Quantum Turbulence in Condensate Collisions: An Application of the Classical Field Method

We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our nonperturbative method includes the effect of quantum noise, and describes collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms.

Figure 1

(a)–(f) Velocity mode populations on the planes $v_z=0$ (left) and $v_x=0$ (right) for the condensate collision described in the text at $t=0$ (top), $t=0.5\mathrm{m}\mathrm{s}$ (middle), and $t=2.0\mathrm{m}\mathrm{s}$ (bottom). The spherical momentum cutoff is clearly visible in the upper plots due to the presence of quantum fluctuations. (g)–(h) Mode populations at $t=2.0\mathrm{m}\mathrm{s}$ for an identical collision excluding vacuum noise.

Figure 2

Correlation functions for the simulation of Fig. 1: (a) average mode population; (b) pair creation correlation; (c),(d) amplitude autocorrelation.

Figure 3

Normalized data collection region populations for the classical field simulations (sold lines) and complex scattering length simulations (dashed lines). Initial condensate numbers are (lowest to highest) $(1,3,6)\times {10}^6$, all with $v_c=10\mathrm{m}\mathrm{m}/\mathrm{s}$. Subplot (b) shows the early times of (a).