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Physical Review A

Measurement of the dipole-dipole interaction of Rb nsnp states by microwave Ramsey interferometry

Hyunwook Park, Thomas F. Gallagher

Published Nov 19, 2012• 3 citations
Publisher

Abstract

We have used the Ramsey method of separated oscillatory fields to probe the dipole-dipole interaction of Rb $nsnp$ pair states of $33\ensuremath{\le}n\ensuremath{\le}41$. In the Ramsey method dipole-dipole broadening in an inhomogeneous sample is manifested as a decrease in the fringe contrast with increasing density. An attractive feature of this approach compared to conventional line broadening is that the effect of the dipole-dipole interaction can be seen near the center of the Ramsey interference pattern, where the signal is large, as opposed to in the wings, where it is small. We observe dipole-dipole broadening which scales as ${n}^{4}$, in agreement with the calculated broadening. In addition, the Ramsey method points to the existence of $nsn{p}_{1/2}$ states which have no dipole-dipole shift.

DOI
10.1103/physreva.86.052510

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We have used the Ramsey method of separated oscillatory fields to probe the dipole-dipole interaction of Rb nsnpnsnpnsnp pair states of 33\ensuremath≤n\ensuremath≤4133\ensuremath{\le}n\ensuremath{\le}4133\ensuremath≤n\ensuremath≤41. In the Ramsey method dipole-dipole broadening in an inhomogeneous sample is manifested as a decrease in the fringe contrast with increasing density. An attractive feature of this approach compared to conventional line broadening is that the effect of the dipole-dipole interaction can be seen near the center of the Ramsey interference pattern, where the signal is large, as opposed to in the wings, where it is small. We observe dipole-dipole broadening which scales as n4{n}^{4}n4, in agreement with the calculated broadening. In addition, the Ramsey method points to the existence of nsnp1/2nsn{p}_{1/2}nsnp1/2​ states which have no dipole-dipole shift.
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.
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.
We demonstrate an experimental observation of coherent population trapping-Ramsey interference in cold 87 Rb atoms by employing the time-domain separated oscillatory fields' method. The interference fringe with line width of 80Hz is obtained. We propose a novel method to measure the cold atom number. The measurement is insensitive to the pump beam intensity, the single photon detuning and even the initial state population. We use this method to normalize the interference signal and to improve the signal-to-noise ratio significantly.
We have observed the ionization of a cold gas of Rb Rydberg atoms which occurs when nsnsnsnsnsns van der Waals pairs of nsnsns atoms of $n\ensuremath{\approx}$ 40 on a weakly repulsive potential are transferred to an attractive dipole-dipole nsnpnsnpnsnp 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 nsnsnsnsnsns 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 nsnsnsnsnsns state to the nsnpnsnpnsnp state over a broad range of internuclear spacings, it is possible to accelerate markedly the evolution to a plasma.
When the dipole-dipole energy transfer, $\mathrm{Rb} {25s}_{1/2}+\mathrm{Rb} {33s}_{1/2}\ensuremath{\rightarrow}\mathrm{Rb} {24p}_{1/2}+\mathrm{Rb} {34p}_{3/2},$ resonant at fields of 3.0 and 3.4 V/cm, is observed in a cold Rydberg gas, the resonances are broader than expected for this dipole-dipole interaction alone. Using a variant of the Ramsey interference method, in which the system is detuned from the resonance, we observe a density-dependent dephasing which we attribute to the inhomogeneities in the always resonant dipole-dipole excitation exchange interactions $\mathrm{Rb} {25s}_{1/2}+\mathrm{Rb} {24p}_{1/2}\ensuremath{\rightarrow}\mathrm{Rb} {24p}_{1/2}+\mathrm{Rb} {25s}_{1/2}$ and $\mathrm{Rb} {33s}_{1/2}+\mathrm{Rb} {34p}_{3/2}\ensuremath{\rightarrow}\mathrm{Rb} {34p}_{3/2}+\mathrm{Rb} {33s}_{1/2}.$ Since the dephasing rate is comparable to the observed widths, it appears that all of these interactions contribute to the observed linewidths.
High contrast transparent Ramsey fringes are observed using double microwave pulses interaction with the prepared atomic coherent state in a warm 87 Rb vapor with mixture buffer gases in a closed cell.The Ramsey fringes are generated by the pulsed technique, a strong coupling light pulse and a weak signal light pulse are applied to prepare the atomic coherent state, followed by the application of double microwave pulses to interact with the atomic coherent state.Afterwards, the light pulses are applied again with weaker intensity and detecting the signal transmission is delected.The central line of the transparent Ramsey fringes has narrow linewidth of 125 Hz and high contrast of 21%.The light shift is dramatically reduced since the interrogating process is not involved the light field, and the cavity pulling effect is negligible due to the low Q requirement, which is promising for building small, compact, and stable atomic clocks.