Physical Review A

Two-body Förster resonance involving Rb nD states in a quasi-electrostatic trap

Jorge Douglas Massayuki Kondo, Luís F. Gonçalves, Jader Cabral, Jonathan Tallant, Luís Gustavo Marcassa

Published Aug 18, 2014• 11 citations

Abstract

In this work, we excite $n{D}_{5/2}$ Rydberg states in a dense and cold Rb atomic sample held in a 10.6 $\ensuremath{\mu}\mathrm{m}$ quasi-electrostatic trap using narrow-bandwidth laser pulses. Our goal is to study the F\"orster resonance process $n{D}_{5/2}+n{D}_{5/2}\ensuremath{\rightarrow}(n\ensuremath{-}2)F+(n+2){P}_{3/2}$ at zero electric field as a function of the total atomic density using pulsed-field ionization in the range $n=37--47$. Such a process is almost degenerate for $n=43$. Younge and coworkers studied this process [K. C. Younge, A. Reinhard, T. Pohl, P. R. Berman, and G. Raithel, Phys. Rev. A 79, 043420 (2009)] and attributed the observed saturation to many-body effects. Our results show that as the ground-state atomic density increases, the $n{D}_{5/2}$ state population and the population transfer starts to saturate, which is consistent with the onset of Rydberg atom blockade and previously published results. However, since our experiment allows the independent measurement of the $n{D}_{5/2}$ and $(n+2){P}_{3/2}$ state populations, we were able to obtain the $(n+2){P}_{3/2}$ state population density dependence. Our results clearly show that the $(n+2){P}_{3/2}$ state population depends quadratically on the total Rydberg atomic population, and consequently, the F\"orster resonance is a two-body process for a ground-state atomic density below $3\ifmmode\times\else\texttimes\fi{}{10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}3}$.

DOI: 10.1103/physreva.90.023413

Related papers

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

Jorge Douglas Massayuki Kondo, Donald W. Booth, Luís F. Gonçalves +2 more

Physical Review AJan 8, 201612 citations

Mesoscopic Rydberg ensembles: Beyond the pairwise-interaction approximation

Kelly Cooper Younge, Aaron Reinhard, Thomas Pohl +2 more

Physical Review AApr 27, 200965 citations

Effect of Förster resonances on the excitation statistics of many-body Rydberg systems

Aaron Reinhard, Kelly Cooper Younge, Georg A. Raithel

Physical Review ADec 18, 200834 citations

Investigation of three-body Förster resonance for various spatial configurations of the three interacting Rubidium Rydberg atoms

I. I. Ryabtsev, I. N. Ashkarin, Ilya I. Beterov +4 more

arXiv:2506.22259Jun 27, 20251 citation

Absence of collective decay in a cold Rydberg gas

Tao Zhou, Benjamin Richards, R. R. Jones

Physical Review AMar 8, 201613 citations

Splitting of the three-body Förster resonance in Rb Rydberg atoms as a measure of the dipole-dipole interaction strength

I. I. Ryabtsev, I. N. Ashkarin, Ilya I. Beterov +4 more

arXiv:2507.13658Physical Review ANov 15, 20253 citations

Physical Review A

Two-body Förster resonance involving Rb nD states in a quasi-electrostatic trap

Jorge Douglas Massayuki Kondo, Luís F. Gonçalves, Jader Cabral, Jonathan Tallant, Luís Gustavo Marcassa

Published Aug 18, 2014• 11 citations

Publisher

Abstract

In this work, we excite

n{D}_{5/2}

Rydberg states in a dense and cold Rb atomic sample held in a 10.6

\ensuremath{\mu}\mathrm{m}

quasi-electrostatic trap using narrow-bandwidth laser pulses. Our goal is to study the F"orster resonance process

n{D}_{5/2}+n{D}_{5/2}\ensuremath{\rightarrow}(n\ensuremath{-}2)F+(n+2){P}_{3/2}

at zero electric field as a function of the total atomic density using pulsed-field ionization in the range

n=37--47

. Such a process is almost degenerate for

n=43

. Younge and coworkers studied this process [K. C. Younge, A. Reinhard, T. Pohl, P. R. Berman, and G. Raithel, Phys. Rev. A 79, 043420 (2009)] and attributed the observed saturation to many-body effects. Our results show that as the ground-state atomic density increases, the

n{D}_{5/2}

state population and the population transfer starts to saturate, which is consistent with the onset of Rydberg atom blockade and previously published results. However, since our experiment allows the independent measurement of the

n{D}_{5/2}

and

(n+2){P}_{3/2}

state populations, we were able to obtain the

(n+2){P}_{3/2}

state population density dependence. Our results clearly show that the

(n+2){P}_{3/2}

state population depends quadratically on the total Rydberg atomic population, and consequently, the F"orster resonance is a two-body process for a ground-state atomic density below

