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arXiv:0907.4275 · Physical Review A

Observation of Stückelberg oscillations in dipole-dipole interactions

C. S. E. van Ditzhuijzen, Atreju Tauschinsky, H. B. van Linden van den Heuvell

Published Dec 3, 2009• 44 citations
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Abstract

We have observed St\"uckelberg oscillations in the dipole-dipole interaction between Rydberg atoms with an externally applied radio-frequency field. The oscillating rf field brings the interaction between cold Rydberg atoms in two separated volumes into resonance. We observe multiphoton transitions when varying the amplitude of the rf field and the static electric field offset. The angular momentum states we use show a quadratic Stark shift, which leads to a fundamentally different behavior than linearly shifting states. Both cases are studied theoretically using the Floquet approach and are compared. The amplitude of the sidebands, related to the interaction strength, is given by the Bessel function in the linearly shifting case and by the generalized Bessel function in the quadratically shifting case. The oscillatory behavior of both functions corresponds to St\"uckelberg oscillations, an interference effect described by the semiclassical Landau-Zener-St\"uckelberg model. The measurements prove coherent dipole-dipole interaction during at least $0.6\text{ }\ensuremath{\mu}\text{s}$.

DOI
10.1103/physreva.80.063407

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We have observed St"uckelberg oscillations in the dipole-dipole interaction between Rydberg atoms with an externally applied radio-frequency field. The oscillating rf field brings the interaction between cold Rydberg atoms in two separated volumes into resonance. We observe multiphoton transitions when varying the amplitude of the rf field and the static electric field offset. The angular momentum states we use show a quadratic Stark shift, which leads to a fundamentally different behavior than linearly shifting states. Both cases are studied theoretically using the Floquet approach and are compared. The amplitude of the sidebands, related to the interaction strength, is given by the Bessel function in the linearly shifting case and by the generalized Bessel function in the quadratically shifting case. The oscillatory behavior of both functions corresponds to St"uckelberg oscillations, an interference effect described by the semiclassical Landau-Zener-St"uckelberg model. The measurements prove coherent dipole-dipole interaction during at least 0.6 \ensuremathμs0.6\text{ }\ensuremath{\mu}\text{s}0.6 \ensuremathμs.
Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using F\"orster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly resolved radio-frequency-assisted F\"orster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced F\"orster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg levels appearing in the rf field. This method can be applied to enhance the interactions of almost arbitrary Rydberg atoms with large principal quantum numbers.
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.
Dipole-dipole interactions between helium atoms in Rydberg-Stark states with principal quantum number n=53n=53n=53 and approximately linear Stark energy shifts, resulting from induced electric dipole moments of approximately 7900 D, have been investigated experimentally. The experiments were performed in pulsed supersonic metastable helium beams, with particle number densities of up to $\ensuremath{\sim}{10}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. In the presence of amplitude-modulated, radio-frequency electric fields, changes in the spectral intensity distributions associated with the transitions to these states that are attributed to dipole-dipole interactions within the ensembles of excited atoms have been observed. The experimental results are in excellent agreement with calculations of the Rydberg energy level structure carried out using Floquet methods, and excitations shared by up to four atoms. The use of these Rydberg-Stark states as sensors for nonresonant broadband radio-frequency electrical noise is also discussed.
The AC Stark shift of electronic levels is ubiquitous in the interaction of intense light fields with atoms and molecules. As the light intensity changes on the rising and falling edges of a femtosecond laser pulse, it shifts the Rydberg states in and out of multiphoton resonances with the ground state. The two resonant pathways for transient excitation arising at the leading and the trailing edges of the pulse generate Young's type interference, generally referred to as the St\"uckelberg oscillations. Here we report the observation of the St\"uckelberg oscillations in the intensity of the coherent free-induction decay following resonant multiphoton excitation. Moreover, combining the experimental results with accurate numerical simulations and a simple model, we use the St\"uckelberg oscillations to recover the population dynamics of strongly driven Rydberg states inside the laser pulse by all-optical measurements after the end of the pulse. We demonstrate the potential of this spectroscopy to characterize lifetimes of Rydberg states dressed by laser fields with strengths far exceeding the Coulomb field between the Rydberg electron and the core.
Long-range interactions between cold Rydberg atoms are being investigated for neutral-atom quantum computing, quantum simulations, phase transitions in cold Rydberg gases and other applications. Fine tuning of the interaction strength can be implemented using Förster resonances between Rydberg atoms controlled by an electric field. The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. The application of the radio-frequency field causes additional Förster resonances between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb( nP 3/2 ) + Rb( nP 3/2 ) → Rb( nS 1/2 ) + Rb([ n + 1] S 1/2 ) for two Rb Rydberg atoms interacting in a time-varying electric field.
The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. In our experiments with a few cold Rb Rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the Förster resonances, since the population transfer at the resonances occurs on a time scale of $\sim$100 ns, which is comparable with the duration of the transients. For example, a short-term ringing at a certain frequency causes additional radio-frequency-assisted Förster resonances, while non-sharp edges lead to asymmetry. The intentional application of the radio-frequency field induces transitions between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb(nP3/2)+Rb(nP3/2)→Rb(nS1/2)+Rb([n+1]S1/2){\rm Rb}(nP_{3/2} )+{\rm Rb}(nP_{3/2} )\to {\rm Rb}(nS_{1/2} )+{\rm Rb}([n+1]S_{1/2} )Rb(nP3/2​)+Rb(nP3/2​)→Rb(nS1/2​)+Rb([n+1]S1/2​) for two Rb Rydberg atoms interacting in a time-varying electric field.