Low-temperature crossover in the momentum distribution of cold atomic gases in one dimension

The momentum distribution function for the two-component 1D gases of bosons and fermions is studied in the limit of strong interatomic repulsion. A pronounced reconstruction of the distribution is found at a temperature much smaller than the Fermi temperature. This new temperature scale, which equals the Fermi temperature divided by the dimensionless coupling strength, is a feature of the two-component model and does not exist in the one-component case. We estimate the parameters relevant for the experimental observation of the crossover effect.

Figure 1

The momentum distribution function $n\left(k\right)$ for two-component fermions. The thick solid curve is our result for $T⪢T_0$. The dashed curve corresponds to $T⪡T_0$ and is obtained by the interpolation of the data (filled circles) from Ref. 17. The thin solid line shows the distribution function for noninteracting two-component fermions. The momentum $k$ is normalized to the Fermi momentum, Eq. (31).

Figure 2

The momentum distribution function $n\left(k\right)$ for two-component bosons. The solid curve is the result for $T⪢T_0$, the dashed curve is for $T⪡T_0$. For convenience we normalize the momentum $k$ to the Fermi momentum $k_{\mathrm{F}}$, Eq. (31), of a fermion system with the same density.