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Journal of Physics B Atomic Molecular and Optical Physics

A novel method for the calculation of widths for avoided crossings of the highly excited Stark states: detailed implementation for alkali-metal atoms

Yong-Lin He

Published Dec 9, 2011• 6 citations
Publisher

Abstract

We have presented a novel method to calculate the widths of the avoided crossings of Rydberg states in a static electric field. The widths of avoided crossings can be decided not directly connected by scanning the static field, but indirectly connected through the Stark electric dipole moments. The method is restricted to the case in which both the two relevant states have linear Stark shifts or only one of the two involved states has linear Stark shifts, but another has no Stark shift. As test examples, we calculated the widths of avoided crossings of Li, Na and K. The Stark electric dipole moments are determined by using the Stark state wavefunctions which are obtained from the diagonalization method at a fixed static electric field amplitude. The results are in excellent agreement with experimental and other theoretical data.

DOI
10.1088/0953-4075/45/1/015001

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We have presented a novel method to calculate the widths of the avoided crossings of Rydberg states in a static electric field. The widths of avoided crossings can be decided not directly connected by scanning the static field, but indirectly connected through the Stark electric dipole moments. The method is restricted to the case in which both the two relevant states have linear Stark shifts or only one of the two involved states has linear Stark shifts, but another has no Stark shift. As test examples, we calculated the widths of avoided crossings of Li, Na and K. The Stark electric dipole moments are determined by using the Stark state wavefunctions which are obtained from the diagonalization method at a fixed static electric field amplitude. The results are in excellent agreement with experimental and other theoretical data.
In this work, numerical calculations were implemented based on the diagonalisation of a matrix representation of the Stark Hamiltonian on a subset of the basis given by the zero-field Hamiltonian. Dipole matrix elements between the involved states were calculated, which allow for the prediction of transition strengths to Stark shifted Rydberg states. The applicability of the numerical methods were confirmed experimentally by precision spectroscopy in a rubidium vapour cell with electrodes using electromagnetically induced transparency (EIT). The numerical methods were then extended to predict ionisation rates of Rydberg states in the highly Stark shifted regime beyond the classical ionisation threshold. For this purpose, a complex absorbing potential (CAP) was specifically adjusted to the Stark Hamiltonian. An experiment was conducted, in which cold atoms from a magneto-optical trap (MOT) were excited to Stark shifted Rydberg states and the arising ions were detected. The obtained ionisation spectra agree well with the results from the numerical calculations. Another extension of the numerical methods was implemented for crossed electric and magnetic fields. This was used for approximate calculations of the motional Stark effect (MSE), which acts on atoms moving through static magnetic fields and thereby experiencing a Lorentz electric field. In a precision spectroscopy, once more using EIT in a vapour cell, the MSE was observed in low magnetic fields for the first time in rubidium. The spectral shift, which is caused by the MSE, matches the prediction from the numerical calculations. In a final experiment, the practical use of the knowledge of several properties of Stark shifted Rydberg states was illustrated. The numerical methods including the CAP were used to specifically select states for their optical accessibility, permanent electric dipole moments and ionisation rates. In the experiment, atoms from a MOT were excited to these states to observe different characteristics of the dipole blockade effect. The detection scheme for this experiment was realised by controlled ionisation using only small changes in the external electric field.
Numerical calculations of the positions and widths for anticrossings in Rydberg Stark states are scarce, largely due to the results' sensitive dependence on the wavefunctions chosen. With wavefunctions derived from a kind of potential model as a basis, we calculate the positions and sizes for the anticrossings of potassium Rydberg states in a static electric field by means of diagonalization, and show that the results are in good agreement with available experimental data. The results show that this potential model can be used to deal with the problem of anticrossings, and the accuracy of the potential model is sensitively and numerically tested in the situation of external fields for the first time.
We have measured the locations and widths of the avoided level crossings between (n+3)s states and n,k Stark states in Rydberg Rb atoms with principal quantum numbers n between 16 and 25. We use two-step laser excitation to excite (n+3)s states in the presence of an electric field and observe a change in the number of atoms driven to higher-lying states by blackbody radiation as the electric field is tuned through the avoided level crossings. We have measured both the positions and widths of the avoided crossings. \textcopyright{} 1996 The American Physical Society.
With a potential model of alkali-metal atoms and B-spline expansion technique,the structure of the energy levels for Rydberg states of Rubidium is investigated.We calculated the positions and widths of anticrossing between(n+3)s and (n,k) Stark states with principal quantum number n between 16 and 25.Our results are in agreement with the experimental data.And we obtained two empirical formulas which can be used to estimate the positions of anticrossing for high Rydberg states of Rubidium in static electric field.
We have measured the avoided crossings between the Cs (n+4)s states and the lowest three members of the adjacent n Stark manifold for 20<or=n<or=24 using a novel technique based on the differences in the pulsed field ionization of the states under study. The measured positions of the avoided crossings are in excellent agreement with values calculated by matrix diagonalization, and the experimentally determined widths of the avoided crossings, which range from 29 to 78 MHz, are in reasonable agreement with the calculated values.
With wavefunctions from a kind of atomic potential model including the fine-structure (FS) interaction as a basis, we calculate the positions and widths of anticrossings due to the FS interaction for the case of K Rydberg states in a static electrical field by using the diagonalization method. The results are in good agreement with experimental data; and we confirm that the influence of the FS interaction is very small on anticrossing brought about by core interaction. The accuracy of the potential model wavefunction including the FS interaction is sensitively and numerically tested in the situation of external fields.