Ground-state blockade of Rydberg atoms and application in entanglement generation

We propose a mechanism of ground-state blockade between two $N$-type Rydberg atoms by virtue of the Rydberg-antiblockade effect and the Raman transition. Inspired by the quantum Zeno effect, the strong Rydberg antiblockade interaction plays a role in frequently measuring one ground state of two, leading to a blockade effect for double occupation of the corresponding quantum state. By encoding the logic qubits into the ground states, we efficiently avoid the spontaneous emission of the excited Rydberg state and maintain the nonlinear Rydberg-Rydberg interaction at the same time. As applications, we discuss in detail the feasibility of preparing two-atom and three-atom entanglement with ground-state blockade in closed and open systems, respectively, which shows that a high fidelity of the entangled state can be obtained with current experimental parameters.

Figure 1

Schematic view of the atomic-level configuration. The ground states $|g\rangle$ and $|e\rangle$ are dispersively coupled to the excited state $|p\rangle$ with Rabi frequencies ${\mathrm{\Omega }}_a$ and ${\mathrm{\Omega }}_b$, respectively. An additional classical field drives the transition $|e\rangle \leftrightarrow |r\rangle$ with the Rabi frequency ${\mathrm{\Omega }}_c$. ${\mathrm{\Delta }}_{p\left(r\right)}$ represents the corresponding single-photon detuning parameter.

Figure 2

The ratios $R_1$ (upper surface) and $R_2$ (lower surface) are plotted as functions $\mathrm{\Delta }/{\mathrm{\Omega }}_{\mathrm{eff}}$ and $\lambda /{\mathrm{\Omega }}_{\mathrm{eff}}$, where $R_1=|E_{+}/(\sqrt{2}{\mathrm{\Omega }}_{\mathrm{eff}}sin\alpha )|$ and $R_2=|E_{-}/(\sqrt{2}{\mathrm{\Omega }}_{\mathrm{eff}}cos\alpha )|$.

Figure 3

Population of state $|e\rangle$ in the process of quantum state transfer for a single $\mathrm{\Lambda }$-type atom versus a common dimensionless time ${\mathrm{\Omega }}_{\mathrm{eff}}t$ with different detuning and decoherence parameters, where $\mathrm{\Omega }={\mathrm{\Omega }}_a={\mathrm{\Omega }}_b$ is assumed for simplicity.

Figure 4

Population of the maximally entangled state $\left(\right|ge\rangle +|eg\rangle )/\sqrt{2}$ during the shortcut to adiabatic passage versus dimensionless interaction time ${\mathrm{\Omega }}_{\mathrm{c}}t$ for different detuning and decoherence parameters. We have chosen $t_{\mathrm{c}}=300/{\mathrm{\Omega }}_c,\tau =0.2t_c$, and $T=0.3t_c$ in Eqs. (16) and (17), and ${\mathrm{\Delta }}_r=20{\mathrm{\Omega }}_c$.

Figure 5

Schematic view of the atomic-level configuration. Compared with Fig. 1, the transition $|g\rangle \leftrightarrow |p\rangle$ is replaced by a quantized cavity field mode with coupling strength $g$, and a resonant transition between $|g\rangle$ and $|e\rangle$ is driven by a microwave field with Rabi frequency $\omega$.

Figure 6

Populations of quantum states versus dimensionless time $g_{\mathrm{eff}}t$ during preparation of the antisymmetric entangled state $|S\rangle$. Other parameters: $\omega =g_{\mathrm{eff}},\kappa =\lambda =10g_{\mathrm{eff}}$, and $\eta =-0.5\pi$.

Figure 7

(a) Population of $W$ state during the shortcut to adiabatic passage versus dimensionless interaction time ${\mathrm{\Omega }}_{\mathrm{c}}t$. Other parameters are the same as those in Fig. 4. (b) Populations of quantum states versus dimensionless time $g_{\mathrm{eff}}t$ during preparation of the three-atom decoherence-free state $|\mathrm{DFS}\rangle$. Other parameters: $\omega =g_{\mathrm{eff}},\kappa =10g_{\mathrm{eff}},\lambda =20g_{\mathrm{eff}}$, and $\eta =-0.5\pi$.

Figure 8

Schematic view of the $N$-type Rydberg atom with the relevant energy level structure of the ${}^{87}\mathrm{Rb}$ atom.