Atomic Color Superfluid via Three-Body Loss

Large three-body loss rates in a three-component Fermi gas confined in an optical lattice can dynamically prevent atoms from tunneling so as to occupy a lattice site with three atoms. This effective constraint not only suppresses the occurrence of actual loss events, but stabilizes BCS-pairing phases by suppressing the formation of trions. We study the effect of the constraint on the many-body physics using bosonization and density matrix renormalization group techniques, and also investigate the full dissipative dynamics including loss for the example of ${}^6\mathrm{Li}$.

Figure 1

Qualitative phase diagram for attractive interactions $U<0$ and equal populations $\overline{n}/3$ of each component in a three-component 1D Fermi gas. These are shown in the SU(3) symmetric case (where all pairwise interactions between different components are of equal strength), (a) without and (b) with a three-body hard-core constraint arising from three-body loss. The unconstrained case is characterized by competition between symmetric (on-site) trions (ST) and a charge-density wave (CDW). The hard-core constraint suppresses trion formation, stabilizing BCS pairing in an atomic color superfluid (ACS), which competes with a CDW and off-site trions (OT).

Figure 2

(a) ACS correlations $P_{\sigma }(x)$ with (solid line) and without (dash-dotted line) the three-body constraint as a function of distance $x$ on a 40 site lattice. (b)–(d) $P_{\sigma }(x)$ with CDW-correlations $C(x)$ and off-site trion correlations $\mathrm{OT}(x)$ for different values of $U$, at a density ${\overline{m}}_1={\overline{m}}_2={\overline{m}}_3=0.2$, with the constraint. In qualitative agreement with bosonization, we observe that for weak coupling (b) CDW clearly dominates. As the coupling is increased (b)–(d), ACS appears to dominate. For the values shown here, ACS dominates off-site trions, with $\mathrm{OT}(x)$ decaying exponentially for strong coupling.

Figure 3

(a) Hubbard parameters $U_1$, $U_2$, $U_3$ and three-body loss rate ${\gamma }_3$ for ${}^6\mathrm{Li}$ as function of external magnetic field $B$, for a lattice depth of $V_{ax}=5$ $E_R$ in axial direction, and $V_{\mathrm{rad}}=20$ $E_R$ in radial direction. (b) ACS correlations for the ground state of $H_C$ at $B=500\mathrm{G}$, computed for a system of 30 lattice sites, ${\overline{m}}_{\sigma }=2/15$, $\sigma =1$, 2, 3. The dash-dotted line shows $P_3(x)$, dashed line $P_1(x)$, dotted line denotes $P_2(x)$. As $U_3<U_2\ll U_1$, we see 1–3 pairing dominate, with all other pairing exponentially suppressed. (c) Left scale, dashed line: Magnetic field $B(t)$ for the ramp. Right scale, solid line: Probability of no three-body loss having occurred at time $t$. (d) ACS correlations after the time-dependent ramp of the magnetic field shown in (c), beginning from the ground state at 615 G, with ${\overline{m}}_{\sigma }=0.167$, on 12 sites.