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Physical Review A

Dipole-dipole resonance line shapes in a cold Rydberg gas

Benjamin Richards, R. R. Jones

Published Apr 18, 2016• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.93.042505

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Influence of Dipole-Dipole Interaction on Electron Dynamics in a Cold Rydberg Gas

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Electron dynamics in dipole-dipole (DD) coupled Rydberg atoms show some unique properties that do not exist in individual atoms.The goal of the research in this dissertation is to reveal and control the electron dynamics influenced by DD interaction in cold Rydberg gases.We have studied the decay of Rydberg excitations in a cold Rb gas and find no evidence for superradiance.The decay rates and population redistribution we observe are consistent with a model that considers only spontaneous emission from, and blackbody redistribution within, isolated atoms.Suppression of superradiant emission is likely due to variations in transition energies across the cold Rydberg atom sample.For initial s states, these variations are dominated by inhomogeneities in DD exchange interactions within the random ensemble.Such inhomogeneities will necessarily be present in any measurement involving a large number of atoms where the separation between atoms is not well defined.For initial p states, the suppression is likely due to a combination of DD exchange and electric field inhomogeneities.We have also explored the evolution of Rydberg wavepackets in the presence of strong dipole-dipole interactions in a frozen gas.The distribution of atom separations results in an inhomogeneity in the strength of the exchange coupling between neighboring atoms, causing a dephasing of the macroscopic coherence.We have also explored the mechanism of wavepacket coherence transfer from one Rydberg atom to a neighboring Rydberg atom via DD interactions utilizing the resonant DD coupling transition 25s33s↔24p34p.The phase-shift of the observed interference modulations in the 34p signal, relative to that in 25s, is a signature of wavepacket coherence transfer between atoms driven by electron correlations resulting from the controlled DD coupling between them.I would like to thank my advisor Professor Bob Jones for his guidance and help, not only in the detailed research performance but also in scientific ethics and methodology.He taught me how to operate most of the instruments as well as helped me fix failing apparatus.His rigorous, yet optimistic, working attitude always inspires me in my research.I don't remember how many times I have felt frustrated after getting nothing from a several days' experiment.At those times, I was always motivated and energetic from his guidance, constructive criticism and sincere encouragement, after even a short talk with him.The accomplishment of this dissertation involved a lot of his help, ranging from grammar checking, to language polishing, to error correction.I really feel grateful and fortunate to have worked with him for more than 5 years.Thanks also goes to my colleagues who have helped me in the research.Brian Richards worked with me a lot to fix failing instruments.He also programmed the data collection software.Sha Li taught me how to build setups to generate the THz radiation and build dye lasers.Kisra Nayomal Egodapitiya helped me adjust lasers and amplifiers many times.I also got invaluable inspiration from daily talks with them.

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Absence of collective decay in a cold Rydberg gas

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We have studied the decay of Rydberg excitations in a cold Rb gas. A 10 ns, pulsed-dye-amplified diode laser excites Rb atoms at $70\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in a magneto-optical trap to $ns$ or $np$ Rydberg states with principal quantum numbers $26\ensuremath{\le}n\ensuremath{\le}40$. Time-delayed state-selective field ionization is used to directly monitor the population in the initial and neighboring Rydberg levels. The measured time dependence of the Rydberg population is well described by numerical simulations which consider only spontaneous emission and population transfer by blackbody radiation. No evidence for collective decay is found at atom densities up to $3\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. This result is in contrast to a previous study [Wang et al., Phys. Rev. A 75, 033802 (2007)], in which superradiant decay was theoretically predicted and experimentally inferred for atom density and laser focal volume conditions very similar to those considered here. Suppression of collective emission is likely due to variations in transition energies within the atom sample, dominated by inhomogeneities in dipole-dipole exchange interactions for initial $s$ states, or by a combination of dipole-dipole and electric field inhomogeneities for the initial $p$ states.

