Physical Review Letters

Resonant Dipole-Dipole Energy Transfer in a Nearly Frozen Rydberg Gas

W. R. Anderson, James Veale, Thomas F. Gallagher

Published Jan 12, 1998• 366 citations

Abstract

In a room temperature vapor of Rb Rydberg atoms, resonant dipole-dipole energy transfer occurs via binary collisions. In contrast, in the $300\ensuremath{\mu}\mathrm{K}$ vapor produced by a magneto-optical trap, the atoms are nearly frozen in place and many atoms interact simultaneously, as in an amorphous solid. As a result of the simultaneous multiple atom interactions, the energy transfer resonances are broadened substantially in frequency.

DOI: 10.1103/physrevlett.80.249

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Dipole-Dipole Interactions in a Frozen Rydberg Gas

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May 1, 19981 citation

Resonant energy transfer Rbns+Rbns+2hν→Rbnp1/2+Rbnp3/2 in a frozen Rydberg gas

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Controlled many-body interactions in a frozen Rydberg gas

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Resonant Dipole-Dipole Energy Transfer Dynamics in a Frozen Rydberg Gas

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Rydberg-wave-packet evolution in a frozen gas of dipole-dipole-coupled atoms

Tao Zhou, Sha Li, R. R. Jones

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Dipole-dipole resonance line shapes in a cold Rydberg gas

Benjamin Richards, R. R. Jones

Physical Review AApr 18, 201615 citations

Physical Review Letters

Resonant Dipole-Dipole Energy Transfer in a Nearly Frozen Rydberg Gas

W. R. Anderson, James Veale, Thomas F. Gallagher

Published Jan 12, 1998• 366 citations

Publisher

Abstract

In a room temperature vapor of Rb Rydberg atoms, resonant dipole-dipole energy transfer occurs via binary collisions. In contrast, in the

300\ensuremath{\mu}\mathrm{K}

vapor produced by a magneto-optical trap, the atoms are nearly frozen in place and many atoms interact simultaneously, as in an amorphous solid. As a result of the simultaneous multiple atom interactions, the energy transfer resonances are broadened substantially in frequency.

DOI: 10.1103/physrevlett.80.249

Related papers

Dipole-Dipole Interactions in a Frozen Rydberg Gas

John R. Lowell

Abstract : We investigate here the characteristics of energy resonant dipole-dipole interactions between Rydberg atoms in Magneto-Optical Trap. These resonant processes occur in a kinetic energy regime in which the atoms may be considered stationary over the time scale of the experiment. Coupled with the long range of the interactions considered, this leads to multi-atom interactions becoming non-negligible. A simple model is outlined to provide insight into the effects of these multi-atom interactions which lead to some interesting behaviors. Experiments which examine the broadening of the dipole-dipole resonances and observe the time dependence of the interaction signal are discussed. Examination of adiabatic character of population transfer caused by slewing across the resonance is discussed in another experiment, as is the scaling behavior of the resonance linewidths and on-resonant signal growth rates. We end by discussing an experiment which takes advantage of some of the characteristics of these interactions to measure the tensor polarizability of Rydberg states of Rb.Abstract : We investigate here the characteristics of energy resonant dipole-dipole interactions between Rydberg atoms in Magneto-Optical Trap. These resonant processes occur in a kinetic energy regime in which the atoms may be considered stationary over the time scale of the experiment. Coupled with the long range of the interactions considered, this leads to multi-atom interactions becoming non-negligible. A simple model is outlined to provide insight into the effects of these multi-atom interactions which lead to some interesting behaviors. Experiments which examine the broadening of the dipole-dipole resonances and observe the time dependence of the interaction signal are discussed. Examination of adiabatic character of population transfer caused by slewing across the resonance is discussed in another experiment, as is the scaling behavior of the resonance linewidths and on-resonant signal growth rates. We end by discussing an experiment which takes advantage of some of the characteristics of these interactions to measure the tensor polarizability of Rydberg states of Rb.

