Polarization Squeezing with Cold Atoms

We study the interaction of a nearly resonant linearly polarized laser beam with a cloud of cold cesium atoms in a high finesse optical cavity. We show theoretically and experimentally that the cross-Kerr effect due to the saturation of the optical transition produces quadrature squeezing on both the mean field and the orthogonally polarized vacuum mode. An interpretation of this vacuum squeezing as polarization squeezing is given and a method for measuring quantum Stokes parameters for weak beams via a local oscillator is developed.

Figure 1

Experimental setup: PBS: polarizing beam splitter; BS: $10/90$ beam splitter; $\lambda /2$: half-wave plate; PZT: piezoelectric ceramic.

Figure 2

Analysis of the circular polarization content of the light transmitted by the cavity and detected by the photodiodes shown in Fig. 1. Polarization switching occurs at point $A$. The power of the incident light is $7\mu \mathrm{W}$.

Figure 3

Schematic energy level diagram for the $X$-like four-level system: ${\gamma }_{\perp }+{\gamma }_{\parallel }=\gamma$ is the optical dipole decay rate; $\Delta$ is the (large) detuning from resonance.

Figure 4

Normalized quadrature noise (a) for the vacuum field mode at 3 MHz and (b) for the mean field mode at 6 MHz. The best squeezing is $13\%$ for the vacuum mode and $5\%$ for the mean field mode.

Figure 5

Normalized quadrature noise at 3 MHz for the vacuum mode ${\widehat{A}}_y$ vs the normalized interference signal: $\cos {\theta }_{hd}$. The general case is shown in curve (a): polarization squeezing is achieved when ${\theta }_{hd}={\theta }_{\mathrm{s}\mathrm{q}}=\pm 30°$: a linear combination of ${\widehat{S}}_2$ and ${\widehat{S}}_3$ is squeezed. In curve (b), ${\widehat{S}}_3$ is squeezed (${\theta }_{\mathrm{s}\mathrm{q}}=\pm \pi /2$).