Physical Review A

Microwave transitions of pairs of cold Rb Rydberg atoms as Forster resonances of Floquet states

Jeonghun Lee, Javed Iqbal, Thomas F. Gallagher

Published Jul 10, 2017• 3 citations

Abstract

Previous measurements of single photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2)f$ transitions by two of us were described as microwave transitions made possible by configuration interaction (CI) between the $n{d}_{5/2}n{d}_{5/2}$ and the nearly degenerate $(n+2){p}_{3/2}(n\ensuremath{-}2)f$ states [Lee and Gallagher, Phys. Rev. A 93, 062509 (2016)]. Here we report the observation of the one photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){s}_{1/2}(n\ensuremath{-}2)f$, two photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){p}_{j}(n\ensuremath{-}2)f$, and three photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+4){s}_{1/2}(n\ensuremath{-}2)f$ microwave transitions. We show that both single and multiphoton microwave transitions are conveniently described as Forster resonant energy transfers between resonant Floquet states, and we show that the Floquet-Forster model reduces to the CI model used previously. Finally, to show that the transitions observed previously are by no means unique, we report pair transitions with different initial and final states as well as radio instead of microwave frequencies.

DOI: 10.1103/physreva.96.012507

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Physical Review A

Microwave transitions of pairs of cold Rb Rydberg atoms as Forster resonances of Floquet states

Jeonghun Lee, Javed Iqbal, Thomas F. Gallagher

Published Jul 10, 2017• 3 citations

Publisher

Abstract

Previous measurements of single photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2)f

transitions by two of us were described as microwave transitions made possible by configuration interaction (CI) between the

n{d}_{5/2}n{d}_{5/2}

and the nearly degenerate

(n+2){p}_{3/2}(n\ensuremath{-}2)f

states [Lee and Gallagher, Phys. Rev. A 93, 062509 (2016)]. Here we report the observation of the one photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){s}_{1/2}(n\ensuremath{-}2)f

, two photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){p}_{j}(n\ensuremath{-}2)f

, and three photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+4){s}_{1/2}(n\ensuremath{-}2)f

microwave transitions. We show that both single and multiphoton microwave transitions are conveniently described as Forster resonant energy transfers between resonant Floquet states, and we show that the Floquet-Forster model reduces to the CI model used previously. Finally, to show that the transitions observed previously are by no means unique, we report pair transitions with different initial and final states as well as radio instead of microwave frequencies.

DOI: 10.1103/physreva.96.012507

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Microwave Transitions of Cold Rydberg Atom Pairs

Jeonghun Lee

This dissertation consists of three microwave spectroscopy experiments performed with cold Rb Rydberg atoms in Magneto Optical Trap.The first experiment is a systematic study of a particular type of transition which was first observed in 2012 that involves a pair of Rydberg atoms.In this transition, even though only one microwave photon is absorbed, both atoms in the pair change states.In particular, we describe the transition with the configuration interaction (CI) model and experimentally verify the scaling of fractional population transfer predicted by the CI model.The second experiment builds on the first experiment and reports observations of additional single and multi photon microwave transitions that are allowed due to the same CI as in the first experiment.The observations show clearly that this type of transition involving a pair of Rydberg atoms are a lot more common than initially thought.We show that the transitions can be conveniently described as Forster resonances of Floquet states.The last experiment reports on the technique we used to measure the ng and nh series quantum defects and the ionic dipole and quadrupole polarizabilities of 85 Rb.The technique allows us to obtain zero field intervals of (n + 1)d 5/2 → ng and (n + 1)d 5/2 → nh intervals despite the fact that we can only control the stray electric field in one direction.Using the technique, the quantum defects of ng and nh were determined to be 0.0039741(16) and 0.0014066(57), respectively.The ionic II dipole and quadrupole polarizabilities were determined to be 9.12(2)a 3 0 and 14(3)a 5 0 , respectively.This dissertation consists of three microwave spectroscopy experiments performed with cold Rb Rydberg atoms in Magneto Optical Trap.The first experiment is a systematic study of a particular type of transition which was first observed in 2012 that involves a pair of Rydberg atoms.In this transition, even though only one microwave photon is absorbed, both atoms in the pair change states.In particular, we describe the transition with the configuration interaction (CI) model and experimentally verify the scaling of fractional population transfer predicted by the CI model.The second experiment builds on the first experiment and reports observations of additional single and multi photon microwave transitions that are allowed due to the same CI as in the first experiment.The observations show clearly that this type of transition involving a pair of Rydberg atoms are a lot more common than initially thought.We show that the transitions can be conveniently described as Forster resonances of Floquet states.The last experiment reports on the technique we used to measure the ng and nh series quantum defects and the ionic dipole and quadrupole polarizabilities of 85 Rb.The technique allows us to obtain zero field intervals of (n + 1)d 5/2 → ng and (n + 1)d 5/2 → nh intervals despite the fact that we can only control the stray electric field in one direction.Using the technique, the quantum defects of ng and nh were determined to be 0.0039741(16) and 0.0014066(57), respectively.The ionic II dipole and quadrupole polarizabilities were determined to be 9.12(2)a 3 0 and 14(3)a 5 0 , respectively.

