Physical Review A

MHz few-body frequency shift detected in a cold 85 Rb Rydberg gas

Jianing Han

Published Nov 28, 2011• 7 citations

Abstract

We have observed a density-dependent frequency shift of more than 4 MHz in a cold ${}^{85}$Rb Rydberg gas trapped in a magneto-optical trap. A one-dimensional linearly aligned four-body model is proposed to explain the experimental data, and the calculation matches the experimental data. The calculation also shows that if the energy detuning between the two coupled states, the $nsnsns(n+1)s$ and $nsnsnpnp$ states in this case, is small, the lowest level of the $nsnsnpnp$ manifold has the maximum mixing probability, causing a frequency shift instead of line broadening. The results reported may be used for few-body blockade, Rydberg single-atom imaging, studying few-body to many-body transitions and interactions, and few-body ionization as well as quantum metrology.

DOI: 10.1103/physreva.84.052516

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Direct evidence of three-body interactions in a cold Rb85 Rydberg gas

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Physical Review ANov 1, 201016 citations

Detecting electric-field-tuned atom–atom level mixing in a cold85Rb Rydberg gas by two-unequal-frequency photons

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Dipole-dipole broadening of Rb ns−np microwave transitions

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Absence of collective decay in a cold Rydberg gas

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

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Physical Review AAug 28, 20200 citations

Physical Review A

MHz few-body frequency shift detected in a cold 85 Rb Rydberg gas

Jianing Han

Published Nov 28, 2011• 7 citations

Publisher

Abstract

We have observed a density-dependent frequency shift of more than 4 MHz in a cold

{}^{85}

Rb Rydberg gas trapped in a magneto-optical trap. A one-dimensional linearly aligned four-body model is proposed to explain the experimental data, and the calculation matches the experimental data. The calculation also shows that if the energy detuning between the two coupled states, the

nsnsns(n+1)s

and

nsnsnpnp

states in this case, is small, the lowest level of the

nsnsnpnp

manifold has the maximum mixing probability, causing a frequency shift instead of line broadening. The results reported may be used for few-body blockade, Rydberg single-atom imaging, studying few-body to many-body transitions and interactions, and few-body ionization as well as quantum metrology.

DOI: 10.1103/physreva.84.052516

Related papers

Direct evidence of three-body interactions in a cold Rb85 Rydberg gas

Jianing Han

Cold Rydberg atoms trapped in a magneto-optical trap (MOT) are not isolated and they interact through dipole-dipole and multipole-multipole interactions. First-order dipole-dipole interactions and van der Waals interactions between two atoms have been intensively studied. However, the facts that the first-order dipole-dipole interactions and van der Waals interactions show the same size of broadening [A. Reinhard, K. C. Younge, T. C. Liebisch, B. Knuffman, P. R. Berman, and G. Raithel, Phys. Rev. Lett. 100, 233201 (2008)] and there are transitions between two dimer states [S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Cote, E. E. Eyler, and P. L. Gould, Phys. Rev. Lett. 91, 183002 (2003); K. R. Overstreet, Arne Schwettmann, Jonathan Tallant, and James P. Shaffer, Phys. Rev. A 76, 011403(R) (2007)] cannot be explained by the two-atom picture. The purpose of this article is to show the few-body nature of a dense cold Rydberg gas by studying the molecular-state microwave spectra. Specifically, three-body energy levels have been calculated. Moreover, the transition from three-body energy levels to two-body coupled molecular energy levels and to isolated atomic energy levels as a function of the internuclear spacing is studied. Finally, single-body, two-body, and three-body interaction regions are estimated according to the experimental data. The results reported here provides useful information for plasma formation, further cooling, and superfluid formation.Cold Rydberg atoms trapped in a magneto-optical trap (MOT) are not isolated and they interact through dipole-dipole and multipole-multipole interactions. First-order dipole-dipole interactions and van der Waals interactions between two atoms have been intensively studied. However, the facts that the first-order dipole-dipole interactions and van der Waals interactions show the same size of broadening [A. Reinhard, K. C. Younge, T. C. Liebisch, B. Knuffman, P. R. Berman, and G. Raithel, Phys. Rev. Lett. 100, 233201 (2008)] and there are transitions between two dimer states [S. M. Farooqi, D. Tong, S. Krishnan, J. Stanojevic, Y. P. Zhang, J. R. Ensher, A. S. Estrin, C. Boisseau, R. Cote, E. E. Eyler, and P. L. Gould, Phys. Rev. Lett. 91, 183002 (2003); K. R. Overstreet, Arne Schwettmann, Jonathan Tallant, and James P. Shaffer, Phys. Rev. A 76, 011403(R) (2007)] cannot be explained by the two-atom picture. The purpose of this article is to show the few-body nature of a dense cold Rydberg gas by studying the molecular-state microwave spectra. Specifically, three-body energy levels have been calculated. Moreover, the transition from three-body energy levels to two-body coupled molecular energy levels and to isolated atomic energy levels as a function of the internuclear spacing is studied. Finally, single-body, two-body, and three-body interaction regions are estimated according to the experimental data. The results reported here provides useful information for plasma formation, further cooling, and superfluid formation.

