Anomalous excitation enhancement with Rydberg-dressed atoms

We develop the research achievement of recent work [Gärttner et al., Phys. Rev. Lett. 113, 233002 (2014)], in which an anomalous excitation enhancement is observed in a three-level Rydberg-atom ensemble with many-body coherence. In our theoretical analysis, this effect is ascribed to the existence of a quasidark state as well as its avoided crossings to nearby Rydberg-dressed states. Moreover, we show that with an appropriate control of the optical detuning to the intermediate state, the enhancement can evoke a direct facilitation to atom-light coupling that even breaks through the conventional $\sqrt{N}$ limit of strong-blockaded ensembles. As a consequence, the intensity of the probe laser for intermediate transition can be reduced considerably, increasing the feasibility of experiments with Rydberg-dressed atoms.

Figure 1

(a) Schematic view of the atomic ensemble. Each atom has a three-level cascaded configuration. See main text for a detailed description. (b) The energy of the Rydberg-dressed states $\left|D{r}_{\pm }\right.〉$ (magenta dashed lines) and dark state $\left|D_2\right.〉$ (black dashed line) are shown as functions of detuning $\mathrm{\Delta }$. The colored solid lines are for the eigenvalues obtained from numerical diagonalization of the Hamiltonian $H_2$. Two ACs are denoted at ${\mathrm{\Delta }}_{+}$ and ${\mathrm{\Delta }}_{-}$. The parameters are $U=50$, $\mathrm{\Omega }=5.0$, and ${\xi }_2=0.1$ (${\omega }_2=0.5$). $\mathrm{\Gamma }$ is the frequency unit. Panel (c) gives a partially enlarged view of (b) (shaded area) where two ACs and energy gaps are clearly distinguishable.

Figure 2

(a) The locations of ${\mathrm{\Delta }}_{\pm }$ versus ${\xi }_2$ for $U=5.0$ (red solid and dash-dotted lines) and $U=50.0$ (black solid and dash-dotted lines). (b) The locations of ${\mathrm{\Delta }}_{\pm }$ versus $U$ for ${\xi }_2=0.1$. Same line-types are used in (c) and (d) with respect to (a) and (b) for the values of energy gaps at ACs. The inset of (c) shows a partially enlarged view for ${\xi }_2\in (0,0.2)$. The case of $U=50$, ${\xi }_2=0.1$ [same as Fig. 1] is pointed out by circles, indicating the energy gap there is 0.055. Other parameters: $\mathrm{\Omega }=5.0$, $\mathrm{\Gamma }$ is the frequency unit.

Figure 3

The steady population $F_r$ versus detuning $\mathrm{\Delta }$. (a) ${\xi }_2=0.1$, $U=50$; (b) ${\xi }_2=0.1$, $U=5.0$; (c) ${\xi }_2=0.5$, $U=50$; (d) ${\xi }_2=0.5$, $U=5.0$. Other parameters are the same as used in Fig. 2.

Figure 4

The variation of relative enhancement factor (a) $E{F}_{+}$ and (b) $E{F}_{-}$ in the space of $({\xi }_2,U)$. The global maximum of $E{F}_{+}$($\approx 8.8$) is marked by a red arrow in (a). White dashed lines for $E{F}_{\pm }=1.0$, label the boundary from suppressed to enhanced excitation.

Figure 5

(a) The steady population $F_r$ as a function of $\mathrm{\Delta }$, which is the same curve as in Fig. 3. The required value ${\omega }_2$ is shown by a blue solid line. (b) The dependence of ${\alpha }_2$ on $\mathrm{\Omega }$ and ${\xi }_2$ in the strong-interaction case $U=10\mathrm{\Omega }$. The white dashed line denotes the boundary where ${\alpha }_2=\sqrt{2}$. Panel (c) is the same as (b) except for the weak-interaction case $U=\mathrm{\Omega }$.

Figure 6

(a) The eigenenergy as a function of $\mathrm{\Delta }$ for the case $N=5$, $U=10\mathrm{\Omega }$, and ${\mathrm{\Delta }}_{\pm }^{max}\approx \pm \mathrm{\Omega }/2$. Maximal enhancement ${\alpha }_N^{max}$ for different atomic numbers, $N$=2, 3, 4, 5, are shown for the strong-interaction case ($U=10\mathrm{\Omega }$) in (b) and weak-interaction case ($U=\mathrm{\Omega }$) in (c). The line styles correspond to cases of different detunings, that is, $\mathrm{\Delta }={\mathrm{\Delta }}_{+}^{max}$ (red line with stars), ${\mathrm{\Delta }}_{-}^{max}$ (blue line with crosses), and 0 (black line with circles). For comparison, the function $\sqrt{N}$ (green dashed line with diamonds) is displayed in the same frame.