Scalable cavity-QED-based scheme of generating entanglement of atoms and of cavity fields

We propose a cavity-QED-based scheme of generating entanglement between atoms. The scheme is scalable to an arbitrary number of atoms, and can be used to generate a variety of multipartite entangled states such as the Greenberger-Horne-Zeilinger, $W$, and cluster states. Furthermore, with a role switching of atoms with photons, the scheme can be used to generate entanglement between cavity fields. We also introduce a scheme that can generate an arbitrary multipartite field graph state.

Figure 1

(Color online) The basic building block of the proposed scheme. The adiabatic interaction between a three-level atom prepared in $|L⟩$ in a cavity and a left-circularly polarized photon $|\mathcal{L}⟩$ transforms the system to the atom in $|R⟩$ and a right-circularly polarized photon $|\mathcal{R}⟩$ and vice versa.

Figure 2

(Color online) The flip probability $P$ vs the temporal width $\tau$ of a Gaussian pulse for the case $g/\kappa =\left(\text{a}\right)0.5$, (b) 1.0, (c) 2.0, and (d) 5.0. It is assumed that $g_L=g_R\equiv g$.

Figure 3

(Color online) Scheme to generate $2N$-atom GHZ state. BS, PBS, M, and D refer, respectively, to a 50/50 beam splitter, polarizing beam splitter, mirror, and detector. We assume that a phase shift of $\pi$ occurs when a photon is reflected from the lower surface of each beam splitter and that each PBS transmits a left-circularly polarized photon and reflects a right-circularly polarized photon. The lines in the figure that connect optical devices can be considered to be optical fibers. The far side of each cavity is assumed to be perfectly reflecting. The photon incident on beam splitter BS1 is left-circularly polarized $|\mathcal{L}⟩$ and atoms $1,2,\dots ,2N-1,2N$ are prepared in state $|LLRRLL\cdots ⟩$.

Figure 4

(Color online) Scheme to generate four-atom $W$ state. A left-circularly polarized photon is incident on beam splitter BS1 and atoms 1, 2, 3, 4 are prepared in state $|LLLL⟩$.

Figure 5

(Color online) Scheme to generate three-atom $W$ state. A left-circularly polarized photon is incident on beam splitter BS1 and atoms 1, 2, 3 are prepared in state $|LLL⟩$. The reflectivity of BS1 is $\frac{1}{3}$ and that of other beam splitters is $\frac{1}{2}$.

Figure 6

(Color online) Scheme to generate linear cluster state. PR refers to polarization rotator that performs the NOT operation $|\mathcal{L}⟩\leftrightarrow |\mathcal{R}⟩$ on a photon. A left-circularly polarized photon is incident on beam splitter BS1 and atoms $1,2,\dots ,N$ are prepared in $|LL\cdots L⟩$.

Figure 7

(Color online) The basic building block of the scheme to generate entanglement between cavity fields. The interaction between a cavity field prepared in a single-photon state $|1⟩$ and a two-level atom in the ground state $|g⟩$ transforms the system to the atom in the excited state $|e⟩$ and the cavity field in vacuum $|0⟩$, and vice versa.

Figure 8

(Color online) Scheme to generate $2N$-field GHZ state. BS, M, and D refer now to atomic beam splitter, atomic mirror, and atomic detector. The atom incident on the atomic beam splitter BS1 is prepared in the ground state $|g⟩$ and cavity fields $1,2,\dots ,2N-1,2N$ are prepared in $|110011\cdots ⟩$.

Figure 9

(Color online) Generation of the two-qubit cluster state between two cavity fields. A two-level atom in its lower level $|g⟩$ goes through in turn, cavity 1 where $\frac{\pi }{2}$-pulse interaction occurs, an external $\pi$ pulse, cavity 2 where a dispersive interaction occurs, and a Ramsey zone.

Figure 10

(Color online) Single polarized-photon injection by using a fourth level.