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Physical Review A

Theory of the light-force technique for measuring polarizabilities

Keith Bonin, Michael A. Kadar-Kallen

Published Feb 1, 1993• 29 citations
Publisher

Abstract

The theory of a method to measure electric-dipole polarizabilities is presented. The method uses two-stage laser ablation to produce a pulsed beam of atoms from a solid target. A pair of slits makes the velocity distribution of the atomic beam nonuniform in a way that is well characterized. The light-force technique uses the polarization forces experienced by an atom in the intense, inhomogeneous electromagnetic field of a standing-wave laser to change the velocity distribution of the atomic beam. The large forces cause measurable Doppler shifts in the resonant frequency of the atoms. These frequency shifts change the amount of absorption of resonant light, yielding information about the change in the velocity distribution of the atoms. The detailed shape of the final absorption distribution is polarizability dependent. In the classical picture of the light force, the standing-wave electric field induces a time-varying dipole moment in each atom. Each atom then experiences a Lorentz force due to coherent interaction of the oscillating dipole moment with the time-varying magnetic field. The quantum-mechanical picture corresponds to the Kapitza-Dirac effect for atoms: an atom absorbs a photon from one of the two beams which form the standing wave, and is then stimulated to emit this photon by the other, counterpropagating beam. This paper provides a classical treatment of the light force experienced by an atom in a standing-wave light field; the polarizability is treated quantum mechanically. The theory presented here can be applied to atoms with a scalar polarizability, such as rubidium, and to atoms with significant tensor components, such as uranium. Experimental results from application of the light-force technique to a measurement of the polarizability of rubidium are also presented.

DOI
10.1103/physreva.47.944

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We have been working on the development of a technique for determining the static polarizabilities of refractory metal atoms. The technique involves producing a dense, cold atomic beam (n {approx equal}10{sup 11} {minus} 10{sup 12} atoms/cm{sup 3}, T {perpendicular} {approx equal} 5 mK) that is illuminated for a short time by a standing wave formed by a Nd:YAG laser. This technique would have an impact on laser isotope separation, ion mobility physics, and theoretical atomic physics. The interaction between the atoms and the laser light results in velocity kicks to the atoms along the two directions defined by the photons in the laser standing wave. The velocity kicks force the atoms to form into planes of alternating high and low density downstream. By Bragg scattering near-resonant light off these planes the static polarizability can be determined. The velocity kicks will also cause the atomic density distribution further downstream to take on a bimodal appearance. A measurement of the separation of the peaks of this distribution can be used to determine the polarizability. Here we report our progress on this technique and the present status of the experiments. A new method for producing focused beams of neutrals, ions, and clusters usingmore » two-stage laser ablation has been developed as a result of our experiments. 7 refs., 12 figs.« less

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We have observed both diffractive and diffusive regimes in the transfer of momentum to an atomic beam by a standing-wave radiation field. The momentum transfer was measured by passing a well-collimated beam of sodium atoms through a focused standing-wave laser waist. A narrow velocity distribution beam was obtained by utilizing a supersonic expansion and a two-state system was realized by optically pumping the beam prior to the interaction. The transverse momentum transferred to the atomic beam by the radiation field was measured by scanning a detector downstream from the interaction. The overall momentum resolution of the apparatus is less than the momentum of a single photon. The transition from diffractive to diffusive behavior is associated with an increase in the average number of spontaneous decays occurring during the interaction. In the diffractive regime, spontaneous decay is insignificant and momentum transfer proceeds by pairs of absorption/stimulated emission processes. This produces momentum exchange quantized in even multiples of photon momentum, the so-called Kapitza-Dirac effect; the deflection patterns show oscillatory structure. In the diffusive regime, spontaneous decay is important and causes fluctuations in the radiative forces. In addition, the recoil distribution associated with spontaneous decay results in a washing out of the diffraction peaks associated with stimulated processes, resulting in a smooth deflection pattern.

