Continuous Variable Entanglement using Cold Atoms

We present an experimental demonstration of both quadrature and polarization entanglement generated via the interaction between a coherent linearly polarized field and cold atoms in a high finesse optical cavity. The nonlinear atom-field interaction produces two squeezed modes with orthogonal polarizations which are used to generate a pair of nonseparable beams, the entanglement of which is demonstrated by checking the inseparability criterion for continuous variables recently derived by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)] and calculating the entanglement of formation [Giedke et al., Phys. Rev. Lett. 91, 107901 (2003)].

Figure 1

Experimental setup: PBS, polarizing beam splitter; $\lambda /2$, half-wave plate; PZT, piezoelectric ceramic; SA, spectrum analyzer. $T=0.1$ is the transmission of the cavity coupling mirror.

Figure 2

(a) Quadrature noise spectra of $A_x$ and $i{A}_y$, at a frequency of 5 MHz, when the relative phase $\theta$ between the LO and the mean field mode is varied in time. (b) Direct measurement of ${\mathcal{I}}_{+45,-45}(\theta )$. (c) Corresponding measurement of ${\mathcal{I}}_{x,y}(\theta )$.

Figure 3

Setup for nonseparable beam generation. Inserting the quarter-wave plates (or not) allows for measuring the fluctuations of $S_3^{\alpha }+S_3^{\beta }$ (or $S_2^{\alpha }+S_2^{\beta }$). The servo loop is used to lock the $B$ field phase to the squeezed quadrature angle.

Figure 4

Normalized noises at 5 MHz of $S_2^{\alpha }+S_2^{\beta }$ (a) and $S_3^{\alpha }+S_3^{\beta }$ (b), the phase ${\theta }_B$ being locked with the value of the squeezed quadrature angle ${\theta }_{\mathrm{sq}}$.