3\ifmmode\times\else\texttimes\fi{}{10}^{11}

{\mathrm{cm}}^{\ensuremath{-}3}

DOI: 10.1103/physreva.90.023413

Related papers

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

Jorge Douglas Massayuki Kondo, Donald W. Booth, Luís F. Gonçalves +2 more

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 $3.0\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.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 $3.0\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.

Physical Review AJan 8, 201612 citations

Mesoscopic Rydberg ensembles: Beyond the pairwise-interaction approximation

Kelly Cooper Younge, Aaron Reinhard, Thomas Pohl +2 more

We examine state mixing in a dense, cold Rydberg gas. Cold Rb atom clouds in an optical dipole trap are excited into $n{D}_{5/2}$ Rydberg levels using narrow-bandwidth laser pulses. For $n=43$ , two atoms excited to $43{D}_{5/2}$ states can be converted to $41{F}_{7/2}$ and $45{P}_{3/2}$ product states via a F\"orster resonance. We find, unexpectedly, that up to 50% of the Rydberg atoms are detected in such product states after only 100 ns of interaction time. The experiment is modeled using many-body quantum simulations. To reproduce the mixing fractions measured near F\"orster resonances, we use an exact, nonperturbative many-atom Hamiltonian in which product states are treated on an equal basis with the laser-excited $n{D}_{5/2}$ Rydberg level. Simplified many-body interaction models based on sums over pairwise atomic potentials cannot reproduce the measured mixing fractions.We examine state mixing in a dense, cold Rydberg gas. Cold Rb atom clouds in an optical dipole trap are excited into $n{D}_{5/2}$ Rydberg levels using narrow-bandwidth laser pulses. For $n=43$, two atoms excited to $43{D}_{5/2}$ states can be converted to $41{F}_{7/2}$ and $45{P}_{3/2}$ product states via a F\"orster resonance. We find, unexpectedly, that up to 50% of the Rydberg atoms are detected in such product states after only 100 ns of interaction time. The experiment is modeled using many-body quantum simulations. To reproduce the mixing fractions measured near F\"orster resonances, we use an exact, nonperturbative many-atom Hamiltonian in which product states are treated on an equal basis with the laser-excited $n{D}_{5/2}$ Rydberg level. Simplified many-body interaction models based on sums over pairwise atomic potentials cannot reproduce the measured mixing fractions.

Physical Review AApr 27, 200965 citations

Effect of Förster resonances on the excitation statistics of many-body Rydberg systems

Aaron Reinhard, Kelly Cooper Younge, Georg A. Raithel

We provide evidence for the dipole blockade of Rydberg excitation by examining the distributions of the number of Rydberg excitations created in ensembles of interacting Rydberg atoms. We show that, over a range of densities, the Rydberg excitation number distributions become significantly narrower when an applied electric field is used to tune the $^{85}\mathrm{Rb}$ interaction channel $45{D}_{5∕2}+45{D}_{5∕2}\ensuremath{\rightarrow}43F+47{P}_{3∕2}$ into F\"orster resonance. Substantially sub-Poissonian distributions that agree with published theory were achieved using very dense atom samples tuned into F\"orster resonance.We provide evidence for the dipole blockade of Rydberg excitation by examining the distributions of the number of Rydberg excitations created in ensembles of interacting Rydberg atoms. We show that, over a range of densities, the Rydberg excitation number distributions become significantly narrower when an applied electric field is used to tune the $^{85}\mathrm{Rb}$ interaction channel $45{D}_{5∕2}+45{D}_{5∕2}\ensuremath{\rightarrow}43F+47{P}_{3∕2}$ into F\"orster resonance. Substantially sub-Poissonian distributions that agree with published theory were achieved using very dense atom samples tuned into F\"orster resonance.

