Figure 1

(a) Schematic setup of the microwave cavity experiments in which a chain of Rydberg atoms from a source $B$ passes through a Ramsey zone $R_1$, a superconducting cavity $C$, and the (second) Ramsey zone $R_2$ before the atoms are field ionized at the detector $D$. The classical field in the Ramsey zones is generated by a microwave source $S$. (b) Temporal matching of the $e\leftrightarrow g$ atomic transition frequency $\left({\omega }_0\right)$ to the frequency ${\omega }_1$ of the first cavity mode and the frequency ${\omega }_2$ of the second mode in the course of the resonant atomic-cavity interaction. Apart from the matching of the atomic frequency (upper half), the lower part of this figure displays the time dependence of the atom-cavity detuning $\Delta \left(t\right)={\omega }_0\left(t\right)-{\omega }_1$, implying a stepwise change from the resonant $A-C_1$ interaction regime to the resonant $A-C_2$ regime. See text for further discussions.Reuse & Permissions

Figure 2

(a) Temporal sequence for generating a four-partite GHZ state associated with the chain of Rydberg atoms $A_1$, $A_2$, $A_3$, and $A_4$. The pictograms in this figures are described in the text. The gray shadowed ellipse denotes the time when the entanglement of four qubits, the two photonic qubits $C_1$, $C_2$ and the two atomic qubits $A_1$, $A_2$ is achieved. (b) The corresponding quantum circuit in which the (four) Rydberg atoms are represented by the four lower lines, being initially prepared in the ground state $|g⟩$, while the source atom $A_s$ is shown as the uppermost line.Reuse & Permissions

Figure 3

(a) Temporal sequence for generating a four-partite $W$ state associated with the chain of Rydberg atoms $A_1$, $A_2$, $A_3$, and $A_4$. Again, the gray shadowed ellipse denotes the time when the entanglement of four qubits, the two photonic qubits $C_1$, $C_2$ and the two atomic qubits $A_1$, $A_2$ is achieved. (b) The corresponding quantum circuit in which the (four) Rydberg atoms are represented by the four lower lines.Reuse & Permissions

Figure 4

(a) Quantum circuit for generating a $N$-partite GHZ state associated with the Rydberg atoms $A_1-A_N$. (b) The same but for the $N$-partite $W$ state; see text for further discussions.Reuse & Permissions

Figure 5

Sequence (a) displays the basic steps of the transversal measurement for the GHZ state (triplet $A_1-C_1-C_2$) given by expression (10). See the text for explanations. Sequence (b) displays the principle of another type of measurement as applied over the same entangled triplet (10).Reuse & Permissions

Figure 6

(a) The temporal sequence for performing transversal measurements on the four-partite GHZ state (quartet $C_1-C_2-A_1-A_2$) given by expression (28). Here the gray shadowed ellipses, triplet and Bell state, correspond to the three-partite GHZ state $\left(C_1-C_2-A_2\right)$ and two-partite entangled state $\left(C_1-C_2\right)$. (b) The quantum circuit that corresponds to the temporal sequence shown in (a).Reuse & Permissions

Figure 7

(a) The temporal sequence for performing transversal measurements on the four-partite $W$ state (quartet $C_1-C_2-A_1-A_2$) given by expression (38). Here the gray shadowed ellipse, Bell state, corresponds to the two-partite entangled state $\left(C_1-C_2\right)$. The time intervals $t_a$ and $t_b$ are given in the text. (b) The quantum circuit that corresponds to the temporal sequence shown in (a).Reuse & Permissions