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arXiv:physics/0604169 · Physical Review A

Resonant electric dipole-dipole interactions between cold Rydberg atoms in a magnetic field

K. Afrousheh, Parisa Bohlouli-Zanjani, J. D. Carter, A. Mugford, J. D. D. Martin

Published Jun 5, 2006• 40 citations
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Abstract

Laser-cooled $^{85}\mathrm{Rb}$ atoms were optically excited to $46{d}_{5∕2}$ Rydberg states. A microwave pulse transferred a fraction of the atoms to the $47{p}_{3∕2}$ Rydberg state. The resonant electric dipole-dipole interactions between atoms in these two states were probed using the linewidth of the two-photon microwave transition $46{d}_{5∕2}\text{\ensuremath{-}}47{d}_{5∕2}$. The presence of a weak magnetic field $\ensuremath{\approx}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{G}$ reduced the observed line broadening, indicating that the interaction is suppressed by the field. The field removes some of the energy degeneracies responsible for the resonant interaction, and this is the basis for a quantitative model of the resulting suppression. A technique for the calibration of magnetic field strengths using the $34{s}_{1∕2}\text{\ensuremath{-}}34{p}_{1∕2}$ one-photon transition is also presented.

DOI
10.1103/physreva.73.063403

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Laser-cooled 85Rb^{85}\mathrm{Rb}85Rb atoms were optically excited to 46d5∕246{d}_{5∕2}46d5∕2​ Rydberg states. A microwave pulse transferred a fraction of the atoms to the 47p3∕247{p}_{3∕2}47p3∕2​ Rydberg state. The resonant electric dipole-dipole interactions between atoms in these two states were probed using the linewidth of the two-photon microwave transition 46d5∕2\ensuremath-47d5∕246{d}_{5∕2}\text{\ensuremath{-}}47{d}_{5∕2}46d5∕2​\ensuremath-47d5∕2​. The presence of a weak magnetic field \ensuremath≈0.5G\ensuremath{\approx}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{G}\ensuremath≈0.5G reduced the observed line broadening, indicating that the interaction is suppressed by the field. The field removes some of the energy degeneracies responsible for the resonant interaction, and this is the basis for a quantitative model of the resulting suppression. A technique for the calibration of magnetic field strengths using the 34s1∕2\ensuremath-34p1∕234{s}_{1∕2}\text{\ensuremath{-}}34{p}_{1∕2}34s1∕2​\ensuremath-34p1∕2​ one-photon transition is also presented.
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis reports the first observation of the resonant electric dipole-dipole interaction between cold Rydberg atoms using microwave spectroscopy, the observation of the magnetic field suppression of resonant interactions, and the development of a unique technique for precise magnetic field measurements. ARydbergstate(46d 5/2) of laser cooled 85 Rb atoms has been optically excited. A fraction of these atoms has been transferred to another Rydberg state (47p 3/2 or 45f 5/2,7/2) to introduce resonant electric dipole-dipole interactions. The line broadening of the two-photon 46d 5/2 − 47d 5/2 microwave transition due to the interaction of 46d 5/2 with 47p 3/2 or 45f 5/2,7/2 atoms has been used as a probe of the interatomic interactions. This experiment has been repeated with a DC magnetic field applied. The application of a weak magnetic field ( ≤ 0.6 G) has reduced
Resonant electric dipole-dipole interactions between cold Rydberg atoms were observed using microwave spectroscopy. Laser-cooled 85Rb atoms in a magneto-optical trap were optically excited to 45d(5/2) Rydberg states using a pulsed laser. A microwave pulse transferred a fraction of these Rydberg atoms to the 46p(3/2) state. A second microwave pulse then drove atoms in the 45d(5/2) state to the 46d(5/2) state, and was used as a probe of interatomic interactions. The spectral width of this two-photon probe transition was found to depend on the presence of the 46p(3/2) atoms, and is due to the resonant electric dipole-dipole interaction between 45d(5/2) and 46p(3/2) Rydberg atoms.
Resonant energy transfer between cold Rydberg atoms was used to determine Rydberg atom energy levels, at precisions approaching those obtainable in microwave spectroscopy. Laser cooled 85Rb^{85}\mathrm{Rb}85Rb atoms from a magneto-optical trap were optically excited to 32d5∕232{d}_{5∕2}32d5∕2​ Rydberg states. The two-atom process $32{d}_{5∕2}+32{d}_{5∕2}\ensuremath{\rightarrow}34{p}_{3∕2}+30g$ is resonant at an electric field of approximately 0.3V∕cm0.3\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}0.3V∕cm. This process is driven by the electric dipole-dipole interaction, which is allowed due to the partial fff character that the ggg state acquires in an electric field. The experimentally observed resonant field, together with the Stark map calculation is used to make a determination of the 85Rb^{85}\mathrm{Rb}85Rb ngngng-series quantum defect ${\ensuremath{\delta}}_{g}(n=30)=0.00405(6)$.
A microwave dressing field was used to induce resonant energy transfer in translationally cold Rydberg atoms. The Rb Rydberg atoms were obtained by laser excitation of cold atoms in a magneto-optical trap. When the amplitude of a 1.356 GHz dressing field was scanned, the two-atom dipole-dipole process 43d5/2 + 43d5/2 → 45p3/2 + 41f5/2,7/2 was enhanced due to the induced degeneracy of the initial and final states. The resulting spectrum had a series of resonant field amplitudes corresponding to different magnetic sublevels possible for the states involved. The scanned field amplitude was calibrated using microwave spectroscopy of the 43d5/2− 41f transition under the influence of non-resonant dressing fields. The calibrated resonant field amplitudes agree well with ac Stark shift calculations performed using the Floquet approach. This method for enhancing interactions is complementary to dc electric field induced resonant energy transfer, but benefits from the ability to shift energy levels in either direction by choice in frequency.
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 n2{n}^{2}n2, a broadening rate scaling as n4{n}^{4}n4 is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm3{}^{3}3 is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the npnpnp 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.
Experiments are carried out on the spectroscopy of the Förster resonance lines Rb(37 P ) + Rb(37 P ) → Rb(37 S ) + Rb(38 S ) and microwave transitions nP → n ′ S , n ′ D between Rydberg states of cold rubidium atoms in a magneto-optical trap (MOT). Under ordinary conditions, all spectra exhibit a linewidth of 2–3 MHz irrespective of the interaction time between atoms or between atoms and microwave radiation, although the limit resonance width should be determined by the inverse interaction time. The analysis of experimental conditions has shown that the main source of line broadening is the inhomogeneous electric field of cold photoions that are generated under the excitation of initial nP Rydberg states by broadband pulsed laser radiation. The application of an additional electric-field pulse that rapidly extracts photoions produced by a laser pulse leads to a considerable narrowing of lines of microwave resonances and the Förster resonance. Various sources of line broadening in cold Rydberg atoms are analyzed.