Jul 13, 20170 citations

Excitonlike exchange in two-photon transitions of pairs of cold Rb Rydberg atoms

Jeonghun Lee, Phatthamon Kongkhambut, Thomas F. Gallagher

We have observed an excitonlike exchange in two-photon microwave transitions between pairs of cold Rb Rydberg atoms, specifically, transitions in which a $n{s}_{1/2}n{s}_{1/2}$ pair undergoes the transition to the $n{p}_{1/2}n{p}_{3/2}$ and $n{p}_{3/2}n{p}_{1/2}$ states. This transition occurs due to the excitonlike $n{s}_{1/2}n{p}_{j}\ensuremath{\leftrightarrow}n{p}_{j}n{s}_{1/2}$ exchange in the intermediate states, and the process can be thought of as a F\"orster resonant energy transfer between Floquet, or dressed, states. In addition, the measurements provide clear evidence of the importance of the three-dimensional nature of the dipole-dipole interaction.We have observed an excitonlike exchange in two-photon microwave transitions between pairs of cold Rb Rydberg atoms, specifically, transitions in which a $n{s}_{1/2}n{s}_{1/2}$ pair undergoes the transition to the $n{p}_{1/2}n{p}_{3/2}$ and $n{p}_{3/2}n{p}_{1/2}$ states. This transition occurs due to the excitonlike $n{s}_{1/2}n{p}_{j}\ensuremath{\leftrightarrow}n{p}_{j}n{s}_{1/2}$ exchange in the intermediate states, and the process can be thought of as a F\"orster resonant energy transfer between Floquet, or dressed, states. In addition, the measurements provide clear evidence of the importance of the three-dimensional nature of the dipole-dipole interaction.

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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.

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Microwave spectroscopy assisted by electromagnetically induced transparency near natural Förster resonance on Rubidium

Naomy Duarte Gomes, Daniel Varela Magalhães, Jorge Douglas Massayuki Kondo +1 more

In this work, we precisely measure the transition energies between the Rydberg state n $\text{D}_{5/2}$ to the nearby Rydberg states $(\e{n}+2)\text{P}_{3/2}$, $(\e{n}-2)\text{F}_{7/2}$ for the range $41\leq \e{n}\leq46$. This was done by carrying out microwave spectroscopy via Electromagnetically Induced Transparency (EIT) in a room temperature vapor reference cell of Rubidium, which is similar to the experimental approach followed by Li et al. [Results in Physics \textbf{29}, 104728 (2021)]. This range is interesting because there is a quasi Förster resonance between the atomic pair $43\text{D}_{5/2}+43\text{D}_{5/2}$ and $45\text{P}_{3/2}+41\text{F}_{7/2}$ . We compared the obtained results with numerically calculated transition energies based on previously tabulated quantum defect numbers by various research groups using both hot and ultra-cold atomic samples. Our data are more consistent with measurements made within ultra-cold atomic systems [Phys. Rev. A \textbf{67}, 052502 (2003), Phys. Rev. A \textbf{74}, 054502 (2006)].In this work, we precisely measure the transition energies between the Rydberg state n$\text{D}_{5/2}$ to the nearby Rydberg states $(\e{n}+2)\text{P}_{3/2}$, $(\e{n}-2)\text{F}_{7/2}$ for the range $41\leq \e{n}\leq46$. This was done by carrying out microwave spectroscopy via Electromagnetically Induced Transparency (EIT) in a room temperature vapor reference cell of Rubidium, which is similar to the experimental approach followed by Li et al. [Results in Physics \textbf{29}, 104728 (2021)]. This range is interesting because there is a quasi Förster resonance between the atomic pair $43\text{D}_{5/2}+43\text{D}_{5/2}$ and $45\text{P}_{3/2}+41\text{F}_{7/2}$. We compared the obtained results with numerically calculated transition energies based on previously tabulated quantum defect numbers by various research groups using both hot and ultra-cold atomic samples. Our data are more consistent with measurements made within ultra-cold atomic systems [Phys. Rev. A \textbf{67}, 052502 (2003), Phys. Rev. A \textbf{74}, 054502 (2006)].