International Laser Science Conference•Jan 1, 1986•0 citations
The theory of a method to measure electric-dipole polarizabilities is presented. The method uses two-stage laser ablation to produce a pulsed beam of atoms from a solid target. A pair of slits makes the velocity distribution of the atomic beam nonuniform in a way that is well characterized. The light-force technique uses the polarization forces experienced by an atom in the intense, inhomogeneous electromagnetic field of a standing-wave laser to change the velocity distribution of the atomic beam. The large forces cause measurable Doppler shifts in the resonant frequency of the atoms. These frequency shifts change the amount of absorption of resonant light, yielding information about the change in the velocity distribution of the atoms. The detailed shape of the final absorption distribution is polarizability dependent. In the classical picture of the light force, the standing-wave electric field induces a time-varying dipole moment in each atom. Each atom then experiences a Lorentz force due to coherent interaction of the oscillating dipole moment with the time-varying magnetic field. The quantum-mechanical picture corresponds to the Kapitza-Dirac effect for atoms: an atom absorbs a photon from one of the two beams which form the standing wave, and is then stimulated to emit this photon by the other, counterpropagating beam. This paper provides a classical treatment of the light force experienced by an atom in a standing-wave light field; the polarizability is treated quantum mechanically. The theory presented here can be applied to atoms with a scalar polarizability, such as rubidium, and to atoms with significant tensor components, such as uranium. Experimental results from application of the light-force technique to a measurement of the polarizability of rubidium are also presented.
A light-force technique for measuring polarizabilities is being used to measure the polarizability of the uranium atom. The technique uses a pulsed Nd:YAG laser to produce an intense, standing-wave field that provides velocity kicks to atoms that traverse the field region. These velocity kicks result in Doppler-shifted absorption by the atoms. The change in absorption of resonant light, provided by a tunable diode laser is measured. This measurement and a measurement of the standing-wave laser fluence allow determination of the polarizability. We plan to report the results of our measurements, along with a new scheme for generating a dense beam of uranium atoms.
We have developed a light-force technique for measuring polarizabilities. This new method uses the polarizaton forces experienced by an atom in the intense, inhomogeneous electric field of a standing-wave laser to deduce the polarizability. Using a Nd:YAG laser at ${\ensuremath{\lambda}}_{\mathrm{SW}}$=1.064 \ensuremath{\mu}m for the light force, we measured the polarizability of rubidium at this wavelength to be \ensuremath{\alpha}(${\mathrm{\ensuremath{\omega}}}_{\mathrm{SW}}$)=114\ifmmode\pm\else\textpm\fi{}9 A˚3{\mathrm{\r{}}}^{3}˚3 (\ensuremath{\sigma}). Conversion of this ac polarizability to a static value using a semiempirical formula gives a value of ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{dc}}$=52 A˚3{\mathrm{\r{}}}^{3}˚3, within 10% of the best published experimental results.
We have been working on the development of a technique for determining the static polarizabilities of refractory metal atoms. The technique involves producing a dense, cold atomic beam (n {approx equal}10{sup 11} {minus} 10{sup 12} atoms/cm{sup 3}, T {perpendicular} {approx equal} 5 mK) that is illuminated for a short time by a standing wave formed by a Nd:YAG laser. This technique would have an impact on laser isotope separation, ion mobility physics, and theoretical atomic physics. The interaction between the atoms and the laser light results in velocity kicks to the atoms along the two directions defined by the photons in the laser standing wave. The velocity kicks force the atoms to form into planes of alternating high and low density downstream. By Bragg scattering near-resonant light off these planes the static polarizability can be determined. The velocity kicks will also cause the atomic density distribution further downstream to take on a bimodal appearance. A measurement of the separation of the peaks of this distribution can be used to determine the polarizability. Here we report our progress on this technique and the present status of the experiments. A new method for producing focused beams of neutrals, ions, and clusters usingmore » two-stage laser ablation has been developed as a result of our experiments. 7 refs., 12 figs.« less
An atom interferometer using Bose-Einstein condensates has been implemented and is used to measure the dynamic polarizability of 87Rb. An off-resonant standing-wave laser beam is used to manipulate the motion of atomic wavepackets in order to implement splitting and reflection operations. It is demonstrated that these operations can be performed with near unity fidelity. Interferometer times of up to 72 ms as well as arm separations of up to 0.42 mm are achieved experimentally. The primary limitation for guided-wave atom interferometers with a large arm separation is found to be the effect of the confining potential along the waveguide axis. Such a potential causes a spatially varying phase shift on the wavepackets as they propagate in the interferometer. Different parts of the cloud therefore interfere with different phases, leading to a reduction of the interferometer contrast. A model of the phase shifts on the wavepackets agrees well with the experimental data. In a different scheme in which the wavepackets oscillate freely in the confining potential, these phase shifts completely cancel. Interference is observed at times up to 0.9 s in this case, but with a fluctuating overall phase of the output, which is attributed to mechanical instabilities. Finally, the dynamic polarizability of 87Rb is measured. A well-calibrated laser beam is applied to one atomic packet and not the other, inducing a differential phase shift. This technique requires relatively low laser intensity and works for arbitrary optical frequencies. For offresonant light, the ac polarizability is obtained with a statistical accuracy of 3% and a calibration uncertainty of 6%. On resonance, the dispersion-shaped behavior of the Stark shift is observed, but with a broadened linewidth that is attributed to multiple and collective light scattering effects. The resulting nonlinearity may prove useful for the production and control of squeezed quantum states. In general, this work also demonstrates the applicability of condensate interferometry to practical measurements.
We show that the dressed-atom approach provides a quantitative understanding of the main features of radiative dipole forces (mean value, fluctuations, velocity dependence) in the high-intensity limit where perturbative treatments are no longer valid. In an inhomogeneous laser beam, the energies of the dressed states vary in space, and this gives rise to dressed-state-dependent forces. Spontaneous transitions between dressed states lead to a multivalued instantaneous force fluctuating around a mean value. The velocity dependence of the mean force is related to the modification, induced by the atomic motion, of the population balance between the different dressed states. The corresponding modification of the atomic energy is associated with a change of the fluorescence spectrum emitted by the atom. The particular case of atomic motion in a standing wave is investigated, and two regimes are identified in which the mean dipole force averaged over a wavelength exhibits a simple velocity dependence. The large values of this force achievable with reasonable laser powers are pointed out with view to slowing down atoms with dipole
We have observed both diffractive and diffusive regimes in the transfer of momentum to an atomic beam by a standing-wave radiation field. The momentum transfer was measured by passing a well-collimated beam of sodium atoms through a focused standing-wave laser waist. A narrow velocity distribution beam was obtained by utilizing a supersonic expansion and a two-state system was realized by optically pumping the beam prior to the interaction. The transverse momentum transferred to the atomic beam by the radiation field was measured by scanning a detector downstream from the interaction. The overall momentum resolution of the apparatus is less than the momentum of a single photon. The transition from diffractive to diffusive behavior is associated with an increase in the average number of spontaneous decays occurring during the interaction. In the diffractive regime, spontaneous decay is insignificant and momentum transfer proceeds by pairs of absorption/stimulated emission processes. This produces momentum exchange quantized in even multiples of photon momentum, the so-called Kapitza-Dirac effect; the deflection patterns show oscillatory structure. In the diffusive regime, spontaneous decay is important and causes fluctuations in the radiative forces. In addition, the recoil distribution associated with spontaneous decay results in a washing out of the diffraction peaks associated with stimulated processes, resulting in a smooth deflection pattern.