Long-lived states with well-defined spins in $\text{spin}-1/2$ homogeneous Bose gases

Many-body eigenfunctions of the total spin operator can be constructed from the spin and spatial wave functions with nontrivial permutation symmetries. Spin-dependent interactions can lead to relaxation of the spin eigenstates to the thermal equilibrium. A mechanism that stabilizes the many-body entangled states is proposed here. Surprisingly, despite coupling with the chaotic motion of the spatial degrees of freedom, the spin relaxations can be suppressed by destructive quantum interference due to spherical vector and tensor terms of the spin-dependent interactions. Tuning the scattering lengths by the method of Feshbach resonances, readily available in cold atomic laboratories, can enhance the relaxation time scales by several orders of magnitude.

Figure 1

The total decay rates for the state with the total spin $S$ and its projection $S_z$ for two values of $S-S_z$. The solid black lines correspond to the background scattering lengths. The dashed blue and dot-dashed red lines show the decay rates minimized by tuning of $a_{\downdownarrows }$ and $a_{\uparrow \downarrow }$, respectively.

Figure 2

The total decay rates for the state with the total spin $S$ and its projection $S_z$ minimized by $a_{\uparrow \downarrow }$ tuning in the vicinity of the Feshbach resonance at $B_0\approx 9.13\mathrm{G}$ in ${}^{87}\mathrm{Rb}$. The solid black, dashed blue, and dot-dashed red lines correspond to $S-S_z=100$, 20, and 5, respectively. The plots of optimal detuning $B-B_0$ for different $S-S_z$ almost coincide.

Figure 3

The total decay rates for the state of $N={10}^4$ atoms of ${}^{87}\mathrm{Rb}$ with the total spin $S$ and its projection $S_z$ minimized by $a_{\downdownarrows }$ tuning in the vicinity of the Feshbach resonance at $B_0\approx 1007.4\mathrm{G}$. The solid black, dashed blue, and dot-dashed red lines correspond to $S-S_z=100$, 20, and 5, respectively. The optimal detuning $B-B_0$ for different $S-S_z$ is presented by three upper lines.