# The spatial distribution of density fluctuations, attributed respectively by adding a half-quantum into each PW (a), SHO (b) and SCB mode (c)

**Figure 1.** The spatial distribution of density fluctuations, attributed respectively by adding a half-quantum into each PW (a), SHO (b) and SCB mode (c). The effective potential *U*_{eff} is defined by equation (13) (d).

**Abstract**

We study the effect of quantum fluctuations on the dynamics of a quasi-one-dimensional Bose gas in an optical lattice at zero temperature using the truncated Wigner approximation with a variety of basis sets for the initial fluctuation modes. The initial spatial distributions of the quantum fluctuations are very different when using a limited number of plane-wave (PW), simple-harmonic-oscillator (SHO) and self-consistently determined Bogoliubov (SCB) modes. The short-time transport properties of the Bose gas, characterized by the phase coherence in the PW basis, are distinct from those gained using the SHO and SCB basis. The calculations using the SCB modes predict greater phase decoherence and stronger number fluctuations than the other choices. Furthermore, we observe that the use of PW modes overestimates the extent to which atoms are expelled from the core of the cloud, while the use of the other modes only breaks the cloud structure slightly, which is in agreement with the experimental observations by Fertig *et al* (2005 *Phys. Rev. Lett. ***94** 120403).