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Observation of the 2D–1D crossover in strongly interacting ultracold bosons


Dimensionality plays an essential role in determining the nature and properties of a physical system. This is particularly evident in quantum systems, where interactions and fluctuations are enhanced in lower dimensions, leading to various different quantum effects. Here we show that strongly interacting ultracold bosons perceive their dimensionality as either one or two, depending on whether they are probed on short or long distances, respectively. We probe this dimensional crossover using a thorough analysis of the momentum distribution to study the characteristic decay of the one-body correlation function in the two dimensionalities and track how the decay is modified during the crossover. We find a varying two-slope structure, which substantiates the main result. These observations demonstrate how quantum properties in the strongly correlated regime evolve in the dimensional crossover as a result of the interplay between dimensionality, interactions and temperature.

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Fig. 1: Conceptual sketch of the experiment.
Fig. 2: Characteristic decay of the longitudinal correlation function G(1)(x, 0).
Fig. 3: Illustration of the mechanism behind the first-order correlation function and its interpretation.
Fig. 4: Dimensional crossover analysis.

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Data availability

The data that support the findings of this study are made publicly available from Zenodo by the authors at (ref. 49).


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The Innsbruck team acknowledges funding by a Wittgenstein prize grant under project number Z336-N36 and by the European Research Council (ERC) under project number 789017. This research was funded in part by the Austrian Science Fund (FWF) W1259-N27 and M.H. thanks the doctoral school Atoms, Light and Molecules (ALM) for hospitality. This work is also supported by the Swiss National Science Foundation under grant number 200020-188687. Numerical calculations make use of the ALPS scheduler library and statistical analysis tools46,47,48.

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Authors and Affiliations



The work was conceived by T.G., H.-C.N., M.L., H.Y. and Y.G. Experiments were performed by Y.G. and S.D. Data were analysed by Y.G., H.Y. and S.R. Theoretical models and simulation were done by H.Y., L.P. and T.G. Preparation of experiments was carried out by Y.G, S.D. and M.H. The main contributors to the preparation of the manuscript were H.-C.N., T.G., Y.G., H.Y. and M.L.

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Correspondence to Hanns-Christoph Nägerl.

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Extended data

Extended Data Fig. 1 A schematic of our imaging setup and an example of the image.

(a) The vectors ky, kz, kw and the imaging direction (blue arrows) all lie in one plane, with kx perpendicular to this plane, see also inset. The red 3D ellipsoid along the kz direction indicates the atomic cloud after TOF starting from an ensemble of 2D layers for Vy = 0Er. The light red 2D ellipsoid along kw direction is the shadow in our absorption image. (b) An example of a projected image after TOF for Vy = 0Er.

Extended Data Fig. 2 Experimental momentum distribution n(kx) along the unmodulated direction x for the 2D and the 1D case, folded over kxa = 0 and rescaled by the maximum density.

The shaded area indicates the error given by the standard deviation for 30 repetitions.

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Guo, Y., Yao, H., Ramanjanappa, S. et al. Observation of the 2D–1D crossover in strongly interacting ultracold bosons. Nat. Phys. 20, 934–938 (2024).

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