Confinement versus deconfinement of Cooper pairs in one-dimensional spin-$3∕2$ fermionic cold atoms

The phase diagram of spin-$3∕2$ fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.

Figure 1

(Color online) Phase diagram of the spin-$3∕2$ Hubbard chain (2) at quarter filling from QMC and DMRG calculations for $V⩽0$ (see text for definitions).

Figure 2

(Color online) Correlation functions for $U=-1.5t$ and $V=0$ obtained by DMRG simulations. (a) Power-law behavior of the quartet correlations parametrized by the Luttinger exponent $K_d$. (b) Short-range behavior of the one-particle Green function and pairing correlations ($\xi$ denotes the correlation lengths).

Figure 3

(a) Fourier transform $N\left(q\right)$ of the density correlations obtained from QMC simulations ($U=-t$ and $V=0$). The linear dispersion at small $q$ gives access to the Luttinger parameter $K_d$. Inset: the scaling of the peak at $2k_F$ vs $L$ signals an ADW phase. (b) Luttinger exponent $K_d$ as a function as $U$.

Figure 4

(Color online) Correlation functions for $U=0$ and $V=-3t$ from DMRG simulations (a) Pair and quartet correlations are algebraic with $Q\left(x\right)\sim P{\left(x\right)}^4$. (b) Short-range behavior of the one-particle Green function.

Figure 5

(a) Fourier transform of the density correlations obtained by QMC simulations for $U=0$ and $V=1.5t$. (b) The Luttinger parameter $K_d$ as a function of $V$ when $U=0$.

Figure 6

(Color online) The BCS-ADW transition from DMRG computations along the $V=-2t$ line. (a) Normalized ratio $R\left(x\right)=P{\left(x\right)}^4∕Q\left(x\right)$ displaying a critical behavior at the transition. (b) In the bulk (at site $x=45$), $R\left(x\right)$ is proportional to $U-U_c$ for $U_c⩽U⩽U^{*}$ with $U^{*}=-t$ and $U_c=-1.19t$. (c) Plot of $R\left(U\right)=\sigma {\left(U\right)}^8$ vs $\tau =(U-U_c)∕(U^{*}-U_c)$ where $\sigma$ is the Ising order parameter.

Figure 7

(Color online) Mott phase for $V<0$. (a) By increasing $U$, pairing correlations obtained from DMRG change from algebraic to exponential decaying. (b)–(d) The BOW Mott transition is seen from DMRG computations with the appearance of the $4k_F$ order parameter $t\left(x\right)$ across the transition.