Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime

By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure.

Figure 1

Total angular momentum of each component with $N_{\mathrm{B}}=1000$, $N_{\mathrm{F}}=25$, and $g=0.5h=2\times {10}^{-3}$. (a) Plateau at zero in $L_{\mathrm{B}}$ arises from the irrotationality. Small steps in $L_{\mathrm{F}}$ arise from the size effect. These steps become invisible for larger $N_{\mathrm{F}}(\gtrsim 500)$. (b) Enlargement of (a) for the fast-rotating regime.

Figure 2

(a) Density, and phase (inset), profiles of the bosonic condensate wave function. (b), (c), (d), (e) Density profiles (upper panels) and mean angular-momentum distributions (lower panels) of the fermionic cloud for $h/g=0$, 1, 1.5, and $2.5$, respectively.

Figure 3

(a), (b), (c) Total angular momentum of each component for three values of $\Omega$. Three plots of ${\tilde{L}}_{\mathrm{B}}$ in each panel denote the results with $N_{\mathrm{F}}=32$, 64, 128 from top down. The plateaus in ${\tilde{L}}_{\mathrm{F}}$ are located at zero or positive integers. (d) Boson-Fermion interaction energy $E_{\mathrm{BF}}$. Jumps in ${\tilde{L}}_{\mathrm{B}}$, ${\tilde{L}}_{\mathrm{F}}$, and $E_{\mathrm{BF}}$ occur at the same values of $h/N_{\mathrm{F}}$ for a fixed $\Omega$.