Competing triangular and stripe supersolid orders in a dipolar quantum gas

Understanding how multiple broken symmetries emerge, compete, and coexist is a central challenge in many-body physics. Supersolids represent a unique platform to study this because they combine global phase coherence with spontaneous spatial ordering, such as crystallinity. While one-dimensional dipolar supersolids have been extensively studied, two-dimensional systems are predicted to support a much richer structural variety, including competing triangular arrays, stripes, and honeycomb patterns. However, experimentally observing this structural richness and the phase transitions connecting them has remained limited. This paper investigates whether tuning both the contact interaction strength and the dipole tilt angle in a confined dipolar quantum gas can give access to these competing two-dimensional supersolid orders and their underlying phase transitions.

The researchers prepare a degenerate quantum gas consisting of approximately 1.4 × 10^5 dysprosium-164 atoms confined in an anisotropic surfboard-shaped harmonic trap. By applying a uniform magnetic field with a tunable magnitude and tilt angle relative to the tight confinement axis, they simultaneously control the atomic scattering length and the orientation of the magnetic dipole moments. Starting from an unmodulated superfluid state, the system is ramped over 100 milliseconds and held in trap. The resulting atomic distributions are then characterized using in-situ absorption imaging to analyze real-space density profiles and structural order, as well as time-of-flight measurements to probe global phase coherence through interference pattern reproducibility.

By systematically varying the scattering length and the dipole tilt angle, the experiment successfully uncovers distinct spatial arrangements. At small tilt angles, density modulations form equilateral triangular arrays of droplets, whereas large tilt angles promote stripe-like patterns aligned along the in-plane axis. A statistical analysis of a structural order parameter reveals an intermediate critical regime characterized by enhanced variance and non-Gaussian fluctuations, signaling strong competition between the triangular and stripe orders. Furthermore, time-of-flight measurements demonstrate that both spatial structures exist in a phase-coherent supersolid regime near the unmodulated-to-modulated transition. Farther from this transition, the system transitions into phase-incoherent insulating states characterized by a loss of global phase coherence.