Figure 1

The Faraday interaction rotates the Stokes vector about the $S_3$ axis by an amount proportional to the collective magnetization $M_z$ of the atoms. For a large ensemble of $N_A$ atoms in identical states, the probability distribution $P(M_z)$ is Gaussian with variance $\Delta M_z^2=N_A\Delta f_z^2$. The light is initially in a coherent state along $S_1$ with shot noise fluctuations along $S_2$ and $S_3$. The quantum uncertainty in $M_z$ leads to a spread in Faraday rotation angles. Shown in schematic are the spread in rotations for atoms initially in (a) a spin coherent state along $x$, $|f,m_x=f{⟩}^{\otimes N_a}$, and (b) the state $|f,m_x=0{⟩}^{\otimes N_a}$. The increased quantum uncertainty in $M_z$ (“projection noise”) translates into increased entanglement between atoms and photons as the corresponding rotations become more distinguishable for a given probe shot noise.Reuse & Permissions

Figure 2

Numerically calculated squeezing (dB). (a) Squeezing as a function of time in units of the scattering rate $\gamma$ for an ensemble of $f=4$ cesium atoms with $\mathrm{OD}=300$, and a probe detuned $\Delta ={10}^3\Gamma =33\mathrm{GHz}$ from the $D2$ line, for three state preparations: SCS [green (triangle) solid line], cat [black (circle) solid line], $0_x$ [red (square) solid line]. The dashed curves include the final squeezing of the internal spin. (b) Peak squeezing of the three state preparations as a function of $f$. The inset includes the final Yurke mapping.Reuse & Permissions