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Simulating Interactions of Rydberg Atoms

Evan Dryfoos

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

Mathematica code and analysis for an example simulation and analysis of data for density vs width of resonance peaks of interacting rydberg atoms.

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Role of multilevel Rydberg interactions in electric-field-tuned Förster resonances

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In this work, we investigate the dc electric-field dependence of two F\"orster resonant processes in ultracold $^{85}\mathrm{Rb}$, $37{D}_{5/2}+37{D}_{5/2}\ensuremath{\rightarrow}35L(L=O,Q)+39{P}_{3/2}$, as a function of the atomic density. At low densities, the $39{P}_{3/2}$ yield as a function of electric field exhibits resonances. With increasing density, the linewidths increase until the peaks merge. Even under these extreme conditions, where the F\"orster resonance processes show little electric-field dependence, the $39{P}_{3/2}$ population depends quadratically on the total Rydberg atom population, suggesting that a two-body interaction is the dominant process. In order to explain our results, we implement a theoretical model which takes into account the multilevel character of the interactions and Rydberg atom blockade process using only atom pair interactions. The comparison between the experimental data and the model is very good, suggesting that the F\"orster resonant processes are dominated by two-body interactions up to atomic densities of $3.0\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.

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We have explored the dipole-dipole mediated, resonant energy transfer reaction, $32{p}_{3/2}+32{p}_{3/2}\ensuremath{\rightarrow}32s+33s$, in an ensemble of cold $^{85}\mathrm{Rb}$ Rydberg atoms. Stark tuning is employed to measure the population transfer probability as a function of the total electronic energy difference between the initial and final atom-pair states over a range of Rydberg densities, $2\ifmmode\times\else\texttimes\fi{}{10}^{8}\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}3\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}$. The observed line shapes provide information on the role of beyond nearest-neighbor interactions, the range of Rydberg atom separations, and the electric field inhomogeneity in the sample. The widths of the resonance line shapes increase approximately linearly with the Rydberg density and are only a factor of 2 larger than expected for two-body, nearest-neighbor interactions alone. These results are in agreement with the prediction [B. Sun and F. Robicheaux, Phys. Rev. A 78, 040701(R) (2008)] that beyond nearest-neighbor exchange interactions should not influence the population transfer process to the degree once thought. At low densities, Gaussian rather than Lorentzian line shapes are observed due to electric field inhomogeneities, allowing us to set an upper limit for the field variation across the Rydberg sample. At higher densities, non-Lorentzian, cusplike line shapes characterized by sharp central peaks and broad wings reflect the random distribution of interatomic distances within the magneto-optical trap (MOT). These line shapes are well reproduced by an analytic expression derived from a nearest-neighbor interaction model and may serve as a useful fingerprint for characterizing the position correlation function for atoms within the MOT.

Physical Review A•Apr 18, 2016•15 citations

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Trapped Circular Rydberg Atoms for Quantum Simulation

Tigrane Cantat-Moltrecht, Thanh Long Nguyen, Rodrigo G. Cortiñas +4 more

Bulletin of the American Physical Society•Jun 9, 2017•0 citations
In this work, we investigate the dc electric-field dependence of two F\"orster resonant processes in ultracold 85Rb^{85}\mathrm{Rb}85Rb, $37{D}_{5/2}+37{D}_{5/2}\ensuremath{\rightarrow}35L(L=O,Q)+39{P}_{3/2}$, as a function of the atomic density. At low densities, the 39P3/239{P}_{3/2}39P3/2​ yield as a function of electric field exhibits resonances. With increasing density, the linewidths increase until the peaks merge. Even under these extreme conditions, where the F\"orster resonance processes show little electric-field dependence, the 39P3/239{P}_{3/2}39P3/2​ population depends quadratically on the total Rydberg atom population, suggesting that a two-body interaction is the dominant process. In order to explain our results, we implement a theoretical model which takes into account the multilevel character of the interactions and Rydberg atom blockade process using only atom pair interactions. The comparison between the experimental data and the model is very good, suggesting that the F\"orster resonant processes are dominated by two-body interactions up to atomic densities of $3.0\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.
We have explored the dipole-dipole mediated, resonant energy transfer reaction, $32{p}_{3/2}+32{p}_{3/2}\ensuremath{\rightarrow}32s+33s$, in an ensemble of cold 85Rb^{85}\mathrm{Rb}85Rb Rydberg atoms. Stark tuning is employed to measure the population transfer probability as a function of the total electronic energy difference between the initial and final atom-pair states over a range of Rydberg densities, $2\ifmmode\times\else\texttimes\fi{}{10}^{8}\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}3\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}$. The observed line shapes provide information on the role of beyond nearest-neighbor interactions, the range of Rydberg atom separations, and the electric field inhomogeneity in the sample. The widths of the resonance line shapes increase approximately linearly with the Rydberg density and are only a factor of 2 larger than expected for two-body, nearest-neighbor interactions alone. These results are in agreement with the prediction [B. Sun and F. Robicheaux, Phys. Rev. A 78, 040701(R) (2008)] that beyond nearest-neighbor exchange interactions should not influence the population transfer process to the degree once thought. At low densities, Gaussian rather than Lorentzian line shapes are observed due to electric field inhomogeneities, allowing us to set an upper limit for the field variation across the Rydberg sample. At higher densities, non-Lorentzian, cusplike line shapes characterized by sharp central peaks and broad wings reflect the random distribution of interatomic distances within the magneto-optical trap (MOT). These line shapes are well reproduced by an analytic expression derived from a nearest-neighbor interaction model and may serve as a useful fingerprint for characterizing the position correlation function for atoms within the MOT.
Abstract This article introduces a novel method to engineer sharply peaked, distance-selective interactions between neutral atoms by exploiting interaction-induced resonances within a resonantly driven Rydberg ladder system. By tuning laser parameters, a subsystem eigenstate twists rapidly and is brought into degeneracy with the atomic ground state at precisely defined interatomic separations, resulting in an effective fourth-order light-shift potential sharply peaked around this resonance distance. The linewidth of the resonant double excitation manifold defines the linewidth of the potential peak. Unlike previous off-resonant macrodimer-based schemes, our approach significantly enhances interaction strength, reaching MHz scales, and provides straightforward experimental tunability without requiring sub-wavelength positional control. Analytic expressions, validated through comprehensive master-equation simulations, detail the interaction profile's amplitude, width, and resonant distance and robustness to laser fluctuations. This precise control facilitates parallel entangling gates crucial for measurement-based quantum computing and enables simulation of complex lattice Hamiltonians with customizable connectivity.