Breathing modes of one-dimensional trapped BEC
Andrii Gudyma (LPTMS)
We calculate the breathing mode frequency in a one-dimensional Bose gas confined to a harmonic trap. We predict a smooth crossover from Thomas–Fermi Bose–Einstein condensate (BEC) regime to Gaussian BEC regime using Hartree approximation and sum rules approach, adopted to small system sizes. Local density approximation (LDA) correctly captures the crossover from Tonks-Girardeau to Thomas-Fermi BEC regimes. Hartree and LDA predictions can be continuously matched for N > 25 particles, providing a complete zero-temperature description for large number of particles and resulting in a non-monotonic reentrant behavior of the breathing frequency. For smaller number of particles (ranging from N = 2 to N = 25) we perform extensive diffusion Monte Carlo simulations. This permits us to obtain a complete picture, applicable to arbitrary number of particles and any repulsive interaction strength. We provide perturbative analysis for both weak and strong coupling regimes. We revisit Innsbrick group experiment [Science 325, 1224 (2009)], analyzing the measurements done in Thomas–Fermi Gaussian BEC crossover, and demonstrate that the breathing frequency follows a reentrant behavior as a function of the interaction strength in full agreement with our theory.