A box trap provides nearly uniform confinement with a sharp boundary, thereby largely removing the trap-induced density inhomogeneity in the central region associated with a harmonic trap and offering a distinct platform for investigating interaction-driven density modulation and rotational phenomena in dipolar quantum gases. In this work, we systematically study the ground-state density distributions and rotation-induced vortex configurations of a dipolar Bose gas confined in a cylindrical box trap. The system is described by the three-dimensional extended Gross-Pitaevskii equation, including the contact interaction, the long-range anisotropic dipole-dipole interaction, the Lee-Huang-Yang quantum-fluctuation correction, and the rotational term -\Omega L_z. The equation is solved by combining imaginary-time evolution with a split-step Crank-Nicolson scheme. The nonlocal dipolar interaction is evaluated using a Fourier-space convolution method, with a spherical cutoff of the dipolar kernel introduced to suppress numerical artifacts associated with the periodicity implicit in the fast Fourier transform.
In the absence of rotation, we find that decreasing the contact scattering length a_s produces two qualitatively different stages of density modulation. First, the radial ring-like modulation continuously increases while the density distribution remains rotationally symmetric. When the scattering length is further reduced to a critical value, the angular density contrast increases abruptly, signaling the spontaneous breaking of continuous rotational symmetry. This behavior differs from that in harmonically trapped dipolar condensates, where radial and angular density modulations are closely connected with roton softening and tend to develop together. The box geometry therefore allows the continuous radial density redistribution and the symmetry-breaking angular modulation to be clearly distinguished.
When rotation is introduced, vortices nucleate only after the rotation frequency exceeds an interaction-dependent critical value. Near the threshold, several vortices enter the condensate almost simultaneously, resulting in a finite jump of the total circulation quantum number Q_\rm t. We attribute this behavior to the softening of surface modes carrying finite angular momentum. Increasing the relative dipolar interaction strength \epsilon_\rm dd=a_\rm dd/a_s enhances the density modulation and further lowers the energetic cost of vortex nucleation, so that vortices can enter the condensate at lower rotation frequencies.
At higher rotation frequencies, the centrifugal effect redistributes atoms toward the outer region of the box and strongly suppresses the density near the center. As a result, vortices become increasingly concentrated in the central region, forming a central high-circulation structure whose internal configuration cannot be resolved at the current spatial resolution. This structure coexists with necklace-like arrays of singly quantized vortices and is markedly different from the Abrikosov vortex lattice in a harmonic trap. For \Omega/2\pi>25~\mathrmHz, the calculated total circulation Q_\rm t exhibits an approximately linear dependence on the rotation frequency.
Our results demonstrate that the sharp boundary of a box trap, the long-range dipolar interaction, and rotation jointly give rise to density-modulated and vortex states that are qualitatively different from those in conventional harmonic confinement. The present work clarifies the mechanisms underlying symmetry breaking, vortex nucleation, and circulation redistribution in rotating dipolar gases, and provides a theoretical basis for future experimental investigations of rotating dipolar superfluids and supersolid-related states in homogeneous box potentials.