May 1, 19981 citation

Resonant energy transfer Rbns+Rbns+2hν→Rbnp1/2+Rbnp3/2 in a frozen Rydberg gas

Jirakan Nunkaew, Raheel Ali, Thomas F. Gallagher

We have observed the process $\mathrm{Rb}ns+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}ns+2h\ensuremath{\nu}\ensuremath{\rightarrow}\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{1/2}+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{3/2}$ from $n=34$ to $n=40$ in a frozen gas of Rb Rydberg atoms. It is resonant when the microwave frequency is halfway between the $ns\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}n{p}_{1/2}$ and $ns\ensuremath{\rightarrow}n{p}_{3/2}$ frequencies, which range from 57 to 106 GHz. The process cannot occur in isolated atoms, nor can it occur if the magnetic quantum numbers are unchanged, an implicit assumption of one-dimensional models. A Floquet-Forster model shows that the coupling between the initial and final states involves the absorption of two microwave photons and the dipole-dipole interaction, which leads to a coupling proportional to the product of the density, the microwave field squared, and ${n}^{*14}$ , where ${n}^{*}$ is the effective quantum number of the $n{p}_{3/2}$ state. We have experimentally verified these dependences. The observed resonances are asymmetric, with a low-frequency tail, which we attribute to the van der Waals shift of the final $n{p}_{1/2}n{p}_{3/2}$ state due to its dipole-dipole interaction with the nearby $ns(n+1)s$ state. While the van der Waals shift is negligible for most of the atoms in the Rydberg gas, it is not for the pairs of close atoms which undergo this transition.We have observed the process $\mathrm{Rb}ns+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}ns+2h\ensuremath{\nu}\ensuremath{\rightarrow}\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{1/2}+\mathrm{Rb}\phantom{\rule{4pt}{0ex}}n{p}_{3/2}$ from $n=34$ to $n=40$ in a frozen gas of Rb Rydberg atoms. It is resonant when the microwave frequency is halfway between the $ns\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}n{p}_{1/2}$ and $ns\ensuremath{\rightarrow}n{p}_{3/2}$ frequencies, which range from 57 to 106 GHz. The process cannot occur in isolated atoms, nor can it occur if the magnetic quantum numbers are unchanged, an implicit assumption of one-dimensional models. A Floquet-Forster model shows that the coupling between the initial and final states involves the absorption of two microwave photons and the dipole-dipole interaction, which leads to a coupling proportional to the product of the density, the microwave field squared, and ${n}^{*14}$, where ${n}^{*}$ is the effective quantum number of the $n{p}_{3/2}$ state. We have experimentally verified these dependences. The observed resonances are asymmetric, with a low-frequency tail, which we attribute to the van der Waals shift of the final $n{p}_{1/2}n{p}_{3/2}$ state due to its dipole-dipole interaction with the nearby $ns(n+1)s$ state. While the van der Waals shift is negligible for most of the atoms in the Rydberg gas, it is not for the pairs of close atoms which undergo this transition.

Physical Review AAug 28, 20200 citations

Controlled many-body interactions in a frozen Rydberg gas

I. Mourachko, Wenhui Li, Thomas F. Gallagher

Previous resonant dipole-dipole energy-transfer experiments of cold Rydberg gases [Anderson et al., Phys. Rev. Lett. 80, 249 (1998); Mourachko et al., Phys. Rev. Lett. 80, 253 (1998)] have been interpreted as providing evidence of many-body, as opposed to purely binary, effects. Here we separate two-body and many-body interactions by introducing an additional Rydberg state, which does not participate directly in the energy-transfer process, but is strongly coupled to one of the final states. We observe broadening of the energy-transfer resonances due to this added Rydberg state, which clearly demonstrates the many-body nature of the dipole-dipole interactions in such a system.Previous resonant dipole-dipole energy-transfer experiments of cold Rydberg gases [Anderson et al., Phys. Rev. Lett. 80, 249 (1998); Mourachko et al., Phys. Rev. Lett. 80, 253 (1998)] have been interpreted as providing evidence of many-body, as opposed to purely binary, effects. Here we separate two-body and many-body interactions by introducing an additional Rydberg state, which does not participate directly in the energy-transfer process, but is strongly coupled to one of the final states. We observe broadening of the energy-transfer resonances due to this added Rydberg state, which clearly demonstrates the many-body nature of the dipole-dipole interactions in such a system.

Physical Review ASep 13, 200454 citations

Resonant Dipole-Dipole Energy Transfer Dynamics in a Frozen Rydberg Gas

Donald P. Fahey

The dipole-dipole interaction strongly couples ultracold highly excited atoms, known as Rydberg atoms, and is the dominant mechanism for energy exchange among such atoms on microsecond time scales. I present the results of experiments that investigate this interaction using rubidium atoms excited to Rydberg states with an all-diode laser system. In the first of these, high resolution dipole-dipole interaction spectra for different magnetic sublevels of the 32d5/2 state are collected and analyzed. In the second experiment, ultracold rubidium atoms are implusively excited to coherent superpositions of three closely spaced |mj|sublevels of the 32d5/2 state in a weak electric field. The magnitude of the field sets the energy level spacing between these states, and hence the frequency of the phase dependent oscillations resulting from interference in resonant energy exchange processes. In the third experiment, the dipole-dipole interaction induced resonant energy exchange between columns of ultracold rubidium Rydberg atoms is imaged using a new technique involving selective field ionization with a spatially sensitive ion detector.The dipole-dipole interaction strongly couples ultracold highly excited atoms, known as Rydberg atoms, and is the dominant mechanism for energy exchange among such atoms on microsecond time scales. I present the results of experiments that investigate this interaction using rubidium atoms excited to Rydberg states with an all-diode laser system. In the first of these, high resolution dipole-dipole interaction spectra for different magnetic sublevels of the 32d5/2 state are collected and analyzed. In the second experiment, ultracold rubidium atoms are implusively excited to coherent superpositions of three closely spaced |mj|sublevels of the 32d5/2 state in a weak electric field. The magnitude of the field sets the energy level spacing between these states, and hence the frequency of the phase dependent oscillations resulting from interference in resonant energy exchange processes. In the third experiment, the dipole-dipole interaction induced resonant energy exchange between columns of ultracold rubidium Rydberg atoms is imaged using a new technique involving selective field ionization with a spatially sensitive ion detector.

