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Rydberg Gas


In 1998, two groups performed experiments where the electronic interaction between the atoms in the gas was not the smallest energy in the system. In these experiments, the atoms were cooled to 1/1,000,000 of room temperature. A large fraction of the atoms were excited into Rydberg states. Because the atoms were cold, they were essentially stationary for the duration of the experiment. The large dipole moments of the atoms gave large interaction between the atoms and the lack of atomic motion gave time for interesting states of matter to evolve.

The frozen Rydberg gas is an interesting new example of a correlated system. The recent focus (both experimentally and theoretically) is for Rydberg atoms in arrays which are a popular platform for quantum simulators and proposed quantum computers. This popularity is due to the possibility of the long range interaction allowing entanglement between atoms separated by more than a micron.

We have performed several studies of this system. In the early days of this field, we focussed on quantum simulations of the developing entanglement by numerical solution of the Schrodinger equation with a simplified interaction between the atoms. More recently, we study methods for accurately calculating the interaction between the atoms and study decoherence processes that can lead to problems with quantum simulators and computers.

Below is a brief description of results in two recent publications.

Hui Yu and F. Robicheaux, "Coherent dipole transport in a small grid of Rydberg atoms," Phys. Rev. A 93, 023618 (2016). PDF (387 kB)

In this paper, we studied how one or two excitations can hop through a grid of Rydberg states.We studied both 1- and 2-dimensional grids of atoms. The idea was to study how different features of the grid affected how the excitation(s) hopped. For example, corners and edges strongly affected the hopping. As another example, if the excitation is on two sites and there is a phase difference, the value of the phase difference will affect the direction the excitation moves. Other cases were examined. We also showed how to define a current for the excitation as it hopped through the grid.




The above image shows the probability for an excitation to hop from the site x=1,y=4 at t=0 to a different site after 2 microsec. The image (a) is for a perfect 7X7 array of atoms. The image (b) is for a 7X7 array but with 20% of the atoms missing. Darker is higher probability. This shows that the hopping of the excitation away from the original site is slowed when there are missing atoms.

F. Robicheaux and N.M. Gill, "Effect of random positions for coherent dipole transport," Phys. Rev. A 89, 053429 (2014). PDF (831 kB)

In this calculation, we studied how the random positions for a gas of Rydberg atoms would affect the hopping of an exciton due to the dipole-dipole interaction. This system should show effects like Anderson localization.



This image shows the long time probability for finding an exciton a distance r from its original atom for 5 different amounts of randomness (from 0.1 to 0.5); the atoms are placed in a line with random displacements along the line. The + are a fit of the numerical results to a stretch exponential. In the more usual Anderson localization, the probability would be an exponential. As expected, larger randomness leads to stronger localization.



This image shows the long time probability for finding an exciton a distance r from its original atom for 5 different amounts of randomness (from 0.1 to 0.5); the atoms are placed in a square array with random displacements along in the plane. Due to computational limitations, none of the calculations are converged. However, the cases with larger randomness have a larger probability for the exciton to be close to the original placement.


Five Recent Publications

F. Robicheaux, T.M. Graham, and M. Saffman, “Photon-recoil and laser-focusing limits to Rydberg gate fidelity,” Phys. Rev. A 103, 022424 (2021). PDF (642 kB) (data for figures at https://doi.org/10.4231/B7CM-VP26)

F. Robicheaux, “Calculations of long range interactions for 87Sr Rydberg states,” J. Phys. B 52, 244001 (2019).

F. Robicheaux, D.W. Booth, and M. Saffman, "Theory of long-range interactions for Rydberg states attached to hyperfine-split cores," Phys. Rev. A 97, 022508 (2018). PDF (678 kB)

F. Robicheaux, M.M. Goforth, and M.A. Phillips, "Simulation of prompt many-body ionization in a frozen Rydberg gas," Phys. Rev. A 90, 022712 (2014). PDF (254 kB)

S. Zhang, F. Robicheaux, and M. Saffman, "Magic-wavelength optical traps for Rydberg atoms," Phys. Rev. A 84, 043408 (2011). PDF (820 kB)

Francis Image

robichf[at]purdue.edu
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