Figure 1

(a) The schematic setup of SQUIDs $(1,2,\dots ,N)$ and an auxiliary SQUID $a$ (dotted-line circle) in a microwave cavity. The magnetic components of the pulses and the cavity mode are in the $Y$ direction. Each SQUID is placed in the $X\text{−}Z$ plane. The auxiliary SQUID is used as a microwave photon generator. (b) Level diagram of a SQUID with the $\Lambda$-type three lowest levels $\mid 0⟩$, $\mid 1⟩$, and $\mid 2⟩$.Reuse & Permissions

Figure 2

The relevant level structures (reduced) of the SQUIDs $(1,2,\dots ,N)$ and the auxiliary SQUID $a$ during GHZ-state preparation. In (a), (b), (c), (d), and (e), figures on the left side represent the level structures for SQUID $a$, while figures on the right size represent the level structures of SQUIDs $(1,2,\dots ,N)$. $g$ is the resonant coupling constant between the cavity mode and the $\mid 0⟩\leftrightarrow \mid 2⟩$ transition of SQUID $a$, while $g^{\prime }$ is the non-resonant coupling strength between the cavity mode and the $\mid 0⟩\leftrightarrow \mid 2⟩$ transition of SQUIDs $(1,2,\dots ,N)$. The $\mid 0⟩\leftrightarrow \mid 2⟩$ and $\mid 1⟩\leftrightarrow \mid 2⟩$ transition frequencies for SQUIDs $(1,2,\dots ,N)$ are, respectively, denoted as ${\omega }_{20}$ and ${\omega }_{21}$ (not shown), while the $\mid 0⟩\leftrightarrow \mid 2⟩$ and $\mid 1⟩\leftrightarrow \mid 2⟩$ transition frequencies for SQUID $a$ are, respectively, indicated by ${\omega }_{20}^{\prime }$ and ${\omega }_{21}^{\prime }$ (not shown). ${\omega }_{\mu w}$ is the carried frequency of the applied microwave pulse. In (e), the level spacings for SQUID $a$ is set to be much different from that for each of SQUIDs $(1,2,\dots ,N)$, such that SQUIDs $(1,2,\dots ,N)$ are decoupled from the applied pulse. In addition, the transition between any two levels linked by a dashed line is far off resonant with the cavity mode.Reuse & Permissions

Figure 3

Sketch of the setup for the preparation of multiatom GHZ states. $C$, $M$, and $D$ represent the cavity, the classical field, and the detector, respectively. The two-level structure inside the left dashed-line box is for atom $a$ while the three-level structure inside the right dashed-line box is for atoms $(1,2,\dots ,N)$.Reuse & Permissions