without parentheses. Style inconsistency only. The missing 'of' in 'FWHM size 570 and 630 nm' raised in the same cluster is judged under C013.
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Typo Missing word: "We measure a typical single atom emission FWHM size 570 and 630 nm along the x and y direction" ('size of' expected; a double space is left in its place).
- p. 5 imaging paragraph
emission FWHM size 570 and 630 nm
Judge's note: Visible on the page 5 image: a wider gap between 'size' and '570' with no 'of'. Meaning is unaffected.
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Typo Doubled full stop: "during which no significant hopping occurs. ."
- p. 6 main text, end of image-analysis paragraph
during which no significant hopping occurs. .
- p. 6 paragraph before the conclusion
no significant hopping occurs. .
Judge's note: Visible on the page 6 image at the end of the paragraph before 'In conclusion': two full stops separated by a space.
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Typo Camera name printed as "Andor Ixon DU888"; the manufacturer's styling is reportedly "iXon".
- p. 9 collection efficiency paragraph
Andor Ixon DU888
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that Andor styles the product name "iXon" (lower-case i, capital X). The page 9 image does print "Andor Ixon DU888". This is capitalisation of a brand name only and cannot be checked from the files.
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Typo Reference 1: "Zoller, P. , Cold bosonic atoms" has a stray space before the comma.
- p. 9 reference 1
Zoller, P. , Cold bosonic atoms
Judge's note: Visible on the page 9 image: there is a space between "P." and the comma in reference 1. The entry also lacks the "&" before the last author that the other entries use. Cosmetic.
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Typo References 16 and 17 print the arXiv identifiers with a colon, "arXiv: 0903:3282 (2009)" and "arXiv: 0904:1532 (2009)", whereas references 21 and 25 use a dot ("arXiv: 0903.4837", "arXiv: 0812.3630").
- p. 10 Reference 16
arXiv: 0903:3282 (2009)
- p. 10 Reference 17
arXiv: 0904:1532 (2009)
- p. 11 Reference 21 (correct format, for comparison)
arXiv: 0903.4837 (2009)
- p. 10 reference 16
arXiv: 0903:3282
Judge's note: The colons are visible on the page 10 image for references 16 and 17, so this is not an extraction artefact. References 21 and 25 were checked in the extracted text for page 11 and use dots, so the list is inconsistent within itself and the dot form is the evident fix.
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Typo Figure 1 caption: "projecting a periodic mask (e) onto the atoms through the objective lens through the same objective via beam splitter (f)" repeats the phrase about the objective.
- p. 12 Figure 1 caption
atoms through the objective lens through the same objective via beam splitter (f)
- p. 12 Figure 1 caption
through the objective lens through the same objective via beam splitter (f)
- p. 12 Figure 1 caption
onto the atoms through the objective lens through the same objective via beam splitter (f)
Judge's note: Read on the page 12 image. The caption says "through the objective lens through the same objective"; the figure shows a single objective (b), so one of the two phrases is an editing leftover. Meaning is unaffected.
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Typo Figure 4 caption: "The blue line denotes a fit to the function using a double Gaussian function for each of the two peaks." The fit is to the histogram, not "to the function", and the wording leaves unclear whether one Gaussian or a double Gaussian was fitted per peak.
- p. 15 Figure 4 caption
The blue line denotes a fit to the function using a double Gaussian function for each of the two peaks.
- p. 15 Figure 4 caption
fit to the function using a double Gaussian function
Judge's note: Read on the page 15 image; the caption is printed as quoted. "a fit to the function using a ... function" is a garbled sentence, presumably meant as a fit to the histogram or distribution. The fit model (two Gaussians in total, or a double Gaussian for each peak) cannot be told from the caption; the plotted curve has two peaks with visibly broad tails, which does not settle it. Copy-editing defect with a small ambiguity about the fit model.
Second check: none (judge only)