Periodically Driven Array of Single Rydberg Atoms

An array of single Rydberg atoms driven by a temporally modulated atom-field detuning is studied. The periodic modulation effectively modifies the Rabi coupling, leading to unprecedented dynamics in the presence of Rydberg-Rydberg interactions, in particular, blockade enhancement, antiblockades, and state-dependent population trapping. Interestingly, the Schrieffer-Wolf transformation reveals a fundamental process in Rydberg gases, correlated Rabi coupling, which stems from the extended nature of the Rydberg-Rydberg interactions. Also, the correlated coupling provides an alternative depiction for the Rydberg blockade, exhibiting a nontrivial behavior in the presence of periodic modulation. The dynamical localization of a many-body configuration in a driven Rydberg lattice is discussed.

Figure 1

The results in the weak driving limit with $\delta =0.4\mathrm{\Omega }$ and ${\mathrm{\Delta }}_0=5\mathrm{\Omega }$. (a) $P_{\beta }(t)$ vs ${\omega }_0$ for $V_0=0.1\mathrm{\Omega }$ and $\mathrm{\Omega }{T}_f=1000$. The vertical lines indicate the resonances. (b) Analytical (dashed and solid lines) and numerical (filled circles and squares) results for ${\omega }_S/\mathrm{\Omega }$ and ${\omega }_D/\mathrm{\Omega }$. (c) The resonance widths.

Figure 2

(a) $P_{\beta }(t)$ vs $\delta$ in the HFL for ${\mathrm{\Delta }}_0=0$, ${\omega }_0=V_0=8\mathrm{\Omega }$, and $\mathrm{\Omega }{T}_f=100$. The antiblockade occurs at $\delta =11.476\mathrm{\Omega }$ (vertical line), where $J_0(\alpha )\sim J_{-1}(\alpha )$. (b) The blockade and (c) population trapping dynamics for $\delta =\mathrm{\Omega }$ and $\delta =19.24\mathrm{\Omega }$.

Figure 3

$P_{ee}$ vs $V_0$ in FPL, with $\mathrm{\Omega }{T}_f=300$ and ${\omega }_0=3\mathrm{\Omega }$. Thin ($\delta =0$) and thick ($\delta =34\mathrm{\Omega }$) solid lines are for ${\mathrm{\Delta }}_0=0$. The dashed line is for ${\mathrm{\Delta }}_0=0.5\mathrm{\Omega }$ and $\delta =34\mathrm{\Omega }$.

Figure 4

Correlations vs $V_0$ for (a) $N=2$ and (b) $N=10$. For both figures, ${\mathrm{\Delta }}_0=0$, ${\omega }_0=8\mathrm{\Omega }$, and $\mathrm{\Omega }{T}_f=150$.

Figure 5

(a) The initial configuration with one excitation at the center of the lattice. (b) $S_p$ vs time for both $\delta =0$ and $\delta \ne 0$ cases with $V_0=5\mathrm{\Omega }$. For the driven case, $\delta =24.0483\mathrm{\Omega }$ and ${\omega }_0=10\mathrm{\Omega }$ [$J_0(\delta /{\omega }_0)=0$]. (c) $\log ({\tau }_G)$ vs $V_0$ for $N=15$.