Spin-charge separation in two-component Bose gases

We show that one of the key characteristics of interacting one-dimensional electronic quantum systems, the separation of spin and charge, can be observed in a two-component system of bosonic ultracold atoms even close to a competing phase separation regime. To this purpose we determine the real-time evolution of a single particle excitation and the single particle spectral function using density-matrix renormalization group techniques. Due to efficient bosonic cooling and good tunability this setup exhibits very good conditions for observing this strong correlation effect. In anticipation of experimental realizations we calculate the velocities for spin and charge perturbations for a wide range of parameters.

Figure 1

(Color online) Snapshots of the time evolution of the charge- and spin-density distribution of a single particle excitation created at time $t=0\hslash /J$: (a) at time $t=0\hslash /J$, (b) at time $t=1.5\hslash /J$, and (c) at time $t=2.5\hslash /J$. The system parameters are $n_{1,2}=0.625$, $U_1/J=2.983$, $U_2/J=2.712$, $U_{12}/J=2.377$. The charge density is shifted by 1.25 for better visibility. The arrows in (c) mark the clear separation of the charge- and the spin-density waves.

Figure 2

One-particle spectral function at momentum $q=20/65\pi /a$. Two peaks corresponding to the spin and the charge excitations can be distinguished. The vertical lines mark the position of $v_{c,s}q$. The following parameters were used: $n=0.625$, $u=3$, $u_{12}=2.1$ on a system with $L=64$ sites and a broadening $\eta =0.1$. Restoring the units, the $x$ axis is $J/\hslash$.

Figure 3

(Color online) Dependence of the charge and spin velocities on the interparticle interaction strength for (a) $u=2$ and $n\approx 0.88$ and (b) $u=3$ and $n\approx 0.63$. A comparison of analytical results (line, see text) and numerical DMRG results (symbols) is shown. Restoring the units of the velocities, they are measured in units $aJ/\hslash$. Note that the errors of the DMRG results increase close to $u_{12}\approx u$.

Figure 4

(Color online) Dependence of the charge and spin velocities on the charge background density. A comparison of analytical results (lines, see text) and numerical DMRG results (symbols) is shown. The parameters used are (a) $u=3$, $u_{12}=1.2$ and (b) $u=3$, $u_{12}=2.7$. Restoring the units of the velocities, they are measured in units $aJ/\hslash$.