Thermally induced local imbalance in repulsive binary Bose mixtures

We study repulsive two-component Bose mixtures with equal populations and confined in a finite-size box through path-integral Monte Carlo simulations. For different values of the $s$-wave scattering length of the interspecies potential, we calculate the local population imbalance in a region of fixed volume inside the box at different temperatures. We find two different behaviors: For phase-separated states at $T=0$, thermal effects induce a diffusion process which reduces the local imbalance, whereas for miscible states at $T=0$, a maximum in the local population imbalance appears at a certain temperature, below the critical one. We show that this intriguing behavior is strongly related to the bunching effect associated with the Bose-Einstein statistics of the particles in the mixture and to an unexpected behavior of the cross pair distribution function.

Figure 1

Schematic view of the method used to estimate the density profiles. The two crosses, in red and in blue, represent the centers of mass of the two species, and the cylinder indicates the volume where the local population imbalance is calculated. The cylinder has the same diameter and length, $L/\sqrt{2}$, where $L$ is the size of the cubic box.

Figure 2

Local population imbalance of the mixture with respect to the total number of particles at $g_{12}/g=0.93$ and $n{a}^3={10}^{-4}$.

Figure 3

Density profiles at different temperatures for different values of $g_{12}/g$. The shaded areas visualize the statistical error obtained by averaging over different configurations.

Figure 4

Local population imbalance as a function of temperature for different values of $g_{12}/g$ with $N=256$. Note that the vertical axis is broken in order to show the different scale when $g_{12}/g>1$.

Figure 5

Local population imbalance as a function of temperature for two different statistics at $g_{12}/g=0.93$ with $N=128$ obeying Bose-Einstein and Maxwell-Boltzmann statistics. The dashed line corresponds to a simulation with particles uniformly distributed in the box.

Figure 6

Pair distribution functions between particles of the same species (left) and of different species (right) at $g_{12}/g=0.9$ with $N=256$ particles. These results have been computed in the same way as in Ref. [22] with periodic boundary conditions. In the left panel we can see the bunching effect between particles of the same species due to the Bose statistics. In the right panel we see an increase in the repulsion between particles of different species until $T_{\text{BEC}}=0.7$, where we start seeing the opposite trend.

Figure 7

Local population imbalance as a function of temperature for different mass ratios. The vertical dashed lines correspond to the $T_{\text{BEC,2}}$.