Physical Review ADec 18, 200834 citations

Investigation of three-body Förster resonance for various spatial configurations of the three interacting Rubidium Rydberg atoms

I. I. Ryabtsev, I. N. Ashkarin, Ilya I. Beterov +4 more

Three-body Förster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms captured in optical traps and laser-excited into strongly interacting Rydberg states. In Ref. [P. Cheinet et al., Quantum Electronics 50(3), 213 (2020)], we proposed and analyzed a new type of three-body Förster resonance ${\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2}$ that can be realized with Rb Rydberg atoms for an arbitrary principal quantum number $n$ . Its peculiarity is that the third atom goes into a state with a total angular moment $J=1/2$ , which has no Stark structure, so two-body Förster resonances are completely absent. In the present work, an extended theoretical study of this three-body Förster resonance is performed for various spatial configurations of three interacting Rb Rydberg atoms and conditions for their experimental implementation are determined. It was found that one of the resonances has a weak dependence of the resonant electric field on the distance between atoms and is therefore most suitable for performing experiments to observe coherent oscillations of populations of collective three-body states and implement three-qubit quantum gates based on them.Three-body Förster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms captured in optical traps and laser-excited into strongly interacting Rydberg states. In Ref. [P. Cheinet et al., Quantum Electronics 50(3), 213 (2020)], we proposed and analyzed a new type of three-body Förster resonance ${\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2}$ that can be realized with Rb Rydberg atoms for an arbitrary principal quantum number $n$. Its peculiarity is that the third atom goes into a state with a total angular moment $J=1/2$, which has no Stark structure, so two-body Förster resonances are completely absent. In the present work, an extended theoretical study of this three-body Förster resonance is performed for various spatial configurations of three interacting Rb Rydberg atoms and conditions for their experimental implementation are determined. It was found that one of the resonances has a weak dependence of the resonant electric field on the distance between atoms and is therefore most suitable for performing experiments to observe coherent oscillations of populations of collective three-body states and implement three-qubit quantum gates based on them.

arXiv:2506.22259Jun 27, 20251 citation

Absence of collective decay in a cold Rydberg gas

Tao Zhou, Benjamin Richards, R. R. Jones

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.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.

Physical Review AMar 8, 201613 citations

Splitting of the three-body Förster resonance in Rb Rydberg atoms as a measure of the dipole-dipole interaction strength

I. I. Ryabtsev, I. N. Ashkarin, Ilya I. Beterov +4 more

Three-body F\"orster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms in optical traps using their laser excitation into strongly interacting Rydberg states. In our recent theoretical paper [Zh. Eksp. Teor. Fiz. 168, 14 (2025)], it was found that the proposed earlier three-body F\"orster resonance $3\ifmmode\times\else\texttimes\fi{}n{P}_{3/2}\ensuremath{\rightarrow}n{S}_{1/2}+(n+1){S}_{1/2}+n{P}_{1/2}$ in Rb Rydberg atoms presents a splitting, with one of the split components having weaker dependence of the resonant electric field (and the corresponding dynamic shift) on the distance $R$ between the atoms. Here we study this effect in more detail, since this resonance appears as the most suitable for performing experiments on observing coherent oscillations of populations of collective three-body states and implementing three-qubit quantum gates based on them. For a linear spatial configuration of three interacting Rydberg atoms, the physical mechanism of this phenomenon is revealed and analytical formulas are obtained that describe the behavior of split structure of the F\"orster resonance depending on $R$ . It is found that the splitting is a measure of the energy of the resonant dipole-dipole exchange interaction with an excitation hopping between neighboring Rydberg states $S$ and $P$ .Three-body F\"orster resonances controlled by a dc electric field are of interest for the implementation of three-qubit quantum gates with single atoms in optical traps using their laser excitation into strongly interacting Rydberg states. In our recent theoretical paper [Zh. Eksp. Teor. Fiz. 168, 14 (2025)], it was found that the proposed earlier three-body F\"orster resonance $3\ifmmode\times\else\texttimes\fi{}n{P}_{3/2}\ensuremath{\rightarrow}n{S}_{1/2}+(n+1){S}_{1/2}+n{P}_{1/2}$ in Rb Rydberg atoms presents a splitting, with one of the split components having weaker dependence of the resonant electric field (and the corresponding dynamic shift) on the distance $R$ between the atoms. Here we study this effect in more detail, since this resonance appears as the most suitable for performing experiments on observing coherent oscillations of populations of collective three-body states and implementing three-qubit quantum gates based on them. For a linear spatial configuration of three interacting Rydberg atoms, the physical mechanism of this phenomenon is revealed and analytical formulas are obtained that describe the behavior of split structure of the F\"orster resonance depending on $R$. It is found that the splitting is a measure of the energy of the resonant dipole-dipole exchange interaction with an excitation hopping between neighboring Rydberg states $S$ and $P$.

