Detuning-enhanced cavity spin squeezing

The unconditional squeezing of the collective spins of an atomic ensemble in a laser driven optical cavity [I. D. Leroux, M. H. Schleier-Smith, and V. Vuletić, Phys. Rev. Lett 104, 073602 (2010)] is studied and analyzed theoretically. Surprisingly, we find that the largely detuned driving laser can improve the scaling of cavity squeezing from $S^{-2/5}$ to $S^{-2/3}$, where $S$ is the total atomic spin. Moreover, we also demonstrate that the experimental imperfection of photon scattering into free space can be efficiently suppressed by detuning.

Figure 1

(a) Schematic illustration of an ensemble of atoms uniformly coupled to optical cavity mode $c$, and a laser field is driving the cavity. (b) Energy diagram of the atom; the transitions between lower states ($|\downarrow \rangle$ and $|\uparrow \rangle$) and excited state $|e\rangle$ are coupled to the cavity mode.

Figure 2

(a) The squeezing parameter ${\xi }_s^2$ as a function of shearing strength $Q$ for $S=50,\delta =-\kappa /2$ and various coupling $\Omega =0.01,0.2,0.4\mathrm{MHz}$. (b) The squeezing parameter ${\xi }_s^2$ as a function of shearing strength $Q_x$ for $S=50,\Omega =0.2\mathrm{MHz}$ and various detuning $\delta =-x\kappa /2,x=0.5,1,500$. (c) The optimal squeezing parameter ${\xi }_s^2$ as a function of the atomic spin $S$ for $\Omega =0.01\mathrm{MHz}$ and the detuning $\delta =-x\kappa /2,x=1$ (black), $x=500$ (red). The other parameters are $\kappa =4\mathrm{MHz}$ and ${\beta }_0=1$.

Figure 3

(a) The squeezing parameter ${\xi }_s^2$ as a function of $Q_x$ for fixed detuning $x=200$, and single-atom cooperativity $\eta$=2, 20, $\infty$. (b) The optimal squeezing parameter ${\xi }_s^2$ as a function of detuning $x$ for the various cooperativity $\eta =1,2,20$. (c) The solid lines are optimal squeezing parameter ${\xi }_s^2$ as a function of the cooperativity $\eta$ for the fixed detuning $x=1$ (green) and optimized detuning (black), and the dashed lines are results for ideal condition $\eta =\infty$ for $x=1$ (red) and $x=200$ (blue). The atomic spin is $S={10}^4$.