Pfaffian State Generation by Strong Three-Body Dissipation

We propose a scheme for preparing and stabilizing the Pfaffian state with high fidelity in rapidly rotating 2D traps containing a small number of bosons. The goal is achieved by strongly increasing three-body loss processes, which suppress superpositions of three particles while permitting pairing. This filtering mechanism gives rise to reasonably small losses if the system is initialized with the right angular momentum. We discuss some methods for tuning independently two- and three-body interactions.

Figure 1

GS phase diagram in the conservative case $H_{\mathrm{trap}}+H_{\mathrm{int}}$ for $N=6$ particles and $c_2=1/6$. Different colors correspond to different angular momenta of the global GS. We identify the Laughlin state ($\nu =1/2$) with $L=N(N-1)=30$, the Pfaffian ($\nu =1$) with $L=N(N-2)/2=12$, the single vortex with $L=N$, and finally $L=0$.

Figure 2

Left panel: fidelity with the Pfaffian and surviving population $\Vert \psi (t){\Vert }^2$ as a function of time, after switching on dissipation $c_3$. The results have been obtained by evolving the initial state $|{\varphi }_0(12)⟩$ with $H_{\mathrm{eff}}$. The fidelity reaches 0.9994 for $c_3=10$. Right panel: threshold time for having lost 25% of population after turning on $c_3$.

Figure 3

Map of the gap between GS and first excited state as a function of the trap parameters ($\delta \omega$, $\epsilon$). The white arrow indicates the chosen path for connecting adiabatically the GS with $L=6$ and the GS with $L=12$.