Spatial Nonlocal Pair Correlations in a Repulsive 1D Bose Gas

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.

Figure 1

Pair correlation $g^{(2)}(r)$ as a function of the relative distance $r$ (in units of $1/n$) in the strongly interacting regime, $\gamma \gg 1$: (a) low-temperature TG regime, Eq. (2), for $\tau =0.01$; (b) regime of high-temperature fermionization, Eq. (3).

Figure 2

Pair correlation $g^{(2)}(r)$ in the weakly interacting and nearly ideal-gas regimes. (a) Solid lines—low-temperature weakly interacting gas at $\tau \ll \gamma \ll 1$, Eq. (4); dashed lines—DC regime, Eq. (7). (b) Solid lines—weakly interacting gas at $\gamma \ll \tau \ll \sqrt{\gamma }$, Eq. (5); dashed lines—DQ regime, Eq. (9).