Jan 1, 20140 citations

Rydberg-wave-packet evolution in a frozen gas of dipole-dipole-coupled atoms

Tao Zhou, Sha Li, R. R. Jones

We have studied the evolution of Rydberg wave packets in the presence of interatomic dipole-dipole interactions in a frozen Rb gas. Rb atoms in a magneto-optical trap (MOT) are first laser excited to $ns$ Rydberg eigenstates. A picosecond THz pulse further excites them into coherent superposition states involving the initial-level and neighboring $np$ states. A second, identical, time-delayed THz pulse probes the wave-packet dynamics. As the wave packets evolve they are influenced by dipole-dipole interactions, predominantly pairwise excitation-exchange processes of the form $|s\ensuremath{\rangle}|p\ensuremath{\rangle}\ensuremath{\leftrightarrow}|p\ensuremath{\rangle}|s\ensuremath{\rangle}$. The coherent electronic evolution of the ensemble dephases due to the variation in dipole-dipole coupling strength between atom pairs in the MOT. The experimental results are in good agreement with numerical calculations that simulate the interactions between nearest neighbors in a frozen gas.We have studied the evolution of Rydberg wave packets in the presence of interatomic dipole-dipole interactions in a frozen Rb gas. Rb atoms in a magneto-optical trap (MOT) are first laser excited to $ns$ Rydberg eigenstates. A picosecond THz pulse further excites them into coherent superposition states involving the initial-level and neighboring $np$ states. A second, identical, time-delayed THz pulse probes the wave-packet dynamics. As the wave packets evolve they are influenced by dipole-dipole interactions, predominantly pairwise excitation-exchange processes of the form $|s\ensuremath{\rangle}|p\ensuremath{\rangle}\ensuremath{\leftrightarrow}|p\ensuremath{\rangle}|s\ensuremath{\rangle}$. The coherent electronic evolution of the ensemble dephases due to the variation in dipole-dipole coupling strength between atom pairs in the MOT. The experimental results are in good agreement with numerical calculations that simulate the interactions between nearest neighbors in a frozen gas.

Physical Review AJun 16, 20147 citations

Dipole-dipole resonance line shapes in a cold Rydberg gas

Benjamin Richards, R. R. Jones

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.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 AApr 18, 201615 citations

In a room temperature vapor of Rb Rydberg atoms, resonant dipole-dipole energy transfer occurs via binary collisions. In contrast, in the

300\ensuremath{\mu}\mathrm{K}

n=34

n=40

in a frozen gas of Rb Rydberg atoms. It is resonant when the microwave frequency is halfway between the $ns\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}n{p}_{1/2}$ and $ns\ensuremath{\rightarrow}n{p}_{3/2}$ frequencies, which range from 57 to 106 GHz. The process cannot occur in isolated atoms, nor can it occur if the magnetic quantum numbers are unchanged, an implicit assumption of one-dimensional models. A Floquet-Forster model shows that the coupling between the initial and final states involves the absorption of two microwave photons and the dipole-dipole interaction, which leads to a coupling proportional to the product of the density, the microwave field squared, and

{n}^{*14}

, where

{n}^{*}

is the effective quantum number of the

n{p}_{3/2}

state. We have experimentally verified these dependences. The observed resonances are asymmetric, with a low-frequency tail, which we attribute to the van der Waals shift of the final

n{p}_{1/2}n{p}_{3/2}

state due to its dipole-dipole interaction with the nearby

ns(n+1)s

state. While the van der Waals shift is negligible for most of the atoms in the Rydberg gas, it is not for the pairs of close atoms which undergo this transition.

We have studied the evolution of Rydberg wave packets in the presence of interatomic dipole-dipole interactions in a frozen Rb gas. Rb atoms in a magneto-optical trap (MOT) are first laser excited to

ns

Rydberg eigenstates. A picosecond THz pulse further excites them into coherent superposition states involving the initial-level and neighboring

np

states. A second, identical, time-delayed THz pulse probes the wave-packet dynamics. As the wave packets evolve they are influenced by dipole-dipole interactions, predominantly pairwise excitation-exchange processes of the form $|s\ensuremath{\rangle}|p\ensuremath{\rangle}\ensuremath{\leftrightarrow}|p\ensuremath{\rangle}|s\ensuremath{\rangle}$. The coherent electronic evolution of the ensemble dephases due to the variation in dipole-dipole coupling strength between atom pairs in the MOT. The experimental results are in good agreement with numerical calculations that simulate the interactions between nearest neighbors in a frozen gas.

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.