Rydberg dressing of a one-dimensional Bose-Einstein condensate

We study the influence of Rydberg-dressed interactions in a one-dimensional (1D) Bose-Einstein condensate (BEC). We show that a 1D geometry offers several advantages over a three-dimensional geometry for observing BEC Rydberg dressing. The effects of dressing are studied by investigating collective BEC dynamics after a rapid switch-off of the Rydberg dressing interaction. The results can be interpreted as an effective modification of the $s$-wave scattering length. We include this modification in an analytical model for the 1D BEC and compare it to numerical calculations of Rydberg dressing under realistic experimental conditions.

Figure 1

Left panel: Characteristic behavior of the Rydberg-dressed interaction in 1D, as a function of BEC linear density, for realistic experimental conditions, using the $35S$ Rydberg state of ${}^{87}\mathrm{Rb}$. The energy functional ${\partial }_{\rho }E\left[\rho \right]$ is plotted for different dressing Rabi frequencies, as parameterized by $\beta =\mathrm{\Omega }/2\left|\mathrm{\Delta }\right|$ for fixed detuning $\mathrm{\Delta }/2\pi =-100$ kHz. Corresponding critical densities ${\rho }_B$ are (curves from bottom to top) 177 $\mu {\mathrm{m}}^{-1}$, 64 $\mu {\mathrm{m}}^{-1}$, 33 $\mu {\mathrm{m}}^{-1}$, and 20 $\mu {\mathrm{m}}^{-1}$. Dashed lines correspond to the variational ansatz $F$, Eq. (3), and dotted lines correspond to a linear increase with density as in the two-body limit. Right panel: Variational parameter $C$ for the energy functional ansatz $F$. Vanishing $C$ for $\beta <0.018$ corresponds to the two-body limit, Eq. (1), while $\beta >0.018$ corresponds to the saturation effect, Eq. (5).

Figure 2

Relative change of the BEC size after sudden switch-off of the dressing lasers ($\kappa$) for different BEC particle numbers and different dressing parameters. Red dashed lines correspond to the self-similar density evolution ($\lambda$).

Figure 3

Relative change of the effective trapping frequency ${\omega }_{\mathrm{eff}}$ (top panel) and relative change of the mean-field coupling $g_{\mathrm{eff}}$ (bottom panel) for different atom numbers $N$ for the fixed dressing parameter (curves from top to bottom: $\beta =0.03$, 0.05, 0.07, and 0.09). Dashed lines correspond to Eq. (5).