Dynamical Fermionization in One-Dimensional Spinor Quantum Gases

Dynamical fermionization refers to the phenomenon in Tonks-Girardeau gases where, upon release from harmonic confinement, the gases’ momentum density profile evolves asymptotically to that of an ideal Fermi gas in the initial trap. This phenomenon has been demonstrated theoretically in hardcore and anyonic Tonks-Girardeau gases and was recently experimentally observed in a strongly interacting Bose gas. We extend this study to a one-dimensional spinor gas of arbitrary spin in the strongly interacting regime and analytically prove that the total momentum distribution after the harmonic trap is turned off approaches that of a spinless ideal Fermi gas, while the asymptotic momentum distribution of each spin component takes the same shape of the initial real space density profile of that spin component. Our work demonstrates the rich physics arising from the interplay between the spin and the charge degrees of freedom in a spinor system.

Figure 1

Real space and momentum space density profiles of two spinor hardcore bosons. The top, middle, and bottom rows correspond to the states ${\mathrm{\Psi }}^S$ [Eq. (17)], ${\mathrm{\Psi }}^T$ [Eq. (19)], and $\mathrm{\Psi }$ [Eq. (21)], respectively. The dashed and solid lines correspond to spin-$\uparrow$ and spin-$\downarrow$, respectively. The dotted lines correspond to two spinless fermions.

Figure 2

Real space and momentum space distributions of two spinor hardcore bosons, initially prepared in state $\mathrm{\Psi }$, as in Eq. (21), after quench.