A preprint reports that a cloud of dysprosium-164 atoms showed a triangular arrangement of density peaks at lower field tilt and stripes at higher tilt. Between those patterns, measurements showed larger, non-Gaussian shot-to-shot fluctuations; the study did not determine whether the triangular-to-stripe transition is first- or second-order.
The work examines what the paper frames as supersolid behavior: an atom cloud with both a repeating spatial pattern and global phase coherence. The first signal came from images taken in the trap; the second was tested by letting the cloud expand and checking whether its interference pattern stayed reproducible from shot to shot.
How the researchers read the pattern
The gas contained about 140,000 164Dy atoms. Researchers varied field tilt from 0° to 70° while also changing the magnetic field, which set the estimated scattering length—a measure of contact interaction strength—from 89 to 109 a0. The two quantities were ramped together over 100 milliseconds, the gas was held for 30 milliseconds, and researchers then took either in-situ images or 50-millisecond time-of-flight images.
To classify the arrangement, the team converted each in-situ image into a Fourier power spectrum, a way to make repeating spatial structure appear as peaks. It defined R as the strength ratio of the two dominant finite-wave-number peaks and calculated the first four cumulants from 30 independent shots at each parameter setting.
A crossover with a noisy middle
R moved from approximately 1 toward approximately 0 as tilt increased. In the study’s measure, that marked a shift from triangular-order signatures toward stripe-order signatures. At about 30° to 45°, R was intermediate, while its variance increased and its distribution became non-Gaussian.
Stripe order was identified at tilts of 45° and above in a range of scattering lengths just below the threshold where modulation began, and it was reported to dominate at 70°. Those bounds were consistent with theory, but they were not presented as a precise thermodynamic phase boundary.
The pattern was not the whole story
Near the unmodulated-to-modulated transition, both triangular and stripe states produced reproducible interference patterns in time-of-flight images. The patterns remained visible when 20 shots were averaged, which the authors classified as global phase coherence.
Farther from modulation onset, the interference became complex and irreproducible and disappeared when shots were averaged. The authors interpreted that behavior as a loss of global phase coherence and an insulating state.
The reported coherence ratio stayed roughly between 0.7 and 1 below onset for most tilt angles, except between 40° and 45°. On that measure, the authors described coherent triangular arrays from 0° to 30° and coherent stripes from 50° to 70°, with the intermediate region remaining the difficult case.
What remains unresolved
Temperature-dependent extended Gross-Pitaevskii simulations, including thermal and quantum fluctuation terms, gave qualitative support for the observations. Across 60 simulated repetitions, R was high in triangular conditions, low in stripe conditions and intermediate—with the largest variance—in the fluctuating regime.
The result is a map of behavior under a coupled protocol. Because field tilt and scattering length were ramped together, the study traced their combined settings rather than varying them independently; the authors say this makes it harder to determine the precise order of the transitions.
The document is labeled arXiv:2608.20327v1 and dated 20 August 2026.
Paper data and sources
Original title: Competing triangular and stripe supersolid orders in a dipolar quantum gas
Authors: Karthik Chandrashekara, Christian Gölzhäuser, Lily Platt et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text