Rydberg Atom Formation in Ultracold Plasmas: Small Energy Transfer with Large Consequences

We present extensive Monte Carlo calculations of electron-impact-induced transitions between highly excited Rydberg states and provide accurate rate coefficients. For moderate energy changes, our calculations confirm the widely applied expressions in P. Mansbach and J. Keck [Phys. Rev. 181, 275 (1969)] but reveal strong deviations at small energy transfer. Simulations of ultracold plasmas demonstrate that these corrections significantly impact the short-time dynamics of three-body Rydberg atom formation. The improved rate coefficients yield quantitative agreement with recent ultracold plasma experiments.

Figure 1

(a) Deexcitation and (b) excitation rate coefficients for different values of the initial energy ${\epsilon }_i$, in increments of $\Delta n_i=25$ at $T=16\mathrm{K}$. The MC data (symbols) are nicely fitted by the improved expressions Eqs. (2) (solid lines) and deviate from the MK results (dashed lines) for small $\Delta \epsilon$. The shaded area marks the energy range investigated in Ref. 14, where both rate formulas agree. The inset shows the relative deviation $|\Delta k/k|$ of the numerical data from Eq. (2).

Figure 2

(a),(b) Actual number of recombined atoms and (c) Rydberg atom refilling rate, as measured in Refs. 21, 37. Compared to the predictions of the MK rates (dashed lines) and the VS rates (dotted lines), plasma simulations based on the present rates (solid lines) yield an improved description of the experimental data (dots). The experimental data points at $t=10\mu \mathrm{s}$ include two separate measurements.

Figure 3

(a) Ionization and (b) recombination rate coefficients for different values of the initial energy ${\epsilon }_i$. The MC data (symbols) are well described by Eq. (3) (solid lines) but are significantly smaller than the MK rates (dashed lines). $n_{\mathrm{th}}=\sqrt{\mathcal{R}/k_{B}T}$ and ${\tilde{k}}_0=n_{\mathrm{th}}^3{\Lambda }^3{\rho }_e{k}_0$.

Figure 4

Normalized steady-state Rydberg population in a recombining plasma, obtained from the MK rates (dashed line) and the new coefficients in Eqs. (2, 3) (solid line). The vertical dotted line marks the bottleneck energy of $4k_{B}T$.

Figure 5

Measured [20] expansion velocity of an ultracold strontium plasma (dots) compared to simulations using the present rate coefficients in Eqs. (2, 3) (solid line) and the MK rate coefficients (dashed line). The dotted line shows the resulting expansion dynamics when recombination is neglected.