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Physical Review Letters

Motional Stark Effect in High Magnetic Fields: A New Technique for Sub-Doppler Spectroscopy

M. Rosenbluh, Terry A. Miller, David M. Larsen, Benjamin Lax

Published Oct 3, 1977• 18 citations
Publisher

Abstract

We have observed transitions between Rydberg states of He with sub-Doppler resolution, using a novel technique. Ordinary Doppler line shapes, observed at low magnetic fields, are completely altered at high fields by the quadratic Stark effect induced by velocity-dependent electric fields arising from atomic motion transverse to the magnetic field. The high-field line shape has an abrupt cutoff, corresponding to ${v}_{\ensuremath{\perp}}\ensuremath{\simeq}0$ atoms, whose slope is primarily limited by the homogeneous linewidth.

DOI
10.1103/physrevlett.39.874

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•Jan 1, 2003•2 citations
We have observed transitions between Rydberg states of He with sub-Doppler resolution, using a novel technique. Ordinary Doppler line shapes, observed at low magnetic fields, are completely altered at high fields by the quadratic Stark effect induced by velocity-dependent electric fields arising from atomic motion transverse to the magnetic field. The high-field line shape has an abrupt cutoff, corresponding to v\ensuremath⊥\ensuremath≃0{v}_{\ensuremath{\perp}}\ensuremath{\simeq}0v\ensuremath⊥​\ensuremath≃0 atoms, whose slope is primarily limited by the homogeneous linewidth.
The high resolution two-photon spectroscopy of hydrogen is often limited by the second-order Doppler effect. To determine this effect, we apply a magnetic field perpendicular to the atomic beam. This field induces a quadratic motional Stark shift proportional, as the second-order Doppler effect, to v(2) (v atomic velocity). For some magnetic field, these two effects are opposite and the total shift due to the atomic velocity is reduced. We present the first observation of this effect for the 1S-3S transition in hydrogen.
Atoms moving through a magnetic field suffer a Stark effect whose magnitude is dependent upon the atom's velocity. This velocity-dependent perturbation has recently been exploited as a Doppler narrowing technique, and in this paper we consider atomic anticrossings induced by it. Experimentally such anticrossings are observed between $n^{3}D\ensuremath{-}n^{1,3}F$ states of He for $n=4\ensuremath{-}9$, with n=8n=8n=8 being considered in detail. Theoretical expressions are derived for motional-Stark-effect-induced anticrossing line shapes. Good agreement with the observed line shapes is obtained and the theoretical analysis allows a value of the $n=^{3}D\ensuremath{-}^{1,3}F$ interval to be obtained which is in good agreement with previous predictions.
Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.
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.
In highly excited Rydberg atoms, the excited electron is in a large, loosely bound orbit. Hence, in contrast with the ground states, the Rydberg states are very sensitive to external electric field and can be ionized in rather weak fields. The low ionization threshold of Rydberg states results in effective state-specific detection by the selective field ionization technique. \t In this thesis, high-resolution spectroscopy of Rydberg states of Rubidium using millimeter wave transitions and selective field ionization has been used as a probe of external electric and magnetic fields. Laser cooling and trapping techniques in a magneto-optical trap (MOT) are employed to have a high density and narrow velocity distribution for the atomic sample. In this work the magnetic field inhomogeneity inherent in a MOT is minimized and the stray electric field present at the trap region is compensated in order to have resolved spectra. The Stark line broadening of the spectra obtained in this work may be used to determine the electric field distribution in an expanding ultra-cold neutral plasma.