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Physical Review A

Influence of an external electric field on thermal collisions between ‘‘circular’’ Rydberg-state atoms and ground-state helium

E. de Prunelé

Published May 1, 1986• 4 citations
Publisher

Abstract

The influence of an external electric field on thermal collisions between a sodium atom excited in a ``circular'' Rydberg state (n=l+1=m+1=20) and a ground-state helium atom is studied numerically within the framework of the impulse approximation. The effect of the field is determined by using parabolic wave functions for the initial and final hydrogenic atomic states. The removal of degeneracy induced by the field appears to have no significant effect for fields in the range of 0--400 V/cm. However, the state-to-state transition cross sections are strongly dependent on the initial orientation as found in previous calculations without electric field.

DOI
10.1103/physreva.33.3554

Related papers

Orientation effects in thermal collisions between ‘‘circular’’–Rydberg-state atoms and ground-state helium

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A general formulation for thermal collisions between a Rydberg-state atom and a ground-state rare-gas atom is developed within the framework of the impulse approximation. This formulation allows calculation of cross sections for state-to-state transitions for an arbitrary initial orientation between the Rydberg-state atom and the relative velocity of the two partners of the collision. It also allows a direct computation of these cross sections averaged over all orientations, a situation corresponding to a cell experiment. In this formulation, the differential cross sections with respect to the modulus of the momentum transfer are obtained analytically in terms of rotation matrix elements. Numerical applications are made for the case of a sodium atom in a ``circular'' Rydberg state (\ensuremath{\Vert}n,l,m〉, with l=m=n-1) colliding with helium. The collisional processes are found to be highly anisotropic. In particular, a selection rule may appear, or disappear, depending upon the initial orientation. The extension to the case where an external electric field is present is also discussed, with special emphasis on symmetry properties.

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The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms ($n=10, 15, \mathrm{and} 20$) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number $m$. The origin of this tendency is discussed.

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Helium atoms have been prepared in the circular $|n=55,\ensuremath{\ell}=54,{m}_{\ensuremath{\ell}}=+54\ensuremath{\rangle}$ Rydberg state using the crossed electric and magnetic fields method. The atoms, initially traveling in pulsed supersonic beams, were photoexcited from the metastable $1s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ level to the outermost, ${m}_{\ensuremath{\ell}}=0$ Rydberg-Stark state with $n=55$ in the presence of a strong electric field and weak perpendicular magnetic field. Following excitation, the electric field was adiabatically switched off causing the atoms to evolve into the circular state with ${m}_{\ensuremath{\ell}}=+54$ defined with respect to the magnetic-field quantization axis. The circular states were detected by ramped electric-field ionization along the magnetic-field axis. The dependence of the circular state production efficiency on the strength of the excitation electric field, and the electric-field switch-off time was studied, and microwave spectroscopy of the circular-to-circular $|55,54,+54\ensuremath{\rangle}\ensuremath{\rightarrow}|56,55,+55\ensuremath{\rangle}$ transition at $\ensuremath{\sim}38.5$ GHz was performed.

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Rydberg states of helium in electric and magnetic fields of arbitrary relative orientation

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A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.

•Apr 1, 2016•5 citations
The influence of an external electric field on thermal collisions between a sodium atom excited in a ``circular'' Rydberg state (n=l+1=m+1=20) and a ground-state helium atom is studied numerically within the framework of the impulse approximation. The effect of the field is determined by using parabolic wave functions for the initial and final hydrogenic atomic states. The removal of degeneracy induced by the field appears to have no significant effect for fields in the range of 0--400 V/cm. However, the state-to-state transition cross sections are strongly dependent on the initial orientation as found in previous calculations without electric field.
A general formulation for thermal collisions between a Rydberg-state atom and a ground-state rare-gas atom is developed within the framework of the impulse approximation. This formulation allows calculation of cross sections for state-to-state transitions for an arbitrary initial orientation between the Rydberg-state atom and the relative velocity of the two partners of the collision. It also allows a direct computation of these cross sections averaged over all orientations, a situation corresponding to a cell experiment. In this formulation, the differential cross sections with respect to the modulus of the momentum transfer are obtained analytically in terms of rotation matrix elements. Numerical applications are made for the case of a sodium atom in a ``circular'' Rydberg state (\ensuremath{\Vert}n,l,m〉, with l=m=n-1) colliding with helium. The collisional processes are found to be highly anisotropic. In particular, a selection rule may appear, or disappear, depending upon the initial orientation. The extension to the case where an external electric field is present is also discussed, with special emphasis on symmetry properties.
The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms (n=10,15,and20n=10, 15, \mathrm{and} 20n=10,15,and20) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number mmm. The origin of this tendency is discussed.
Alignment and orientation effects in collisions of helium with Rydberg atoms due to the presence of static electric and magnetic fields are predicted. Analytical expressions are obtained for the cross sections of the state-to-state transitions within the manifold with the same principal quantum number. For moderate field-induced inelasticity, the curves of the cross sections vs the fields intensity show modulations that are explained in terms of the phase differences accumulated by the wave functions of the states involved in the collision. Due to the presence of the magnetic field, transitions involving inversion of high magnetic quantum numbers are dramatically quenched. The possibility of observing the predicted effects is discussed. The reported analytical cross sections are expected to help in the understanding of the results.
We report on field induced inelasticity effects in state-to-state transitions caused by collisions of helium with Rydberg atoms in the presence of parallel static electric and magnetic fields. Due to the phases accumulated by the wavefunctions of the states involved into the collision events, the transition cross sections plotted as a function of the external fields exhibit modulations. When the relative velocity of the colliding atoms is high enough, these modulations are wiped out, while sizable modifications of the cross sections may take place due to the alteration of the wavefunctions' spatial localization. The possibility of using the field-assisted collisions as a probe giving information on localization of the Rydberg states is discussed.
Helium atoms have been prepared in the circular $|n=55,\ensuremath{\ell}=54,{m}_{\ensuremath{\ell}}=+54\ensuremath{\rangle}$ Rydberg state using the crossed electric and magnetic fields method. The atoms, initially traveling in pulsed supersonic beams, were photoexcited from the metastable 1s2s3S11s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}1s2s3S1​ level to the outermost, ${m}_{\ensuremath{\ell}}=0$ Rydberg-Stark state with n=55n=55n=55 in the presence of a strong electric field and weak perpendicular magnetic field. Following excitation, the electric field was adiabatically switched off causing the atoms to evolve into the circular state with ${m}_{\ensuremath{\ell}}=+54$ defined with respect to the magnetic-field quantization axis. The circular states were detected by ramped electric-field ionization along the magnetic-field axis. The dependence of the circular state production efficiency on the strength of the excitation electric field, and the electric-field switch-off time was studied, and microwave spectroscopy of the circular-to-circular $|55,54,+54\ensuremath{\rangle}\ensuremath{\rightarrow}|56,55,+55\ensuremath{\rangle}$ transition at $\ensuremath{\sim}38.5$ GHz was performed.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.