Cavity QED Engineering of Spin Dynamics and Squeezing in a Spinor Gas

We propose a method for engineering spin dynamics in ensembles of integer-spin atoms confined within a high-finesse optical cavity. Our proposal uses cavity-assisted Raman transitions to engineer a Dicke model for integer-spin atoms, which, in a dispersive limit, reduces to effective atom-atom interactions within the ensemble. This scheme offers a promising and flexible new avenue for the exploration of a wide range of spinor many-body physics. As an example of this, we present results showing that this method can be used to generate spin-nematic squeezing in an ensemble of spin-1 atoms. With realistic parameters, the scheme should enable substantial squeezing on time scales much shorter than current experiments with spin-1 Bose-Einstein condensates.

Figure 1

Level diagram for the implementation of an effective Dicke model using the $F=1$ ground state of ${}^{87}\mathrm{Rb}$. Interactions are engineered via Raman transitions on the $D_1$ line mediated by a cavity mode (blue dashed line) and ${\sigma }_{+}$ (green dotted line) or ${\sigma }_{-}$ (red dot-dashed line) polarized laser fields.

Figure 2

(Top) Time evolution of the spin-nematic squeezing for $N=120$ atoms without damping (red line) and, with damping rate $\mathrm{\Gamma }=0.05\mathrm{\Lambda }$, an ensemble average of 1000 trajectories (dark blue line) and a single trajectory in which no jumps occur (dashed dark blue line). The phase angle in each case is just below $\theta =170°$. (Bottom left) Populations in each of the states $m=\pm 1$ for $\mathrm{\Gamma }=0$ (solid line) and $\mathrm{\Gamma }=0.05\mathrm{\Lambda }$ (dashed lines). (Bottom right) Optimized squeezing scaling with atom number with and without damping. With damping, ensemble averages of 1000 trajectories were used to estimate the master equation result.

Figure 3

Values of ${\xi }_x^2$ (in decibels) as a function of the time and phase angle for $\mathrm{\Gamma }/\mathrm{\Lambda }=0.05$ with $N=120$ atoms (left) and in the undepleted mode approximation ($N\to \infty$), Eq. (12) (right).