arXiv:2406.17735Jun 25, 20240 citations

Microwave spectroscopy assisted by electromagnetically induced transparency near natural Förster resonance on Rubidium

Naomy Duarte Gomes, Daniel Varela Magalhães, Jorge Douglas Massayuki Kondo +1 more

In this work, we precisely measure the transition energies between the Rydberg state n D 5 / 2 to the nearby Rydberg states ( n + 2 ) P 3 / 2 , ( n − 2 ) F 7 / 2 in 85 Rb for the range 41 ≤ n ≤ 46 . This was done by carrying out microwave spectroscopy via electromagnetically induced transparency (EIT) in a room temperature vapor reference cell of rubidium, which is similar to the experimental approach followed by Li et al., (2021). This range is interesting because there is a quasi Förster resonance between the atomic pair 43 D 5 / 2 + 43 D 5 / 2 and 45 P 3 / 2 + 41 F 7 / 2 . We compared the obtained results with numerically calculated transition energies based on previously tabulated quantum defect numbers by various research groups using both hot and ultra-cold atomic samples. Our data are more consistent with measurements made within ultra-cold atomic systems (Li et al., 2003; Han et al., 2006). • Precision Metrology. • Quantum Atomic Sensor. • Quantum Information Processing. • Quantum Computation. • Quantum Technologies.In this work, we precisely measure the transition energies between the Rydberg state n D 5 / 2 to the nearby Rydberg states ( n + 2 ) P 3 / 2 , ( n − 2 ) F 7 / 2 in 85 Rb for the range 41 ≤ n ≤ 46 . This was done by carrying out microwave spectroscopy via electromagnetically induced transparency (EIT) in a room temperature vapor reference cell of rubidium, which is similar to the experimental approach followed by Li et al., (2021). This range is interesting because there is a quasi Förster resonance between the atomic pair 43 D 5 / 2 + 43 D 5 / 2 and 45 P 3 / 2 + 41 F 7 / 2 . We compared the obtained results with numerically calculated transition energies based on previously tabulated quantum defect numbers by various research groups using both hot and ultra-cold atomic samples. Our data are more consistent with measurements made within ultra-cold atomic systems (Li et al., 2003; Han et al., 2006). • Precision Metrology. • Quantum Atomic Sensor. • Quantum Information Processing. • Quantum Computation. • Quantum Technologies.

