Spin-Charge Separation in Ultracold Quantum Gases

We investigate the physical properties of quasi-1D quantum gases of fermionic atoms confined in harmonic traps. Using the fact that for a homogeneous gas the low-energy properties are exactly described by a Luttinger model, we analyze the nature and manifestations of spin-charge separation, where in the case of atoms “spin” and “charge” refer to two internal atomic states and the atomic mass density, respectively. We discuss the necessary physical conditions and experimental limitations confronting possible experimental implementations.

Figure 1

(a) A two component quasi-1D Fermi gas in a harmonic potential. At time $t=0$ a short laser pulse focused near the center of the trap excites a density or a spin wave packet. (b) Wave packet dynamics for different times as a function of position: spin-charge separation manifests itself in a spatial separation of the spin (dark-gray line) and density (pale-gray line) wave packets (shown at half a trap oscillation period $\omega t=\pi /2$), which can be probed by a second short laser pulse at a later time. The parameters correspond to $N={10}^3$ ${}^{\mathrm{6}}\mathrm{L}\mathrm{i}$ atoms (with coupling parameter $\xi =1$, see text).

Figure 2

Level spacing (in units of $\omega$) of the spin (gray curve) and the charge (black curve) modes for a Fermi gas. The level spacing is shown as a function of $\xi =g/\pi \hslash v_F(0)$.