Noise correlations in the expansion of an interacting one-dimensional Bose gas from a regular array

We consider the one-dimensional expansion of a system of interacting bosons, starting from a regular array. Without interactions the familiar Hanbury Brown and Twiss effect for bosons gives rise to a series of peaks in the density-density correlations of the expanded system. Infinitely repulsive particles likewise give a series of dips, a signature of the underlying description in terms of free fermions. In the intermediate case of finite interaction, the noise correlations consist of a set of Fano resonance lineshapes, with an asymmetry parameter determined by the scattering phase shift of a pair of particles and a width depending on the initial momentum spread of the particles.

Figure 1

1D expansion of atoms from an optical lattice of spacing $\Delta$. The spread of the initial wavepackets is $\ell$. Noise correlations will be present in an absorption image of the expanded cloud.

Figure 2

(Top) Normalized correlation function $N[\frac{\mathcal{C}(x_1,x_2;t)}{\mathcal{C}(0,0;t)}-1]$ from Eq. (16) for $c\Delta =2$, $\ell /\Delta =0.2$. (Bottom) A slice with $x_1=-x_2$ for the same parameters, showing the evolution of the Fano asymmetry between successive peaks.

Figure 3

(Top) Diagram representing a term that survives integration over $x_j$, $j\ne 1,2$. At the top are the positions $\left\{y_{{\sigma }_1\left(i\right)}\right\}$, and at the bottom are $\left\{{\tilde{y}}_{{\sigma }_2\left(i\right)}\right\}$. The thick red lines correspond to the two coordinates $x_1$ and $x_2$ that are not integrated over in the two-body density matrix Eq. (3). (Bottom) Usual contribution to the noninteracting HBT effect.

Figure 4

Simplest “new” contribution, smaller by $e^{-2c\Delta }$.