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Physical Review A

Precision mapping of electrostatic fields using interference-narrowed Stark resonances

Donghai Yang, David H. Lieberman, P. van der Straten, Thomas H. Bergeman, Harold J. Metcalf

Published Nov 1, 1989• 12 citations
Publisher

Abstract

We have exploited the interference narrowing of Stark resonances to map electrostatic fields to a previously unattained level of accuracy and spatial resolution. The technique involves stepwise excitation with tightly focused laser light, an atomic beam, and temporal observation of ionization over a region of interference narrowing. Field inhomogeneities as small as 70 ppm have been detected with spatial resolution of 250 \ensuremath{\mu}m in three dimensions. The method is used here with rubidium atoms at fields of 3--4 kV/cm, but any alkali-metal atom over a range from a few tens of V/cm to a few tens of kV/cm is appropriate. Ionization rates may be calculated with the WKB quantum-defect method, but the field-mapping results are independent of the theory. Here this mapping technique is used to evaluate two electrode configurations for precision Stark spectroscopy. Field inhomogeneities produced by an electrode with a narrow slit, when properly constructed, are found to be in good agreement with detailed electrostatic calculations. However, discrepancies between field measurements and calculations for a metal mesh over an aperture indicate the presence of unavoidable crinkles of the mesh. We conclude that the slot is the preferred arrangement, and we present calculations that give the field inhomogeneity as a function of the slot size.

DOI
10.1103/physreva.40.5026

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We have exploited the interference narrowing of Stark resonances to map electrostatic fields to a previously unattained level of accuracy and spatial resolution. The technique involves stepwise excitation with tightly focused laser light, an atomic beam, and temporal observation of ionization over a region of interference narrowing. Field inhomogeneities as small as 70 ppm have been detected with spatial resolution of 250 \ensuremath{\mu}m in three dimensions. The method is used here with rubidium atoms at fields of 3--4 kV/cm, but any alkali-metal atom over a range from a few tens of V/cm to a few tens of kV/cm is appropriate. Ionization rates may be calculated with the WKB quantum-defect method, but the field-mapping results are independent of the theory. Here this mapping technique is used to evaluate two electrode configurations for precision Stark spectroscopy. Field inhomogeneities produced by an electrode with a narrow slit, when properly constructed, are found to be in good agreement with detailed electrostatic calculations. However, discrepancies between field measurements and calculations for a metal mesh over an aperture indicate the presence of unavoidable crinkles of the mesh. We conclude that the slot is the preferred arrangement, and we present calculations that give the field inhomogeneity as a function of the slot size.
We report measurements of the temporal decay of sodium Stark resonances over regions of interference narrowing and compare with calculations using Wentzel-Kramers-Brillouin quantum-defect (WKB-QD) Stark theory. The measurements are performed with a beam of sodium atoms in a uniform electric field of \ensuremath{\sim}3.2 kV/cm excited via the 3 2P^{2}P2P state to \ensuremath{\sim}285 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (n∗{n}^{\mathrm{*}}n∗\ensuremath{\sim}20) below the zero-field ionization threshold, and hence substantially above the classical saddle-point energy. For mixed states at level crossings, the discrete-continuum couplings interfere, yielding resonances that are stabilized against ionization over a small interval of the field. Measurements of the maximum lifetimes of \ensuremath{\Vert}m\ensuremath{\Vert}=1 levels here are not limited by laser bandwidth, as were our previous spectral observations of m=0 resonances. For three narrowing regions studied here, the observed maximum lifetime values of 127--191 nsec are 10--20 % less than values obtained from WKB-QD calculations, while experimental error limits are \ensuremath{\sim}5%. After considering estimates for competing processes, namely radiative decay and transfer by blackbody radiation, a slight discrepancy remains.
Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.
The controlled deflection of Rydberg atoms in an inhomogeneous electric field is demonstrated and shown to be in agreement with predictions based on a well-defined Stark map. Krypton atoms in a supersonic beam are excited in a two-colour multiphoton process to selected Stark states with n = 16-19 and undergo deflections in the field of an electrostatic dipole. The spatial distribution of the deflected atoms is monitored by ion imaging. The atoms travelling ~10 cm in the beam direction after excitation are deflected from the beam axis by distances of up to 3 mm, the interaction with the field taking place over 40 µs. Simulations of the trajectories agree well with the experimental results, demonstrating that the detected Rydberg atoms are those which have not undergone decay processes in the 40 µs applied field.
We report on the measurement of Stark shifted energy levels of 87 Rb Rydberg atoms in static electric fields by means of electromagnetically induced transparency (EIT). Electric field strengths of up to 500 V cm −1 , ranging beyond the classical ionization threshold, were applied using electrodes inside a glass cell with rubidium vapour. Stark maps for principal quantum numbers n = 35 and n = 70 have been obtained with high signal-to-noise ratio for comparison with results from ab initio calculations following the method described in (Zimmerman et al 1979 Phys. Rev. A 20 2251 ), which was originally only verified for states around n = 15. We also calculate the dipole matrix elements between low-lying states and Stark shifted Rydberg states to give a theoretical estimate of the relative strength of the EIT signal. The present work significantly extends the experimental verification of this numerical method in the range of both high principal quantum numbers and high electric fields with an accuracy of up to 2 MHz.
Quantum computing and quantum simulation with ultracold neutral atoms require Rydberg excitation of individual atoms in atomic arrays. Rydberg states are extremely sensitive to external electric fields, therefore precise three-dimensional control of the electric field is essential. We performed a spectroscopic study of three-photon Rydberg excitation of a single Rb atom in an optical dipole trap in the presence of an external DC electric field. The field was generated by eight electrodes deposited on the inner surfaces of an ultrahigh-vacuum glass cell. The used three-photon scheme of laser excitation of Rydberg \textit{nP} states allows the Stark shift and the splitting of the resonances to be observed simultaneously, which simplifies calibration of the electric field. In addition, in the commonly used two-photon Rydberg excitation schemes, the light shifts can complicate accurate determination of the DC Stark shift, particularly when the external electric field is scanned across different spatial directions, and different Stark components are excited. These shifts are absent in the three-photon excitation scheme used in our experiment. We demonstrated the ability to independently tune the electric field along all three spatial directions and to compensate for stray electric fields. The measured three-photon spectra exhibit Stark shifts and splittings of the three-photon resonance that are in good agreement with theoretical calculations. These results are also of interest for Rydberg electrometry.