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Physical Review A

Dynamic Stark shift and alignment-to-orientation conversion

Matthew C. Kuntz, Robert C. Hilborn, Alison M. Spencer

Published Jan 15, 2002• 9 citations
Publisher

Abstract

We have observed alignment-to-orientation conversion in the $(5d6p)$ ${}^{1}P$ state of atomic barium due to the combined effects of a static Zeeman shift and a dynamic Stark shift associated with the electric field of a pulsed laser beam. The measurements yield a value for the frequency-dependent tensor polarizability of the state in reasonable agreement with a simple perturbation theory calculation. With a tunable laser producing the dynamic Stark shift, we can both enhance the magnitude of the effect by tuning close to a resonance and reverse the sign of the orientation by tuning above or below the resonance. This method of producing an oriented atomic state is quite general, and with easily available field strengths can produce large orientations.

DOI
10.1103/physreva.65.023411

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We have observed alignment-to-orientation conversion in the (5d6p)(5d6p)(5d6p) 1P{}^{1}P1P state of atomic barium due to the combined effects of a static Zeeman shift and a dynamic Stark shift associated with the electric field of a pulsed laser beam. The measurements yield a value for the frequency-dependent tensor polarizability of the state in reasonable agreement with a simple perturbation theory calculation. With a tunable laser producing the dynamic Stark shift, we can both enhance the magnitude of the effect by tuning close to a resonance and reverse the sign of the orientation by tuning above or below the resonance. This method of producing an oriented atomic state is quite general, and with easily available field strengths can produce large orientations.
We present an alternative method for changing atomic alignment to orientation through interactions with orthogonal static electric and magnetic fields. Experimental results demonstrating this effect in the 5d6p 1^{1}1P state of atomic barium and the F=4 hyperfine level of the ground state of atomic cesium are presented. The theory of this effect for a j=0 to j=1 electric dipole transition is discussed in detail. The tensor polarizability of the 5d6p 1^{1}1P state of Ba is determined to be 1.31(15) MHz/(kV/cm)2{)}^{2})2, in good agreement with the results of van Leeuwen and Hogervorst [Z. Phys. A 310, 37 (1983)].
The Stark shift of the (6s)2{)}^{2})2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}(6s6p)1{)}^{1})1P1{\mathit{P}}_{1}P1​ transition in barium was measured using a laser to excite an atomic beam as it traversed a uniform electric field and a field-free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using an acousto-optic modulator which frequency shifted the laser by a specified amount. The Stark-shift rate was found to be -28.532\ifmmode\pm\else\textpm\fi{}0.060 kHz/(kV/cm)2{)}^{2})2. The hyperfine splitting of the 135,137Ba^{135,137}\mathrm{Ba}135,137Ba F=1/2 level relative to 138Ba^{138}\mathrm{Ba}138Ba of the (6s6p)1{)}^{1})1P1{\mathit{P}}_{1}P1​ state was determined to be -549.47\ifmmode\pm\else\textpm\fi{}0.12 MHz, where the minus sign indicates that the 138Ba^{138}\mathrm{Ba}138Ba transition is at a lower frequency.
The time evolution of alignment and orientation of excited atoms in an electric field is described using a density-matrix treatment. Orientation is produced by applying a tilted static electric field on levels aligned by beam-foil interaction. The modulation of polarization of the light is observed either inside the zone of constant field, by moving along the atomic beam, or downstream, in the field-free zone, by sweeping the field strength. Two different geometries are used for relative directions of ion beam, electric field vector, and foil normal. Tensor polarizabilities and cross sections for excitation of Zeeman sublevels are deduced from frequencies and amplitudes of quantum beat signals. Results are given for n 1{\mathrm{}}^{1}1D2{D}_{2}D2​ levels of 4i(n=3^{4}\phantom{\rule{0ex}{0ex}}\mathrm{i}\phantom{\rule{0ex}{0ex}}(\mathit{n}=34i(n=3, 4, and 5).
The Stark shift of the (6s) 2 1 S 0 to (6s6p) 3 P 1 transition in ytterbium was measured using a laser to excite an atomic beam first in a uniform electric field and subsequently in a field-free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using isotope and hyperfine splittings that have been measured previously. The Stark shift rate was found to be -15.419+or-0.048 kHz kV -2 cm -2 and the tensor polarizability of the (6s6p) 3 P 1 state was determined to be alpha 2 =5.81+or-0.13 kHz kV -2 cm -2 .
We present a detailed theoretical model and experimentally measured signals of alignment to orientation conversion (AOC) in the 7D3/2 and 9D3/2 states of cesium atoms in the presence of an external dc electric field [1]. Alignment produced by linearly polarized light can be converted into orientation by the quadratic Stark effect in an electric field if the angle between the electric field and the polarization vector of the exciting radiation is neither 0 or 90 degrees and if there are magnetic sublevels with Δm = ±1 that cross as the electric field is scanned. The appearance of orientation is verified by the appearance of a net circular polarization in the laser induced fluorescence. The theoretical model is based on the optical Bloch equation and extends models previously developed to solve the rate equations for Zeeman coherences in single-step [2] and double step laser excitation [3] of atoms. The agreement between the simulated and measured signals is excellent.
We demonstrate that when laser light is circularly polarized and properly detuned, the ac Stark shift of an alkali-metal atom in its ground state takes the form of a pure Zeeman shift. The condition is satisfied when the laser frequency is between the D1D1D1 and D2D2D2 transition frequencies, with the size of the detuning from the D2D2D2 resonance twice that from the D1D1D1 resonance. The direction of the effective magnetic field is along the laser propagation axis, and its magnitude is proportional to the vector polarizability of the atom and to the laser intensity. We use stimulated Raman spectroscopy on an optically pumped slow atomic beam from a magneto-optical trap to measure the vector polarizability and saturated absorption spectroscopy to show that the scalar polarizability vanishes at the particular detuning.