Generation of multimode squeeze operators and multipartite entangled states for continuous variables

A scheme is presented for generating unitarily multimode field squeezing, cluster entanglement, and Greenberger-Horne-Zeilinger (GHZ) entanglement via cavity quantum electrodynamics. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter proportional to the number of atoms. The physical mechanism is attributed to the multiple four-photon processes and the dispersive atom-cavity-field interaction in large detuning systems.

Figure 1

The multichannel scheme. Each driving field (Rabi frequency ${\Omega }_j$, $j=1,2,\cdots ,n$, $n\ge 1$) drives one transition. In each channel, two photons from the driving field ${\Omega }_j$ are absorbed, and two sideband photons (annihilation operators $a_{2j-1}$ and $a_{2j}$) are generated.

Figure 2

The possible setup for the creation of cluster entanglement and GHZ entanglement of six cavity fields (denoted by the annihilation operators $a_{1-6}$).

Figure 3

Possible cluster states for different numbers of red sidebands $a_{2i-1}$ and blue sidebands $a_{2j}$, $i=1\sim m$ and $j=1\sim n$. For $m=1$, (i) $n=2$, (ii) $n=4$, and (iii) $n=8$. For $m=2$, (iv) $n=2$, (v) $n=3$, and (vi) $n=4$. Each vertex takes the role of one mode, and edges represent the interactions between the connected vertices. $\left\{a_{2i-1}\right\}$ and $\left\{a_{2j}\right\}$ are in two different families.

Figure 4

The (dimensionless) output zero- frequency spectra $Y_C\left(0\right)$ as functions of $x$ (dimensionless) for different mode numbers $m,n$.

Figure 5

The (dimensionless) output zero-frequency spectra $Y_1\left(0\right)$ as functions of $x$ (dimensionless) for different mode numbers $m,n$.

Figure 6

The (dimensionless) output zero-frequency spectra $Y_{2,3}\left(0\right)$ as functions of $x$ (dimensionless) for different mode numbers $m,n$.

Figure 7

Possible GHZ states for different numbers of red sidebands $a_{2i-1}$ and blue sidebands $a_{2j}$, $i=1\sim m$ and $j=1\sim n$. For $m=1$, (i) $n=2$, (ii) $n=4$, and (iii) $n=8$. For $m=2$, (iv) $n=2$, (v) $n=3$, (vi) $n=4$. Each vertex takes the role of one mode, and edges represent the interactions between the connected vertices.