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Physical Review A

Dipole-dipole broadening of Rb ns−np microwave transitions

Hyunwook Park, Paul J. Tanner, Brigitte J. C. Claessens, E. S. Shuman, Thomas F. Gallagher

Published Aug 5, 2011• 40 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.84.022704

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The dipole-dipole broadening of ns\ensuremath−npns\ensuremath{-}npns\ensuremath−np microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for 28\ensuremath⩽n\ensuremath⩽5128\ensuremath{\leqslant}n\ensuremath{\leqslant}5128\ensuremath⩽n\ensuremath⩽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×\else\texttimes\fi10\ensuremath−15n48.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}8.2\ifmmode×\else\texttimes\fi10\ensuremath−15n4 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.
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.
Microwave pump-probe experiments starting with a cold gas of Rb 34s34s34s atoms confirm that cusped line shapes observed in dipole-dipole broadened microwave transitions are due to atoms which are widely separated and exhibit small dipole-dipole energy shifts. When the experiments are interpreted in terms of a nearest-neighbor model, they demonstrate that it is possible to select pairs of atoms based on their separation and orientation.
By using a magneto-optical trap we have measured the Rb $ns\ensuremath{-}(n+1)s$ and ${\mathrm{nd}}_{j}{\ensuremath{-}(n+1)d}_{j}$ two-photon millimeter-wave transitions for 32< n< 37,32<~n<~37,32< n< 37, observing 100-kHz-wide resonances, in spite of the trap's 10 G/cm magnetic-field gradient, in which one might expect to observe resonances 5 MHz wide. This resolution is possible because of the similarity of the gj{g}_{j}gj​ factors in the initial and final states. Under the same conditions, the single-photon ns-np resonances are \ensuremath{\sim}5 MHz wide. To make useful measurements of these intervals, we turned off the trap field and used the 300-K atoms of the background Rb vapor. Together these measurements improve the accuracy of the s, p, and d quantum defects by an order of magnitude.
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 $46{d}_{5∕2}\text{\ensuremath{-}}47{d}_{5∕2}$. 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.
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.