Composite fermionization of one-dimensional Bose-Bose mixtures

We study the ground states of one-dimensional Bose-Bose mixtures under harmonic confinement. As we vary the interspecies coupling strength up to the limit of infinite repulsion, we observe a generalized, composite-fermionization crossover. The initially coexisting phases demix as a whole for weak intraspecies interactions, whereas the atoms localize individually for strong intraspecies repulsion. By symmetry, the two components end up with strongly overlapping profiles, albeit sensitive to symmetry-breaking perturbations. Different pathways emerge if the two components have different atom numbers, different intraspecies interactions, or different masses and/or trap frequencies.

Figure 1

Composite fermionization of a mixture with $N_{\sigma =A,B}=2$ bosons with intracomponent interaction $g_{\sigma }=0.4$. Top: density profiles $\rho \left(x\right)$; bottom: two-body correlation functions ${\rho }_{\sigma \sigma }\left(x_1,x_2\right)$ and ${\rho }_{AB}\left(x_A,x_B\right)$ for interspecies couplings $g_{AB}=0.4$, 4.7, and 25, from left to right. (All quantities in harmonic-oscillator units throughout; see text.)

Figure 2

Same as Fig. 1, but with $g_A=g_B=4.7$.

Figure 3

Same as Fig. 1, but with $g_A=g_B=25$.

Figure 4

(Color online) Instability under symmetry-breaking perturbation, $U_{\sigma }\left(x\right)=\frac{1}{2}{x}^2+d_{\sigma }x$ $\left(d_A=-d_B=0.1\right)$. Left: Densities ${\rho }_{\sigma }\left(x\right)$ for $g_{\sigma }=0.4$; right: $g_{\sigma }=25$. Shown are the coupling strengths $g_{AB}=0.4,4.7,25$ from top to bottom.

Figure 5

Demixing for different particle numbers $N_A=3$, $N_B=2$: Density profiles ${\rho }_A\left(x\right)$ (top) and ${\rho }_B\left(x\right)$ (bottom) for intraspecies interaction strengths $g_{\sigma }=0.4$, 4.7, and 25 (from left to right).

Figure 6

Demixing for different intracomponent interactions $g_A=4.7$, $g_B=0.4$: Density profiles ${\rho }_A\left(x\right)$ (top) and ${\rho }_B\left(x\right)$ (bottom) for an $N_{\sigma }=2$ mixture at different couplings $g_{AB}=0.4$, 4.7, and 25.

Figure 7

Coherence properties of the system in Fig. 6. Top: momentum distributions ${\tilde{\rho }}_{\sigma }\left(k\right)$; bottom: one-body density matrices ${\rho }_{\sigma }\left(x_{\sigma },x_{\sigma }^{\prime }\right)$ for $g_{AB}=0.4$, 4.7, and 25 (from left to right).

Figure 8

Demixing for different masses $M_B/M_A=9$: Density profiles ${\rho }_A\left(x\right)$ (top) and ${\rho }_B\left(x\right)$ (bottom) for a $2+2$ mixture with $g_{\sigma }=0.4$ at different couplings $g_{AB}$.

Figure 9

Demixing for different energy scales $M_B=1/{\omega }_B=3$: Density profiles ${\rho }_A\left(x\right)$ (top) and ${\rho }_B\left(x\right)$ (bottom) for a $2+2$ mixture with $g_A=25$ and $g_B=0.4$, at different couplings $g_{AB}$.