Physical Review A

Millimeter-wave rubidium Rydberg van der Waals spectroscopy

Jianing Han, Thomas F. Gallagher

Published May 12, 2009• 34 citations

Abstract

We have observed the diatomic $nsns\ensuremath{\rightarrow}ns(n+1)s\ensuremath{\rightarrow}(n+1)s(n+1)s$ microwave transitions of pairs of cold Rb Rydberg atoms for $36<n<48$. The $ns(n+1)s$ state has by far the largest van der Waals shift due to its near degeneracy with the nearby $n{p}_{3/2}n{p}_{3/2}$ state. In fact, the energy difference and the van der Waals shift change sign at $n=38$ and we observe shifts of both signs. The combined excitation of the $ns(n+1)s$ and $(n+1)s(n+1)s$ states leads to an unusual line shape which can be described by a three-level Floquet model.

DOI: 10.1103/physreva.79.053409

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Physical Review A

Millimeter-wave rubidium Rydberg van der Waals spectroscopy

Jianing Han, Thomas F. Gallagher

Published May 12, 2009• 34 citations

Publisher

Abstract

We have observed the diatomic

nsns\ensuremath{\rightarrow}ns(n+1)s\ensuremath{\rightarrow}(n+1)s(n+1)s

microwave transitions of pairs of cold Rb Rydberg atoms for

36<n<48

. The

ns(n+1)s

state has by far the largest van der Waals shift due to its near degeneracy with the nearby

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

state. In fact, the energy difference and the van der Waals shift change sign at

n=38

and we observe shifts of both signs. The combined excitation of the

ns(n+1)s

and

(n+1)s(n+1)s

states leads to an unusual line shape which can be described by a three-level Floquet model.

DOI: 10.1103/physreva.79.053409

Related papers

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

Rydberg-Rydberg interaction in the second-harmonic generation from rubidium atoms

Natalia R. de Melo, S. S. Vianna

We report on the observation of long range interaction in the second-harmonic generation from rubidium Rydberg atoms. The asymmetric spectral broadening of the resonant lines provides evidence of the van der Waals interaction between pairs of Rydberg atoms. This effect is investigated when the two-photon transition is resonant with $nd$ levels for $n\ensuremath{\approx}13$.We report on the observation of long range interaction in the second-harmonic generation from rubidium Rydberg atoms. The asymmetric spectral broadening of the resonant lines provides evidence of the van der Waals interaction between pairs of Rydberg atoms. This effect is investigated when the two-photon transition is resonant with $nd$ levels for $n\ensuremath{\approx}13$.

Physical Review AFeb 27, 20081 citation

Ionization of Rb Rydberg atoms in the attractive nsnp dipole-dipole potential

Hyunwook Park, E. S. Shuman, Thomas F. Gallagher

We have observed the ionization of a cold gas of Rb Rydberg atoms which occurs when $nsns$ van der Waals pairs of $ns$ atoms of $n\ensuremath{\approx}$ 40 on a weakly repulsive potential are transferred to an attractive dipole-dipole $nsnp$ potential by a microwave transition. Comparing the measurements to a simple model shows that the initial 300-$\ensuremath{\mu}$K thermal velocity of the atoms plays an important role. Excitation to a repulsive dipole-dipole potential does not lead to more ionization on a 15-$\ensuremath{\mu}$s time scale than leaving the atoms in the weakly repulsive $nsns$ state. This observation is slightly surprising since a radiative transition must occur to allow ionization in the latter case. Finally, by power broadening of the microwave transition, to allow transitions from the initial $nsns$ state to the $nsnp$ state over a broad range of internuclear spacings, it is possible to accelerate markedly the evolution to a plasma.We have observed the ionization of a cold gas of Rb Rydberg atoms which occurs when $nsns$ van der Waals pairs of $ns$ atoms of $n\ensuremath{\approx}$ 40 on a weakly repulsive potential are transferred to an attractive dipole-dipole $nsnp$ potential by a microwave transition. Comparing the measurements to a simple model shows that the initial 300-$\ensuremath{\mu}$K thermal velocity of the atoms plays an important role. Excitation to a repulsive dipole-dipole potential does not lead to more ionization on a 15-$\ensuremath{\mu}$s time scale than leaving the atoms in the weakly repulsive $nsns$ state. This observation is slightly surprising since a radiative transition must occur to allow ionization in the latter case. Finally, by power broadening of the microwave transition, to allow transitions from the initial $nsns$ state to the $nsnp$ state over a broad range of internuclear spacings, it is possible to accelerate markedly the evolution to a plasma.

Physical Review ANov 9, 201130 citations

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

Jeonghun Lee, Javed Iqbal, Thomas F. Gallagher

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.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.

Physical Review AJul 10, 20173 citations

Long-range interactions in a cold Rydberg gas

P. L. Gould, S. M. Farooqi, D. Tong +5 more

Quantum Electronics and Laser Science ConferenceDec 10, 20050 citations

Van der Waals Interactions and Dipole Blockade in a Cold Rydberg Gas Probed by Microwave Spectroscopy

Thanh Long Nguyen, R Teixeira, Carla Hermann-Avigliano +5 more

Bulletin of the American Physical SocietyMay 26, 20160 citations

We have observed the diatomic

nsns\ensuremath{\rightarrow}ns(n+1)s\ensuremath{\rightarrow}(n+1)s(n+1)s

microwave transitions of pairs of cold Rb Rydberg atoms for

36<n<48

. The

ns(n+1)s

state has by far the largest van der Waals shift due to its near degeneracy with the nearby

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

state. In fact, the energy difference and the van der Waals shift change sign at

n=38

and we observe shifts of both signs. The combined excitation of the

ns(n+1)s

and

(n+1)s(n+1)s

states leads to an unusual line shape which can be described by a three-level Floquet model.

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.

nd

levels for $n\ensuremath{\approx}13$.

We have observed the ionization of a cold gas of Rb Rydberg atoms which occurs when

nsns

van der Waals pairs of

ns

atoms of $n\ensuremath{\approx}$ 40 on a weakly repulsive potential are transferred to an attractive dipole-dipole

nsnp

potential by a microwave transition. Comparing the measurements to a simple model shows that the initial 300-$\ensuremath{\mu}$K thermal velocity of the atoms plays an important role. Excitation to a repulsive dipole-dipole potential does not lead to more ionization on a 15-$\ensuremath{\mu}$s time scale than leaving the atoms in the weakly repulsive

nsns

state. This observation is slightly surprising since a radiative transition must occur to allow ionization in the latter case. Finally, by power broadening of the microwave transition, to allow transitions from the initial

nsns

state to the

nsnp

state over a broad range of internuclear spacings, it is possible to accelerate markedly the evolution to a plasma.

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.