arXiv:2507.13658Physical Review ANov 15, 20253 citations

In this work, we excite

n{D}_{5/2}

Rydberg states in a dense and cold Rb atomic sample held in a 10.6

\ensuremath{\mu}\mathrm{m}

quasi-electrostatic trap using narrow-bandwidth laser pulses. Our goal is to study the F"orster resonance process

n{D}_{5/2}+n{D}_{5/2}\ensuremath{\rightarrow}(n\ensuremath{-}2)F+(n+2){P}_{3/2}

at zero electric field as a function of the total atomic density using pulsed-field ionization in the range

n=37--47

. Such a process is almost degenerate for

n=43

n{D}_{5/2}

n{D}_{5/2}

and

(n+2){P}_{3/2}

state populations, we were able to obtain the

(n+2){P}_{3/2}

state population density dependence. Our results clearly show that the

(n+2){P}_{3/2}

state population depends quadratically on the total Rydberg atomic population, and consequently, the F"orster resonance is a two-body process for a ground-state atomic density below

3\ifmmode\times\else\texttimes\fi{}{10}^{11}

{\mathrm{cm}}^{\ensuremath{-}3}

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 $3.0\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.

We examine state mixing in a dense, cold Rydberg gas. Cold Rb atom clouds in an optical dipole trap are excited into

n{D}_{5/2}

Rydberg levels using narrow-bandwidth laser pulses. For

n=43

, two atoms excited to

43{D}_{5/2}

states can be converted to

41{F}_{7/2}

and

45{P}_{3/2}

product states via a F\"orster resonance. We find, unexpectedly, that up to 50% of the Rydberg atoms are detected in such product states after only 100 ns of interaction time. The experiment is modeled using many-body quantum simulations. To reproduce the mixing fractions measured near F\"orster resonances, we use an exact, nonperturbative many-atom Hamiltonian in which product states are treated on an equal basis with the laser-excited

n{D}_{5/2}

Rydberg level. Simplified many-body interaction models based on sums over pairwise atomic potentials cannot reproduce the measured mixing fractions.

^{85}\mathrm{Rb}

interaction channel $45{D}_{5∕2}+45{D}_{5∕2}\ensuremath{\rightarrow}43F+47{P}_{3∕2}$ into F\"orster resonance. Substantially sub-Poissonian distributions that agree with published theory were achieved using very dense atom samples tuned into F\"orster resonance.

{\rm 3}\times nP_{3/2} \to nS_{1/2} +(n+1)S_{1/2} +nP_{1/2}

that can be realized with Rb Rydberg atoms for an arbitrary principal quantum number

n

. Its peculiarity is that the third atom goes into a state with a total angular moment

J=1/2

, which has no Stark structure, so two-body Förster resonances are completely absent. In the present work, an extended theoretical study of this three-body Förster resonance is performed for various spatial configurations of three interacting Rb Rydberg atoms and conditions for their experimental implementation are determined. It was found that one of the resonances has a weak dependence of the resonant electric field on the distance between atoms and is therefore most suitable for performing experiments to observe coherent oscillations of populations of collective three-body states and implement three-qubit quantum gates based on them.

ns

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.

R

between the atoms. Here we study this effect in more detail, since this resonance appears as the most suitable for performing experiments on observing coherent oscillations of populations of collective three-body states and implementing three-qubit quantum gates based on them. For a linear spatial configuration of three interacting Rydberg atoms, the physical mechanism of this phenomenon is revealed and analytical formulas are obtained that describe the behavior of split structure of the F\"orster resonance depending on

R

. It is found that the splitting is a measure of the energy of the resonant dipole-dipole exchange interaction with an excitation hopping between neighboring Rydberg states

S

and

P