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Publisher's Note: Line shapes and time dynamics of the Förster resonances between two Rydberg atoms in a time-varying electric field [Phys. Rev. A 94 , 043417 (2016)]

Elena A. Yakshina, Denis B. Tretyakov, Ilya I. Beterov +7 more

The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. In our experiments with a few cold Rb Rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the Förster resonances, since the population transfer at the resonances occurs on a time scale of $\sim$100 ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted Förster resonances, while non-sharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances ${\rm Rb}(nP_{3/2} )+{\rm Rb}(nP_{3/2} )\to {\rm Rb}(nS_{1/2} )+{\rm Rb}([n+1]S_{1/2} )$ for two Rb Rydberg atoms interacting in a time-varying electric field.

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Microwave pump-probe spectroscopy of the dipole-dipole interaction in a cold Rydberg gas

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Microwave pump-probe experiments starting with a cold gas of Rb $34s$ atoms confirm that cusped line shapes observed in dipole-dipole broadened microwave transitions are due to atoms which are widely separated and exhibit small dipole-dipole energy shifts. When the experiments are interpreted in terms of a nearest-neighbor model, they demonstrate that it is possible to select pairs of atoms based on their separation and orientation.

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Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.

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Line shapes and time dynamics of the Förster resonances between two Rydberg atoms in a time-varying electric field

Elena A. Yakshina, Denis B. Tretyakov, Ilya I. Beterov +7 more

The observation of the Stark-tuned F\"orster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the F\"orster resonance. In our experiments with a few cold Rb Rydberg atoms, we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the F\"orster resonances, since the population transfer at the resonances occurs on a time scale of $\ensuremath{\sim}100$ ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted F\"orster resonances, while nonsharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the F\"orster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned F\"orster resonances $\mathrm{Rb}(n{P}_{3/2})+\mathrm{Rb}(n{P}_{3/2})\ensuremath{\rightarrow}\mathrm{Rb}(n{S}_{1/2})+\mathrm{Rb}([n+1]{S}_{1/2})$ for two Rb Rydberg atoms interacting in a time-varying electric field.

