Figure 1

An illustration of the proposed pulse sequence with pulse envelope $\Omega /{\Omega }_0$ vs time $t$ in arbitrary units, and the associated spin distributions on Bloch spheres. (a) The multipulse sequence is cyclic, with one period between $n{t}_c$ and $(n+1)t_c$ (shaded) and zoomed in (b). Each period contains two $\pi /2$ pulses. A red pulse rotates the spin from along the positive $z$ axis to the $x$ axis, and a blue one coherently phased to achieve the opposite is a $-\pi /2$ pulse, as shown on the large Bloch sphere of (b). The four small Bloch spheres are located at their corresponding times. The spin distributions for the upper two are centered on the $x$ axis, while the lower two are centered on the $z$ axis, due to the applications of red and blue $\pi /2$ pulses. The twistings from the OAT interaction (1) are illustrated with counterrotating circular arrows pierced by the $x$ or $z$ axis of all Bloch spheres.Reuse & Permissions

Figure 2

Spin squeezing parameter at different pulse numbers $N_c=10$ (upper), 100 (middle), and 1000 (lower) compared with the effective TAT $H_{\mathrm{eff}}$ dynamics in black solid lines with the actual ones (1) by using the proposed sequence of pulses in red solid lines. The black dot-dashed lines denote OAT results, all for $N=1250$ atoms.Reuse & Permissions

Figure 3

Top-higher panel: Spin squeezing parameter calculated from the actual dynamics of (1) for $N_c=20$ pulses shown by red and blue dots, respectively, for time windows after the first (red) and second (blue) pulses of each cycle. For comparison, the black solid (dot-dashed) line denotes results from the associated TAT (OAT) model. The top-lower panel shows the corresponding optimal squeezing measurement angle. The dichotomy of two narrow distributions around $\pm \pi /4$ is due to the repeated $\pi /2$ pulses rotating between the $x$ and $z$ axes. For the TAT around the $z$ or $x$ axis, this angle is simply a flat distribution at $\pm \pi /4$, as shown by black dashed lines. At the reduced number of cycles $N_c=20$, the TAT is not yet fully effective, which is the cause for small sloped distributions through $\pm \pi /4$. The slopes eventually reduce to zero with the increase of $N_c$. The bottom panels display in detail the shaded region where the slopes are now displayed in absolute values, all for $N=1250$ atoms.Reuse & Permissions