Dissipative generation of a steady three-atom singlet state based on Rydberg pumping

Multiparticle singlet states are special quantum entangled states that have been shown to have many interesting applications. We develop a simple scheme to prepare a steady three-atom singlet state with a dissipative Rydberg pumping process, which combines dissipative dynamics and Rydberg interactions. The numerical simulations show that the fidelity of the created three-atom singlet state can reach up to 0.9947 under certain conditions. The scheme does not require a cavity, initial-state preparation, and exact controlling of operation time, which reduces the difficulty of the experiment. Finally, the experimental feasibility of the scheme is discussed.

Figure 1

Schematic illustration of a single $W$-type Rydberg atom and the relevant transitions. The three circles on the right show that three atoms are arranged in a regular triangular structure.

Figure 2

Illustration of the eigenspaces and eigenvalues of the operator $H_0$. The operator $H_0$ has six eigenspaces $G_i$ ($i=0,1,2a,2b,3a,3b$) with the corresponding eigenvalues $E_i$ whose values are shown in the figure.

Figure 3

Fidelity $F\left(t\right)=\langle S_3\left|\rho \left(t\right)\right|S_3\rangle$ as a function of evolution time for three initial states shown in the inset, with the parameters $\mathrm{\Omega }/2\pi =0.02\mathrm{MHz}, \omega =0.01\mathrm{\Omega }, \gamma =1\mathrm{kHz}, \mathrm{\Delta }/2\pi =2\mathrm{MHz}, U_1=2\mathrm{\Delta }$, and $U_2=1.2\mathrm{\Delta }$.

Figure 4

Steady-state fidelity $F_s=\langle S_3|{\rho }_s|S_3\rangle$ with respect to Rabi frequency $\mathrm{\Omega }/2\pi$ and detuning $\mathrm{\Delta }/2\pi$, with the parameters $\omega =0.01\mathrm{\Omega }, \gamma =1\mathrm{kHz}, U_1=2\mathrm{\Delta }$, and $U_2=1.2\mathrm{\Delta }$.

Figure 5

Steady-state fidelity $F_s$ versus $U_2/\mathrm{\Delta }$ and $U_1/\mathrm{\Delta }$ with the parameters $\omega =0.01\mathrm{\Omega }, \gamma =1\mathrm{kHz}, \mathrm{\Delta }/2\pi =2\mathrm{MHz}$, and $\mathrm{\Omega }/2\pi =0.02\mathrm{MHz}$.

Figure 6

Steady-state fidelity $F_s$ with respect to ${\mathrm{\Omega }}_L/\mathrm{\Delta }$ and ${\mathrm{\Omega }}_R/\mathrm{\Delta }$ with the parameters $\mathrm{\Delta }/2\pi =2\mathrm{MHz}, \omega /2\pi =200\mathrm{Hz}, \gamma =1\mathrm{kHz}, U_1=2\mathrm{\Delta }$, and $U_2=1.2\mathrm{\Delta }$.