Physical Review A•Oct 21, 2016•21 citations
We have explored the dipole-dipole mediated, resonant energy transfer reaction, 32p3/2+32p3/2\ensuremath→32s+33s32{p}_{3/2}+32{p}_{3/2}\ensuremath{\rightarrow}32s+33s32p3/2​+32p3/2​\ensuremath→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×\else\texttimes\fi108\ensuremath≤\ensuremathρ\ensuremath≤3\ifmmode×\else\texttimes\fi109cm\ensuremath−32\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}2\ifmmode×\else\texttimes\fi108\ensuremath≤\ensuremathρ\ensuremath≤3\ifmmode×\else\texttimes\fi109cm\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.
Electron dynamics in dipole-dipole (DD) coupled Rydberg atoms show some unique properties that do not exist in individual atoms.The goal of the research in this dissertation is to reveal and control the electron dynamics influenced by DD interaction in cold Rydberg gases.We have studied the decay of Rydberg excitations in a cold Rb gas and find no evidence for superradiance.The decay rates and population redistribution we observe are consistent with a model that considers only spontaneous emission from, and blackbody redistribution within, isolated atoms.Suppression of superradiant emission is likely due to variations in transition energies across the cold Rydberg atom sample.For initial s states, these variations are dominated by inhomogeneities in DD exchange interactions within the random ensemble.Such inhomogeneities will necessarily be present in any measurement involving a large number of atoms where the separation between atoms is not well defined.For initial p states, the suppression is likely due to a combination of DD exchange and electric field inhomogeneities.We have also explored the evolution of Rydberg wavepackets in the presence of strong dipole-dipole interactions in a frozen gas.The distribution of atom separations results in an inhomogeneity in the strength of the exchange coupling between neighboring atoms, causing a dephasing of the macroscopic coherence.We have also explored the mechanism of wavepacket coherence transfer from one Rydberg atom to a neighboring Rydberg atom via DD interactions utilizing the resonant DD coupling transition 25s33s↔24p34p.The phase-shift of the observed interference modulations in the 34p signal, relative to that in 25s, is a signature of wavepacket coherence transfer between atoms driven by electron correlations resulting from the controlled DD coupling between them.I would like to thank my advisor Professor Bob Jones for his guidance and help, not only in the detailed research performance but also in scientific ethics and methodology.He taught me how to operate most of the instruments as well as helped me fix failing apparatus.His rigorous, yet optimistic, working attitude always inspires me in my research.I don't remember how many times I have felt frustrated after getting nothing from a several days' experiment.At those times, I was always motivated and energetic from his guidance, constructive criticism and sincere encouragement, after even a short talk with him.The accomplishment of this dissertation involved a lot of his help, ranging from grammar checking, to language polishing, to error correction.I really feel grateful and fortunate to have worked with him for more than 5 years.Thanks also goes to my colleagues who have helped me in the research.Brian Richards worked with me a lot to fix failing instruments.He also programmed the data collection software.Sha Li taught me how to build setups to generate the THz radiation and build dye lasers.Kisra Nayomal Egodapitiya helped me adjust lasers and amplifiers many times.I also got invaluable inspiration from daily talks with them.
We have studied the decay of Rydberg excitations in a cold Rb gas. A 10 ns, pulsed-dye-amplified diode laser excites Rb atoms at $70\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in a magneto-optical trap to nsnsns or npnpnp Rydberg states with principal quantum numbers $26\ensuremath{\le}n\ensuremath{\le}40$. Time-delayed state-selective field ionization is used to directly monitor the population in the initial and neighboring Rydberg levels. The measured time dependence of the Rydberg population is well described by numerical simulations which consider only spontaneous emission and population transfer by blackbody radiation. No evidence for collective decay is found at atom densities up to $3\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. This result is in contrast to a previous study [Wang et al., Phys. Rev. A 75, 033802 (2007)], in which superradiant decay was theoretically predicted and experimentally inferred for atom density and laser focal volume conditions very similar to those considered here. Suppression of collective emission is likely due to variations in transition energies within the atom sample, dominated by inhomogeneities in dipole-dipole exchange interactions for initial sss states, or by a combination of dipole-dipole and electric field inhomogeneities for the initial ppp states.
The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. In our experiments with a few cold Rb Rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the Förster resonances, since the population transfer at the resonances occurs on a time scale of $\sim$100 ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted Förster resonances, while non-sharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb(nP3/2)+Rb(nP3/2)→Rb(nS1/2)+Rb([n+1]S1/2){\rm Rb}(nP_{3/2} )+{\rm Rb}(nP_{3/2} )\to {\rm Rb}(nS_{1/2} )+{\rm Rb}([n+1]S_{1/2} )Rb(nP3/2​)+Rb(nP3/2​)→Rb(nS1/2​)+Rb([n+1]S1/2​) for two Rb Rydberg atoms interacting in a time-varying electric field.
Microwave pump-probe experiments starting with a cold gas of Rb 34s34s34s atoms confirm that cusped line shapes observed in dipole-dipole broadened microwave transitions are due to atoms which are widely separated and exhibit small dipole-dipole energy shifts. When the experiments are interpreted in terms of a nearest-neighbor model, they demonstrate that it is possible to select pairs of atoms based on their separation and orientation.
Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.
The observation of the Stark-tuned F\"orster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the F\"orster resonance. In our experiments with a few cold Rb Rydberg atoms, we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the F\"orster resonances, since the population transfer at the resonances occurs on a time scale of $\ensuremath{\sim}100$ ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted F\"orster resonances, while nonsharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the F\"orster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned F\"orster resonances $\mathrm{Rb}(n{P}_{3/2})+\mathrm{Rb}(n{P}_{3/2})\ensuremath{\rightarrow}\mathrm{Rb}(n{S}_{1/2})+\mathrm{Rb}([n+1]{S}_{1/2})$ for two Rb Rydberg atoms interacting in a time-varying electric field.