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Bloch oscillations of a soliton in a one-dimensional quantum fluid

Nature Physics volume 21, pages 1541–1547 (2025)Cite this article

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Abstract

The motion of a quantum system under an external force often challenges classical intuition. A notable example is the dynamics of a single particle in a periodic potential, which undergoes Bloch oscillations under the action of a constant force. Similar oscillations can also occur in one-dimensional quantum fluids without a lattice. The generalization of Bloch oscillations to a weakly bounded ensemble of interacting particles has so far been limited to the experimental study of the two-particle case, where the observed period is halved compared to the single-particle case. In this work, we observe the oscillations of the position of a mesoscopic solitonic wave packet—consisting of approximately 1,000 atoms—in a one-dimensional Bose gas subjected to a constant uniform force and in the absence of a lattice potential. The oscillation period scales inversely with the number of atoms, revealing its collective nature. We demonstrate the role of the phase coherence of the quantum bath in which the wave packet moves and investigate the underlying topology of the associated superfluid currents. Our measurements highlight the periodicity of the dispersion relation of collective excitations in one-dimensional quantum systems.

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Fig. 1: Soliton preparation and BOs in a tube.
Fig. 2: Principle of the experiment.
Fig. 3: Evolution of the phase of the bath component during BOs.
Fig. 4: Oscillation of one and two solitons under a constant force in a ring geometry.

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Data availability

The experimental data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The codes used for the analysis are available from the corresponding author on reasonable request.

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Acknowledgements

We acknowledge support from the ERC (Grant Agreement No 863880). We thank N. Pavloff for sharing personal notes and A. Minguzzi, N. Cooper, W. Zwerger and M. Fleischhauer for fruitful discussions and C. Heintze for his participation at the early stage of the project.

Author information

Author notes

  1. These authors contributed equally: F. Rabec, G. Chauveau.

Authors and Affiliations

  1. Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, Paris, France

    F. Rabec, G. Chauveau, G. Brochier, S. Nascimbene, J. Dalibard & J. Beugnon

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  1. F. Rabec
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  2. G. Chauveau
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  3. G. Brochier
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Contributions

F.R., G.C. and G.B. developed the experimental protocol, performed the experiments and analysed the data. S.N., J.D. and J.B. supervised the project. All authors contributed to the interpretation of the results and production of the paper.

Corresponding author

Correspondence to J. Beugnon.

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Extended data

Extended Data Fig. 1 Magnetic soliton at rest.

a, Absorption image of the minority component wave packet in \(\left\vert 2\right\rangle\). The axis of the tube is horizontal. The color is in arbitrary units proportional to the atomic surface density. The horizontal solid line corresponds to a length of 10 μm. b, Mean linear density along the tube direction (x). The solid line is a fit of the data to the analytical profile of the magnetic soliton. c, We vary the atom number transferred to the minority component and monitor the short time evolution of the size of the wave packet. Solid lines are fits of the function t ↦ σ0 + γt2 to the data. The error bars correspond to the statistical error obtained from the fit of the density profiles. d, Evolution of the expansion coefficient γ as a function of the atom number N2. The value Ns corresponds to the atom number for which the wave packet is stationary. This experiment thus demonstrates the realization of a magnetic soliton at rest. Error bars in c) d) represent the statistical errors obtained from the repetitions of each experiment.

Source data

Extended Data Fig. 2 Full width at half maximum and depletion of a magnetic soliton.

We focus on the soliton at rest (u = 0 and \(\tilde{J}=0\)). This graph is plotted using typical parameters of the experiment: n0 = 330 μm−1 and ξs = 2 μm.

Extended Data Fig. 3 The family of soliton solutions.

Each ellipse corresponds to a given value of \(\tilde{N}\). Each point of an ellipse is a soliton with a given velocity u and a given Ω. During a Bloch oscillation the system follows a trajectory from the bottom of ellipse at the initial time to the top of the ellipse at the first turning point and then comes back to its initial position. The shaded area is the region where no solitonic solutions exist, corresponding to Ω < u2/4 − 1.

Supplementary information

Supplementary Information (download PDF )

Supplementary Figs. 1–5 and discussion.

Source data

Source Data Fig. 1 (download ZIP )

Density profile (b), center of mass position (c) of the soliton. Measured oscillation frequency for different parameters (d).

Source Data Fig. 3 (download ZIP )

Absorption images of the matter wave interference data for different hold times.

Source Data Fig. 4 (download ZIP )

Center of mass position and winding number for different hold times.

Source Data Extended Data Fig. 1 (download ZIP )

Density profile (b), width of the wave packet (c) and expansion coefficient (d) of the soliton.

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Rabec, F., Chauveau, G., Brochier, G. et al. Bloch oscillations of a soliton in a one-dimensional quantum fluid. Nat. Phys. 21, 1541–1547 (2025). https://doi.org/10.1038/s41567-025-02970-1

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