Continuous Variable Entanglement in an Optical Parametric Oscillator Based on a Nondegenerate Four Wave Mixing Process in Hot Alkali Atoms

We present the measurement of entanglement between twin beams generated with a doubly resonant optical parameter oscillator (OPO) based on four-wave mixing in hot ${}^{85}\mathrm{Rb}$ vapor above threshold. This is the first measurement of entanglement in an OPO with a ${\chi }^{(3)}$ media above threshold. We reconstruct the covariance matrix for several configurations and based on a full picture of the four side band mode state, we study entanglement between all possible bipartitions. We show a robust generation of entanglement with stronger generation for a specific pair of modes. For this system, we show that atomic density is a determinant factor for the generation and loss of quantum correlations. The generation of entangled fields with an atomic OPO operating close to atomic resonance of alkali atoms enables a natural integration into quantum networks.

Figure 1

Representation of frequency sidebands surrounding their corresponding mode carriers “$a$” and “$b$.” The figure on the right shows all seven possible bipartitions that need to be analyzed with the Simon criteria.

Figure 2

Sketch of the experimental setup. Mirror (M), confocal Fabry-Perot (FP), flip mirror (FM), analysis cavity (AC), piezoelectric actuator (PZT), and demodulating chain and data acquisition (PC). Other definitions are given in the text.

Figure 3

Top: Duan criterion as a function of $\sigma =P/P_{\mathrm{Th}}$ with $P_{\mathrm{Th}}=199\mathrm{mW}$. Bottom: Duan Criterion as a function of temperature. The threshold power evolves as $P_{\mathrm{Th}}=174$, 125, 90, 61.8, 50 mW for $T=97$, 101, 105, 109, and $113°\mathrm{C}$, respectively. For both figures, we consider analysis frequencies of 7 (black circles) and 10 MHz (blue triangles) for a cavity with $\mathcal{F}=15$. Values less than 2 indicate the presence of entanglement.

Figure 4

Smallest symplectic eigenvalues for all possible bipartitions after partial transposition as a function of $\sigma$, the pump power normalized to the threshold power. For all data we use an analysis frequency of 10 MHz and a temperature of $97°\mathrm{C}$ for $\mathcal{F}=13$, 15, 17, which leads to $P_{\mathrm{Th}}=274$, 199, 138 mW, respectively.

Figure 5

Smallest symplectic eigenvalues for all possible bipartitions after partial transposition as a function of temperature. For all data, we use an analysis frequency of 10 MHz and $\sigma =1.42$ for $T=97$, 101, 105, 109, $113°\mathrm{C}$, which leads to $P_{\mathrm{Th}}=174$, 125, 90, 61.8, 50 mW, respectively.