Ultrafast many-body dynamics of dense Rydberg gases and ultracold plasma

TL;DR

This work addresses the ultrafast, strongly coupled dynamics in a dense $^{87}$Rb Bose-Einstein condensate subjected to a single femtosecond pulse, exploring the transition between ultracold plasma and dense Rydberg gases by tuning across the two-photon ionization threshold. It combines energy-resolved electron detection with fully microscopic molecular dynamics simulations that treat electrons and ions as individual Coulomb-interacting particles, enabling generation of final-state classifications into bound (Rydberg), plasma, and free electrons. A key finding is that the initial few nanoseconds of dynamics determine the ultimate electron composition, with substantial three-photon ionization (3PI) at BEC densities driving a high charge imbalance and suppressing re-assembly into Rydberg states, a behavior distinct from ultracold neutral plasma. The study demonstrates that broad-bandwidth ultrafast excitation can overcome the Rydberg blockade to create dense ensembles of Rydberg atoms or transient strongly coupled plasmas, providing microscopic insight with potential implications for ultrafast quantum control and simulation in strongly interacting many-body systems.

Abstract

Within femtoseconds the strong light field of an ultrashort laser pulse can excite and ionize a few thousand atoms in an ultracold quantum gas. Here we investigate the rich many-body dynamics unfolding in a $^{87}$Rb Bose-Einstein condensate after exposure to a single femtosecond laser pulse. By tuning the laser wavelength over the two-photon ionization threshold, we adjust the initial energy of the electrons and can thus investigate the transition from an ultracold plasma to a dense Rydberg gas. Our experimental setup provides access to the kinetic energy of the released electrons, which allows us to distinguish between bound, free and plasma electrons. The large bandwidth of the ultrashort laser pulse makes it possible to overcome the Rydberg blockade which fundamentally limits the density in excitation schemes with narrow-band lasers. To understand the many-body dynamics at the microscopic level, we employ molecular dynamics simulations where the electrons are modeled as individual particles including collisional ionization and recombination processes. We find that the ultrafast dynamics within the first few nanoseconds is responsible for the final distribution of free, bound and plasma electrons and agrees well with the experimental observation. We find distinctly different dynamics compared to the expected transition from an ultracold neutral plasma to a dense Rydberg gas.

Figures (10)

