Supersolidity of cnoidal waves in an ultracold Bose gas

A one-dimensional Bose-Einstein condensate may experience nonlinear periodic modulations known as cnoidal waves. We argue that such structures represent promising candidates for the study of supersolidity-related phenomena in a nonequilibrium state. A mean-field treatment makes it possible to rederive Leggett's formula for the superfluid fraction of the system and to estimate it analytically. We determine the excitation spectrum, for which we obtain analytical results in the two opposite limiting cases of (i) a linearly modulated background and (ii) a train of dark solitons. The presence of two Goldstone (gapless) modes, associated with the spontaneous breaking of U(1) symmetry and of continuous translational invariance, at long wavelength is verified. We also calculate the static structure factor and the compressibility of cnoidal waves, which show a divergent behavior at the edges of each Brillouin zone.

Automated summary

This study examines the nonlinear periodic modulations in a one-dimensional Bose-Einstein condensate known as cnoidal waves, suggesting their potential for studying supersolidity-related phenomena. Through mean-field treatment, Leggett's formula for superfluid fraction is rederived and analytically estimated. The excitation spectrum is determined, with analytical results obtained in two opposing cases, and the presence of two gapless modes at long wavelength is confirmed. Additionally, calculations of static structure factor and compressibility of cnoidal waves show divergent behavior at the edges of Brillouin zones.