Dicke State Generation and Extreme Spin Squeezing via Rapid Adiabatic Passage

Considering the unique energy level structure of the one-axis twisting Hamiltonian in combination with standard rotations, we propose the implementation of a rapid adiabatic passage scheme on the Dicke state basis. The method permits to drive Dicke states of the many-atom system into entangled states with maximum quantum Fisher information. The designed states allow us to overcome the classical limit of phase sensitivity in quantum metrology and sensing. We show how to generate superpositions of Dicke states, which maximize metrological gain for a Ramsey interferometric measurement. The proposed scheme is remarkably robust to variations of the driving field and has favorable time scaling, especially for a small to moderate ($\sim 1000$) number of atoms, where the total time does not depend on the number of atoms.

Figure 1

Example of the energy levels of the five lowest Dicke states as a function of time. The solid lines represent the instantaneous eigenvalues of the Hamiltonian in Eq. (1) (adiabatic picture), and the dashed curves are the diagonal values, $E_m$, (diabatic picture). The coupling pulse goes up to ${\mathrm{\Omega }}_{\max }=0.4\chi$. It starts to turn off at $t=0$ and is entirely off at $\alpha t/\chi =1$. The chirp rate is $\alpha =0.1{\chi }^2$.

Figure 2

Population dynamics of the ten-atom Dicke states. The solid black line shows the coupling pulse shape, $\mathrm{\Omega }(t)$. The chirp rate is $\alpha =0.1{\chi }^2$.

Figure 3

Quantum Fisher information, ${\mathcal{F}}_x$, as a function of time for the RAP transfer from $|S,S⟩$ to $|S,0⟩$ for three values of $\overline{\alpha }=\alpha /{\chi }^2$, ${\overline{\alpha }}_1={10}^{-4}$, ${\overline{\alpha }}_2={10}^{-2}$, and ${\overline{\alpha }}_3={10}^{-1}$; $N=10$. We also present snapshots of the Wigner function of the collective state at the selected time.

Figure 4

Generation of the ESS state via RAP, the chirp rate is $\alpha =0.1{\chi }^2$. Upper panel: the Dicke state population dynamics, the time-dependent coupling with the maximum ${\mathrm{\Omega }}_{\max }=0.88\chi$ is shown by a black solid line. The Wigner function of the generated state at $t=5\chi /\alpha$ is in the inset. Bottom panel: the infidelity as a function of time.

Figure 5

Comparison between the metrological gain as a function of the atom number for ideal ESS states and ESS states created by RAP. The results share the HL scaling.