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arXiv:0706.0110 · Physical Review Letters

Spatially Resolved Observation of Dipole-Dipole Interaction between Rydberg Atoms

C. S. E. van Ditzhuijzen, A. Femius Koenderink, J. V. Hernández, F. Robicheaux, Lambertus D. Noordam, H. B. van Linden van den Heuvell

Published Jun 20, 2008• 144 citations
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Abstract

We have observed resonant energy transfer between cold Rydberg atoms in spatially separated cylinders. Resonant dipole-dipole coupling excites the 49s atoms in one cylinder to the 49p state while the 41d atoms in the second cylinder are transferred down to the 42p state. We have measured the production of the 49p state as a function of separation of the cylinders (0-80 microm) and the interaction time (0-25 micros). In addition, we measured the width of the electric field resonances. A full many-body quantum calculation reproduces the main features of the experiments.

DOI
10.1103/physrevlett.100.243201

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We have observed resonant energy transfer between cold Rydberg atoms in spatially separated cylinders. Resonant dipole-dipole coupling excites the 49s atoms in one cylinder to the 49p state while the 41d atoms in the second cylinder are transferred down to the 42p state. We have measured the production of the 49p state as a function of separation of the cylinders (0-80 microm) and the interaction time (0-25 micros). In addition, we measured the width of the electric field resonances. A full many-body quantum calculation reproduces the main features of the experiments.
Radio-frequency (rf) fields in the MHz range are used to induce resonant energy transfer between cold Rydberg atoms in spatially separated volumes. After laser preparation of the Rydberg atoms, dipole-dipole coupling excites the 49s49s49s atoms in one cylinder to the 49p49p49p state while the 41d41d41d atoms in the second cylinder are transferred down to the 42p42p42p state. The energy exchanged between the atoms in this process is 33GHz33\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}33GHz. An external rf field brings this energy transfer into resonance. The strength of the interaction has been investigated as a function of amplitude (0−−1V∕cm)(0--1\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm})(0−−1V∕cm) and frequency (1−−30MHz)(1--30\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})(1−−30MHz) of the rf field and as a function of a static-field offset. Multiphoton transitions up to fifth order as well as selection rules prohibiting the process at certain fields have been observed. The width of the resonances has been reduced compared to earlier results by switching off external magnetic fields of the magneto-optical trap, making sub-MHz spectroscopy possible. All features are well reproduced by theoretical calculations taking the strong ac Stark shift due to the rf field into account.
The dipole-dipole interaction strongly couples ultracold highly excited atoms, known as Rydberg atoms, and is the dominant mechanism for energy exchange among such atoms on microsecond time scales. I present the results of experiments that investigate this interaction using rubidium atoms excited to Rydberg states with an all-diode laser system. In the first of these, high resolution dipole-dipole interaction spectra for different magnetic sublevels of the 32d5/2 state are collected and analyzed. In the second experiment, ultracold rubidium atoms are implusively excited to coherent superpositions of three closely spaced |mj|sublevels of the 32d5/2 state in a weak electric field. The magnitude of the field sets the energy level spacing between these states, and hence the frequency of the phase dependent oscillations resulting from interference in resonant energy exchange processes. In the third experiment, the dipole-dipole interaction induced resonant energy exchange between columns of ultracold rubidium Rydberg atoms is imaged using a new technique involving selective field ionization with a spatially sensitive ion detector.
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.
Previous resonant dipole-dipole energy-transfer experiments of cold Rydberg gases [Anderson et al., Phys. Rev. Lett. 80, 249 (1998); Mourachko et al., Phys. Rev. Lett. 80, 253 (1998)] have been interpreted as providing evidence of many-body, as opposed to purely binary, effects. Here we separate two-body and many-body interactions by introducing an additional Rydberg state, which does not participate directly in the energy-transfer process, but is strongly coupled to one of the final states. We observe broadening of the energy-transfer resonances due to this added Rydberg state, which clearly demonstrates the many-body nature of the dipole-dipole interactions in such a system.
The long-range, anisotropic nature of the interaction among atoms in an ultracold dipolar gas leads to a rich array of possibilities for studying many-body physics. In this work, an ultracold gas of highly excited atoms is used to study energy transport due to the long-range dipole-dipole interaction. A technique is developed to measure both the internal energy states of the interacting Rydberg atoms and their positions in space. This technique is demonstrated by observing energy exchange between two spatially separated groups of Rydberg atoms excited to two different internal states. Simulations confirm the general features of the energy transport in this system and highlight subtleties associated with the homogeneity of the electric field used in this experiment.
We have explored the dipole-dipole mediated, resonant energy transfer reaction, $32{p}_{3/2}+32{p}_{3/2}\ensuremath{\rightarrow}32s+33s$, in an ensemble of cold 85Rb^{85}\mathrm{Rb}85Rb Rydberg atoms. Stark tuning is employed to measure the population transfer probability as a function of the total electronic energy difference between the initial and final atom-pair states over a range of Rydberg densities, $2\ifmmode\times\else\texttimes\fi{}{10}^{8}\ensuremath{\le}\ensuremath{\rho}\ensuremath{\le}3\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{cm}}^{\ensuremath{-}3}$. The observed line shapes provide information on the role of beyond nearest-neighbor interactions, the range of Rydberg atom separations, and the electric field inhomogeneity in the sample. The widths of the resonance line shapes increase approximately linearly with the Rydberg density and are only a factor of 2 larger than expected for two-body, nearest-neighbor interactions alone. These results are in agreement with the prediction [B. Sun and F. Robicheaux, Phys. Rev. A 78, 040701(R) (2008)] that beyond nearest-neighbor exchange interactions should not influence the population transfer process to the degree once thought. At low densities, Gaussian rather than Lorentzian line shapes are observed due to electric field inhomogeneities, allowing us to set an upper limit for the field variation across the Rydberg sample. At higher densities, non-Lorentzian, cusplike line shapes characterized by sharp central peaks and broad wings reflect the random distribution of interatomic distances within the magneto-optical trap (MOT). These line shapes are well reproduced by an analytic expression derived from a nearest-neighbor interaction model and may serve as a useful fingerprint for characterizing the position correlation function for atoms within the MOT.