Magnetic Phase Transitions in One-Dimensional Strongly Attractive Three-Component Ultracold Fermions

We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.

Figure 1

Schematic configuration of Bethe ansatz quasimomenta $k$, spin momenta $\Lambda$ and $\lambda$ in the complex plane ($N=29$ with $N_1=6$, $N_2=4$, and $N_3=5$) at zero temperature. For strongly attractive interaction, the unpaired and paired quasimomenta can penetrate into the central region occupied by tightly bound trions.

Figure 2

Phase diagram determined by the energy transfer relations (7) with chemical potentials (6) with $|c|=10$ and $n=1$. Panels (a) and (b) show the polarizations $n_1/n$ and $n_2/n$ vs the fields $H_1$ and $H_2$. The figure reveals a novel trion phase $C$, a pairing phase $B$, an unpaired phase $A$, and four different mixtures of these states.

Figure 3

Ground-state energy vs Zeeman splitting for $|c|=10$ and $n=1$. In the vicinity of the multicritical points and the phase boundaries, the energy surface varies continuously with $H_1$ and $H_2$. The insets indicate configurations for the cases of small $H_1$ and small $H_2$. The dashed lines in the insets indicate the average Zeeman energy $\overline{ϵ}$.