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Physical Science International Journal

Laser Cooling of Radium Atoms, Computational Investigation

Nafie Abdallatief Almuslet, Iman Elhaj

Published Dec 9, 2017• 0 citations
Publisher

Abstract

In this work Matlab simulation of the atomic Liouville equation for spontaneous emissions was developed for laser cooling of Radium atoms. The atomic decay time driven was determined according to the photon account. The theory includes the mechanical light effect for to atomic structure. The study followed the stimulating solution of Optical Bloch Equations (OBE’s) for four levels system in an atom trap, where the center of mass motion is described quantum mechanically. The results showed that the laser cooling approach to Maxwell’s law, the reduction of the velocity leads to new distribution of velocities and the atoms moving towards the light source will resonate the light field (crossing resonance).

DOI
10.9734/psij/2017/37726

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In this work Matlab simulation of the atomic Liouville equation for spontaneous emissions was developed for laser cooling of Radium atoms. The atomic decay time driven was determined according to the photon account. The theory includes the mechanical light effect for to atomic structure. The study followed the stimulating solution of Optical Bloch Equations (OBE’s) for four levels system in an atom trap, where the center of mass motion is described quantum mechanically. The results showed that the laser cooling approach to Maxwell’s law, the reduction of the velocity leads to new distribution of velocities and the atoms moving towards the light source will resonate the light field (crossing resonance).
A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.
The bichromatic force allows laser cooling using stimulated processes only. We provide details of our simulations of the bichromatic force when the effects of spontaneous emission are suppressed by restricting the atom-light interaction time to be short enough that there cannot be a significant number of spontaneous emission events. This short interaction time requires that the simulation include dynamics of the atomic motion through the light field that is coupled to the internal state dynamics that determine the force on the atom. The simulation is first tested with several standard optical field configurations to confirm its accuracy. Then the results, using conditions that match our experiment, are presented and compared with our measurements. The simulation shows that the resolution of the experiment greatly obscures the degree of cooling. Our simulation predicts an observed velocity distribution reduced by up to a factor of 4 in width over a time comparable to the excited state lifetime. This technique can allow the direct laser cooling of atoms and molecules without closed cycling transitions.
In the limit of asymptotically small photon momentum, a Fokker–Planck equation for the center-of-mass Wigner function suffices to describe laser cooling of an atom. We have devised a procedure to compute the light pressure force and the diffusion tensor for an atom with an arbitrary level structure, traveling with an arbitrary velocity in any given three-dimensional light field. The scheme is based on solving a set of differential equations closely related to the density matrix equations of motion encountered in conventional recoilless laser spectroscopy. Computer programs have been written that automatically construct and solve the required equations from broad specifications of the problem, such as energies and angular momenta of the atomic levels. A Langevin equation stochastic simulation has been implemented to solve the Fokker-Planck equation of laser cooling using the computed force and diffusion. Comparisons of optical-molasses experiments and simulations carried out for a model sodium atom with a J = 2→J = 3 transition show qualitative similarities such as sub-Doppler limit temperatures, but the quantitative agreement of theory and experiment is not satisfactory.
A theory to describe collisions between pairs of atoms that are being cooled by a laser field is presented. The derivation uses the Heisenberg picture and results in a set of coupled optical Bloch equations and associated equations for the translational motion. By defining a correlation variable between the two atoms, we obtain a system of linear equations that may be solved numerically. If the interaction is ignored, the usual cooling curve is obtained: In the full simulation it is found that long-range collisions (0.1ƛ → 10ƛ) can significantly alter the atomic velocities. Depending on how the atoms approach each other, there are various effects: jumps in velocity at the center of the collision, interruptions of the cooling cycle, and signs of collective effects for long-range collisions. If the atom density is sufficiently large and the atoms are moving slowly, these collisional mechanisms may prevent any further cooling.
A discrete velocity model of the Boltzmann equation is established to investigate the effect of atomic beam slowing and cooling by means of laser light. Due to momentum transfer, caused by absorption and emission processes of photons, atoms are slowed. The Doppler effect, however, allows only selected atoms within a certain resonance range to interact with the laser field. To overcome this problem an external electric field is maintained. Semianalytical results of the velocity distribution as a function of the deceleration path of both ground level atoms and excited atoms are presented in detail and studied explicitly for various values of the laser intensity. A cooling limit is given and compared with quantum mechanical results.
We present a theoretical analysis of a new one-dimensional laser-cooling scheme that was recently demonstrated on a beam of metastable 4He atoms. Both internal and translational degrees of freedom are treated quantum mechanically. Unlike semiclassical approaches, such a treatment can be applied to situations in which the atomic coherence length is of the same order of or larger than the laser wavelength, which is the case for atoms cooled below the one-photon recoil energy. We introduce families of states that are closed with respect to absorption and stimulated emission, and we establish the generalized optical Bloch equations that are satisfied by the corresponding matrix elements. The existence of velocity-selective trapping states that are linear combinations of states with different internal and translational quantum numbers is demonstrated, and the mechanism of accumulation of atoms in these trapping states by fluorescence cycles is analyzed. From a numerical solution of the generalized optical Bloch equations, we study in detail how the final atomic-momentum distribution depends on the various physical parameters: interaction time, width of the initial distribution, laser detuning, laser power, and imbalance between the two counterpropagating waves. We show that the final temperature decreases when the interaction time increases, so that there is no fundamental limit to the lowest temperature that can be achieved by such a method. Finally, possible extensions of this method to two-dimensional cooling are presented.