Physical Review ANov 1, 201016 citations

Detecting electric-field-tuned atom–atom level mixing in a cold85Rb Rydberg gas by two-unequal-frequency photons

Jianing Han

We use two-unequal-frequency microwave photons as sensitive probes to study the n s n s to the n p( n + m − 1)p Rydberg pair state transition in a cold 85 Rb gas, where n and m are integers. The principal quantum number n dependence of the energy differences between n s( n + 1)s and n p 3/2 n p 3/2 as well as n s( n + 2)s and n p 1/2 ( n + 1)p 1/2 has been measured and the results are consistent with the calculated values. Additionally, we demonstrate that the pair state Stark shift is the sum of the Stark shifts of both isolated Rydberg atoms. Finally, we tune the dipole–dipole mixing probability by applying an electric field to tune the energy difference between the dipole–dipole coupled states, n s( n + 2)s and n p 1/2 ( n + 1)p 1/2 . The results reported here are essential steps towards electric-field-controlled chemical reactions [1], quantum gates, molecular autoionization and few-body correlations.We use two-unequal-frequency microwave photons as sensitive probes to study the n s n s to the n p( n + m − 1)p Rydberg pair state transition in a cold 85 Rb gas, where n and m are integers. The principal quantum number n dependence of the energy differences between n s( n + 1)s and n p 3/2 n p 3/2 as well as n s( n + 2)s and n p 1/2 ( n + 1)p 1/2 has been measured and the results are consistent with the calculated values. Additionally, we demonstrate that the pair state Stark shift is the sum of the Stark shifts of both isolated Rydberg atoms. Finally, we tune the dipole–dipole mixing probability by applying an electric field to tune the energy difference between the dipole–dipole coupled states, n s( n + 2)s and n p 1/2 ( n + 1)p 1/2 . The results reported here are essential steps towards electric-field-controlled chemical reactions [1], quantum gates, molecular autoionization and few-body correlations.

Journal of Physics B Atomic Molecular and Optical PhysicsNov 19, 20107 citations

Dipole-dipole broadening of Rb ns−np microwave transitions

Hyunwook Park, Paul J. Tanner, Brigitte J. C. Claessens +2 more

The dipole-dipole broadening of $ns\ensuremath{-}np$ microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for $28\ensuremath{\leqslant}n\ensuremath{\leqslant}51$. Since the electric dipole transition matrix elements scale as ${n}^{2}$ , a broadening rate scaling as ${n}^{4}$ is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm ${}^{3}$ is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the $np$ atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.The dipole-dipole broadening of $ns\ensuremath{-}np$ microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for $28\ensuremath{\leqslant}n\ensuremath{\leqslant}51$. Since the electric dipole transition matrix elements scale as ${n}^{2}$, a broadening rate scaling as ${n}^{4}$ is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm${}^{3}$ is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the $np$ atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.

Physical Review AAug 5, 201140 citations

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

Spectroscopy of the three-photon laser excitation of cold Rubidium Rydberg atoms in a magneto-optical trap

Vasily M. Entin, Elena A. Yakshina, Denis B. Tretyakov +2 more

The spectra of the three-photon laser excitation 5 S 1/2 → 5 P 3/2 → 6 S 1/2 nP of cold Rb Rydberg atoms in an operating magneto-optical trap based on continuous single-frequency lasers at each stage are studied. These spectra contain two partly overlapping peaks of different amplitudes, which correspond to coherent three-photon excitation and incoherent three-step excitation due to the presence of two different ways of excitation through the dressed states of intermediate levels. A four-level theoretical model based on optical Bloch equations is developed to analyze these spectra. Good agreement between the experimental and calculated data is achieved by introducing additional decay of optical coherence induced by a finite laser line width and other broadening sources (stray electromagnetic fields, residual Doppler broadening, interatomic interactions) into the model.The spectra of the three-photon laser excitation 5 S 1/2 → 5 P 3/2 → 6 S 1/2 nP of cold Rb Rydberg atoms in an operating magneto-optical trap based on continuous single-frequency lasers at each stage are studied. These spectra contain two partly overlapping peaks of different amplitudes, which correspond to coherent three-photon excitation and incoherent three-step excitation due to the presence of two different ways of excitation through the dressed states of intermediate levels. A four-level theoretical model based on optical Bloch equations is developed to analyze these spectra. Good agreement between the experimental and calculated data is achieved by introducing additional decay of optical coherence induced by a finite laser line width and other broadening sources (stray electromagnetic fields, residual Doppler broadening, interatomic interactions) into the model.

Journal of Experimental and Theoretical PhysicsMay 1, 201327 citations

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

We have observed a density-dependent frequency shift of more than 4 MHz in a cold

{}^{85}

nsnsns(n+1)s

and

nsnsnpnp

states in this case, is small, the lowest level of the

nsnsnpnp

{n}^{2}

, a broadening rate scaling as

{n}^{4}

is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm

{}^{3}

is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the

np

atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.

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.

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.