Results in PhysicsDec 17, 20241 citation

Microwave transitions from pairs of Rb nd5/2nd5/2 atoms

Jeonghun Lee, Thomas F. Gallagher

We have observed resonant microwave transitions between pairs of atoms. Specifically, we have observed the processes $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2){f}_{7/2}$ and $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+2){p}_{3/2}(n\ensuremath{-}1){d}_{5/2}$ for $35\ensuremath{\le}n\ensuremath{\le}44$. These transitions are allowed due to the dipole-dipole-induced configuration interaction between the $n{d}_{5/2}n{d}_{5/2}$ state and the energetically nearby $(n+2){p}_{3/2}(n\ensuremath{-}2){f}_{7/2}$ state, which admixes some of the latter into the former. The resulting microwave transitions are analogous to two-photon transitions in which one of the photons has been replaced by the dipole-dipole interaction. We have developed a configuration interaction description of the transitions, which gives a good description of the interaction over the range $35\ensuremath{\le}n\ensuremath{\le}42$. Over this range of $n$ the detuning varies from 0.095 to 1.482 GHz, the microwave frequencies vary from 26.970 to 45.916 GHz, and the requisite microwave powers vary by a factor of over 1000.We have observed resonant microwave transitions between pairs of atoms. Specifically, we have observed the processes $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2){f}_{7/2}$ and $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+2){p}_{3/2}(n\ensuremath{-}1){d}_{5/2}$ for $35\ensuremath{\le}n\ensuremath{\le}44$. These transitions are allowed due to the dipole-dipole-induced configuration interaction between the $n{d}_{5/2}n{d}_{5/2}$ state and the energetically nearby $(n+2){p}_{3/2}(n\ensuremath{-}2){f}_{7/2}$ state, which admixes some of the latter into the former. The resulting microwave transitions are analogous to two-photon transitions in which one of the photons has been replaced by the dipole-dipole interaction. We have developed a configuration interaction description of the transitions, which gives a good description of the interaction over the range $35\ensuremath{\le}n\ensuremath{\le}42$. Over this range of $n$ the detuning varies from 0.095 to 1.482 GHz, the microwave frequencies vary from 26.970 to 45.916 GHz, and the requisite microwave powers vary by a factor of over 1000.

Physical Review AJun 20, 20165 citations

Previous measurements of single photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2)f

transitions by two of us were described as microwave transitions made possible by configuration interaction (CI) between the

n{d}_{5/2}n{d}_{5/2}

and the nearly degenerate

(n+2){p}_{3/2}(n\ensuremath{-}2)f

states [Lee and Gallagher, Phys. Rev. A 93, 062509 (2016)]. Here we report the observation of the one photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){s}_{1/2}(n\ensuremath{-}2)f

, two photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){p}_{j}(n\ensuremath{-}2)f

, and three photon

n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+4){s}_{1/2}(n\ensuremath{-}2)f

We have observed an excitonlike exchange in two-photon microwave transitions between pairs of cold Rb Rydberg atoms, specifically, transitions in which a

n{s}_{1/2}n{s}_{1/2}

pair undergoes the transition to the

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

and

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

states. This transition occurs due to the excitonlike $n{s}_{1/2}n{p}_{j}\ensuremath{\leftrightarrow}n{p}_{j}n{s}_{1/2}$ exchange in the intermediate states, and the process can be thought of as a F\"orster resonant energy transfer between Floquet, or dressed, states. In addition, the measurements provide clear evidence of the importance of the three-dimensional nature of the dipole-dipole interaction.

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.

In this work, we precisely measure the transition energies between the Rydberg state n

\text{D}_{5/2}

to the nearby Rydberg states $(\e{n}+2)\text{P}_{3/2}$, $(\e{n}-2)\text{F}_{7/2}$ for the range $41\leq \e{n}\leq46$. This was done by carrying out microwave spectroscopy via Electromagnetically Induced Transparency (EIT) in a room temperature vapor reference cell of Rubidium, which is similar to the experimental approach followed by Li et al. [Results in Physics \textbf{29}, 104728 (2021)]. This range is interesting because there is a quasi Förster resonance between the atomic pair

43\text{D}_{5/2}+43\text{D}_{5/2}

and

45\text{P}_{3/2}+41\text{F}_{7/2}

. We compared the obtained results with numerically calculated transition energies based on previously tabulated quantum defect numbers by various research groups using both hot and ultra-cold atomic samples. Our data are more consistent with measurements made within ultra-cold atomic systems [Phys. Rev. A \textbf{67}, 052502 (2003), Phys. Rev. A \textbf{74}, 054502 (2006)].

n{d}_{5/2}n{d}_{5/2}

state and the energetically nearby $(n+2){p}_{3/2}(n\ensuremath{-}2){f}_{7/2}$ state, which admixes some of the latter into the former. The resulting microwave transitions are analogous to two-photon transitions in which one of the photons has been replaced by the dipole-dipole interaction. We have developed a configuration interaction description of the transitions, which gives a good description of the interaction over the range $35\ensuremath{\le}n\ensuremath{\le}42$. Over this range of

n

the detuning varies from 0.095 to 1.482 GHz, the microwave frequencies vary from 26.970 to 45.916 GHz, and the requisite microwave powers vary by a factor of over 1000.