• Figure 1: From ultracold plasma to dense Rydberg gases. Manipulating a BEC with a femtosecond laser pulse can lead to a variety of different systems: By reducing the excess energy of electrons, the dynamics can be tuned from that of a highly charged microplasma (a) with large electron orbits around the ionic cloud to more neutral plasmas (b) close to the ionization threshold. For vanishing excess energy (c), Rydberg atoms are created due to the large bandwidth of the laser pulse and Rydberg recombination can occur. For negative excess energies (d), the system enters the regime of Rydberg gases with Penning ionization due to overlap of Rydberg orbitals. (e) The excitation spectra for two-photon processes at wavelengths ranging from 580 nm to 620 nm are plotted for a pulse duration of 170 fs. The vertical lines mark the ionization threshold (black dotted line) as well as the $s$-states of $^{87}$Rb (red) and the $d$-states (green) which can be addressed.
• Figure 2: Energy-resolved detection of electrons emerging from ultrafast ionization of a BEC.a A fraction of a $^{87}$Rb BEC is ionized by a focused femtosecond laser pulse with tuneable wavelength ranging from 580 - 640 nm. The emerging electrons and ions are separated by an extraction field and spatially resolved by two microchannel plates and phosphor screens. The kinetic energy of the electrons is translated into spatial information during their propagation towards the detector. Comparing the recorded detector image with CPT simulations (b) of monoenergetic electron distributions allows to estimate the maximum kinetic energy in a range between 0.01 eV to 2 eV. c Two- and three-photon ionization of $^{87}$Rb at wavelengths of 580 nm, 594 nm and 640 nm. At the threshold, the bandwidth of the two-photon process is $\sigma_{2\gamma} = 9.1$ meV FWHM. Below the threshold, the two-photon process yields ultrafast excitation of $s$- and $d$-states. d To detect Rydberg states excited at wavelengths below the ionization threshold, a Rydberg ionization pulse at $\lambda_{\text{Ry,PI}} = 1064$ nm is used, yielding photoelectrons with a kinetic energy of approximately $0.8-1.2$ eV, depending on the binding energy of the Rydberg state. The difference of the mean images with and without this ionization pulse shows a clear signature of these electrons.
• Figure 3: Electron composition of dense Rydberg gases and ultracold plasma.a Measured detector brightness and corresponding electron numbers $N_\mathrm{e}$ separated into plasma (green), Rydberg (red) and free/3PI (yellow) electrons as a function of the excess energy for a BEC (top) and a dilute thermal cloud (bottom). The ionization continuum is indicated as dotted gray line. Shaded areas show the standard deviation on the detector brightness. b Exemplary mean detector image without Rydberg ionization pulse. The signal marked yellow in the image is accounted to free/3PI electrons (compare to Fig. \ref{['fig2']}b at 2 eV). The dotted green circle shows the mask used to extract the plasma electrons with kinetic energy smaller than 0.1 eV. c-e Kinetic energy distribution of the Rydberg electrons for a BEC exposed to femtosecond laser pulses at $E_\text{exc}=0$ eV c, at $E_\text{exc}=-0.1$ eV d, and at $E_\text{exc}=-0.23$ eV e. f-h Kinetic energy distribution of the Rydberg electrons for a dilute cloud at the same excess energy values than for a BEC.
• Figure 4: Underlying dynamics of plasma and overlapping Rydberg orbits. All simulations have been performed at a density corresponding to a BEC ($\rho_\mathrm{BEC} = 1.6 \times 10^{20}\,\mathrm{m}^{-3}$). a-d Simulated electron trajectories referenced to the nearest ion $d_{\text{Rb}^+,\text{e}}$ over 2 ns. The electrons are either plasma electrons (green), Rydberg electrons (red) or electrons escaping the system (yellow). a-b At $E_\text{exc}=40$ meV, free electrons quickly leave the system a. On smaller length scales (b) plasma electrons inside the ion cloud become evident as the electron-ion distance is shorter than the mean ion-ion distance $\bar{d}_{\text{Rb}^,+\text{Rb}^+}$. c At $E_\text{exc}=-65$ meV, Rydberg states are initially populated but quickly decay into plasma. d At $E_\text{exc}=-229$ meV, the population of Rydberg states remains stable throughout the simulated time frame. e Comparison between the ratio of Rydberg (red), plasma (green) and 3PI/free electrons (yellow) in the experiment (dots, shaded area indicates standard deviation) and simulation after 2 ns (triangles). f-i Simulations with (plain lines) and without 3PI (dotted lines) of the evolution of the number of electrons in Rydberg states (red), plasma electrons (green) and free electrons (yellow) within the first 100 ps. f At $E_\text{exc}=40$ meV, the simulation without 3PI shows an almost neutral plasma with recombination of cold electrons into Rydberg states, while 3PI leads to the formation a highly charged microplasma. g At $E_\text{exc}=0$ meV, 3PI also leads to the formation a highly charged microplasma. h At $E_\text{exc}=-65$ meV, the Rydberg population remains stable when neglecting 3PI, otherwise it quickly decays into plasma. i At $E_\text{exc}=-229$ meV, the Rydberg population remains stable within the simulated time frame for both cases.
• Figure 5: Field configuration of the detector setup. The extraction meshes of the detector assembly are set to $V_\mathrm{ext} = \pm 300$ V and the MCPs are set to 268 V at the electron side and $-1000$ V at the ion side. To illustrate the field configuration, equipotential lines are shown with positive potentials up to $300$ V shaded in green and negative potentials down to $-1000$ V colored in red. The bold black line marks an equipotential of 0 V, revealing a slight asymmetry along the central axis of the setup. In the interaction region the extraction field in this configuration is $E_\mathrm{ext} \approx 162$ V/m.