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Journal of Modern Optics

The Effect of a Fluctuating Laser Field on the Process of Decelerating Atoms in the Zeeman Tuning Technique

Reginaldo de Jesus Napolitano, Vanderlei Salvador Bagnato

Published Feb 1, 1993• 2 citations
Publisher

Abstract

We present a study on the process of atomic deceleration in the Zeeman tuning technique when a fluctuating laser is used. The characterization of the deceleration is made through the analysis of velocity trajectories (k v(z)) from integration of the averaged equation of motion obtained from the Bloch optical equations. Atomic motion described from an accelerated frame of reference aids the analysis of the process. It is shown that the capability of an atom to follow a magnetic field profile is more sensitive to amplitude than to phase fluctuations. The analysis presented here permits evaluation of laser quality beam on optical deceleration of atoms.

DOI
10.1080/09500349314550331

Related papers

Deceleration of atoms with a fluctuating laser field

Reginaldo de Jesus Napolitano, Vanderlei Salvador Bagnato

In a recent publication1 we have analyzed the stability of the deceleration process of atoms in the Zeeman tuning technique2 by looking at the velocity profile of the atoms along the magnetic field. When the velocity [v(z)] follows the field profile [B(z)] we refer to this as adiabatic following of atoms because the absorption is adiabatically adjusted to each position so that v(z) follows B(z). This situation does not hold everywhere; in fact, at points where the absorption cannot be adiabatically adjusted the velocity ceases to follow the field interrupting the deceleration. The existence of fluctuations on the laser field produces dramatic changes on the expected behavior of the atoms during the deceleration. We have made numerical simulation and analytical investigation where v(z) is obtained for cases where the laser field has frequency and amplitude fluctuations produced by Markovian and Gaussian stochastic processes. In both cases, the deceleration is dependent on the spectral densities of the fluctuations. The process seems to be more sensitive to amplitude than to frequency fluctuation. These results are important in determining the desired characteristics of the laser source on atoms deceleration experiments.

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We report on the use of a stimulated Raman transition in a slowed atomic beam to produce a narrow velocity distribution of atoms in a selected electronic state, which could be used for atomic collisions studies in the low temperature regime(1). The velocity selection is part of the deceleration process and in this sense it is unique. The atomic beam is decelerated by the radiation pressure force exerted on the atoms by a counter- propagating laser beam. The resonance condition is maintained along the deceleration path because the changing Doppler shift is compensated by Zeeman tuning the electronic sublevels(2) with a spatialy inhomogneous magnetic field. At the end of the slowing process, the initial Maxwell-Boltzman distribution is compressed to a narrow velocity distribution (Δv ~ 50 m/s), centered close to v = 0. This velocity bunching(3) increases considerably the number of atoms in each velocity class, allowing the use of velocity selection techniques as a feasible way of studying low velocity collisions.

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We report an observation of atoms stopped by laser light in an experiment using the Zeeman tuning technique. In contrast to previous experiments using the same technique, we are able to stop the atoms outside the slower solenoid using a single laser. The deceleration process is monitored through the measurement of the fluorescence along the deceleration path in such a way that the slower laser is also used for diagnosis. This technique also permits the realization of a few interesting observations on the process such as the position where the atoms stop scattering photons.

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Atomic motion in resonant fluctuating laser radiation

R. J. Cook

The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.

Physical Review A•Jan 1, 1980•26 citations
We present a study on the process of atomic deceleration in the Zeeman tuning technique when a fluctuating laser is used. The characterization of the deceleration is made through the analysis of velocity trajectories (k v(z)) from integration of the averaged equation of motion obtained from the Bloch optical equations. Atomic motion described from an accelerated frame of reference aids the analysis of the process. It is shown that the capability of an atom to follow a magnetic field profile is more sensitive to amplitude than to phase fluctuations. The analysis presented here permits evaluation of laser quality beam on optical deceleration of atoms.
In a recent publication1 we have analyzed the stability of the deceleration process of atoms in the Zeeman tuning technique2 by looking at the velocity profile of the atoms along the magnetic field. When the velocity [v(z)] follows the field profile [B(z)] we refer to this as adiabatic following of atoms because the absorption is adiabatically adjusted to each position so that v(z) follows B(z). This situation does not hold everywhere; in fact, at points where the absorption cannot be adiabatically adjusted the velocity ceases to follow the field interrupting the deceleration. The existence of fluctuations on the laser field produces dramatic changes on the expected behavior of the atoms during the deceleration. We have made numerical simulation and analytical investigation where v(z) is obtained for cases where the laser field has frequency and amplitude fluctuations produced by Markovian and Gaussian stochastic processes. In both cases, the deceleration is dependent on the spectral densities of the fluctuations. The process seems to be more sensitive to amplitude than to frequency fluctuation. These results are important in determining the desired characteristics of the laser source on atoms deceleration experiments.
We report on the use of a stimulated Raman transition in a slowed atomic beam to produce a narrow velocity distribution of atoms in a selected electronic state, which could be used for atomic collisions studies in the low temperature regime(1). The velocity selection is part of the deceleration process and in this sense it is unique. The atomic beam is decelerated by the radiation pressure force exerted on the atoms by a counter- propagating laser beam. The resonance condition is maintained along the deceleration path because the changing Doppler shift is compensated by Zeeman tuning the electronic sublevels(2) with a spatialy inhomogneous magnetic field. At the end of the slowing process, the initial Maxwell-Boltzman distribution is compressed to a narrow velocity distribution (Δv ~ 50 m/s), centered close to v = 0. This velocity bunching(3) increases considerably the number of atoms in each velocity class, allowing the use of velocity selection techniques as a feasible way of studying low velocity collisions.
We report an observation of atoms stopped by laser light in an experiment using the Zeeman tuning technique. In contrast to previous experiments using the same technique, we are able to stop the atoms outside the slower solenoid using a single laser. The deceleration process is monitored through the measurement of the fluorescence along the deceleration path in such a way that the slower laser is also used for diagnosis. This technique also permits the realization of a few interesting observations on the process such as the position where the atoms stop scattering photons.
The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.