Increasing the Brightness of Cold Ion Beams by Suppressing Disorder-Induced Heating with Rydberg Blockade

A model for the equilibrium coupling of an ion system with varying initial hard-sphere Rydberg blockade correlations is used to quantify the suppression of disorder-induced heating in Coulomb-expanding cold ion bunches. We show that bunches with experimentally achievable blockade parameters have an emittance reduced by a factor of 2.6 and increased focusability and brightness compared to a disordered bunch. Demonstrating suppression of disorder-induced heating is an important step in the development of techniques for the creation of beam sources with sufficient phase-space density for ultrafast, single-shot coherent diffractive imaging.

Figure 1

Equilibrium Coulomb coupling parameter ${\mathrm{\Gamma }}_{\text{eq}}$ of cold ion bunches with hard-sphere blockade parameter $r_b/a$ calculated using the Percus-Yevick hard-sphere distribution function ${\mathrm{\Gamma }}_{\mathrm{PY}}$ (solid line) and by molecular dynamics simulation for configurations generated by random sequential addition (circles) and for a random-close-packed distribution at $r_b/a=1.7$ (square). Uncertainties in the MD data result from residual kinetic energy oscillations.

Figure 2

Disorder-induced heating of nonexpanding ion bunches with hard-sphere initial correlations, labeled by the blockade parameter $r_b/a$. Emittance and temperature are calculated in time and in plasma phase $\phi$, which is $2\pi$ times the number of plasma periods after ionization, for ${}^{85}\mathrm{Rb}$ ions at density $n^{\prime }={10}^{16}{\mathrm{m}}^{-3}$. Damped kinetic energy oscillations at twice the plasma frequency ${\omega }_p$ due to harmonic ion motion are observed. Hard-sphere Rydberg blockade reduces the equilibrium temperatures from the disordered ($r_b=0$) correlation temperature $T_{\text{corr}}=2.6\mathrm{K}$, to near the crystallization phase boundary at $T_{\text{crit}}=34\mathrm{mK}$.

Figure 3

Dimensionless emittance $\tilde{\epsilon }$ and effective temperature growth caused by disorder-induced heating in freely expanding ${{}^{85}\mathrm{Rb}}^{+}$ ion bunches at ${10}^{16}{\mathrm{m}}^{-3}$ initial density, calculated by molecular-dynamics simulation. A model for the bunch temperature evolution [17] is found to overpredict the emittance growth at times beyond the first oscillation maxima. The presence of Rydberg blockade, labeled by the blockade radius in terms of the Wigner-Seitz radius, increases the initial ion correlations thereby reducing the heating.

Figure 4

Suppression of disorder-induced heating, expressed as the ratio of blockaded to disordered emittance for different blockade parameters at different expansion times. The suppression remains constant throughout the linear Coulomb expansion process, as predicted with the hard-sphere model for the thermal equilibrium coupling parameter (solid line).