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Communications in Theoretical Physics

Optical forces on neutral atoms in the presence of fluctuating laser fields: numerical analysis

Forough Bozorgzadeh, Masoud Yousefi, Mohsen Akbari

Published Nov 1, 2022• 1 citation
Publisher

Abstract

Abstract Doppler cooling of 88Sr atoms is studied in the presence of off-resonant red-detuned fluctuating laser fields. Using a semi-classical approach, we show that the relevant physical quantities in the cooling process, such as optical forces, the damping coefficient, Doppler temperature, and atom number in the trap, are strongly affected by the laser amplitude and phase fluctuations. We find that the Doppler cooling limit is higher than the predicted Doppler theory for non-fluctuating lasers. This implies an additional heating mechanism exists due to the laser fluctuations. Furthermore, our numerical analysis shows that the effect of laser power stability on reducing the number of trapped atoms in a magneto-optical trap is more substantial than the effect of laser linewidth.

DOI
10.1088/1572-9494/ac9f09

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Abstract Doppler cooling of 88Sr atoms is studied in the presence of off-resonant red-detuned fluctuating laser fields. Using a semi-classical approach, we show that the relevant physical quantities in the cooling process, such as optical forces, the damping coefficient, Doppler temperature, and atom number in the trap, are strongly affected by the laser amplitude and phase fluctuations. We find that the Doppler cooling limit is higher than the predicted Doppler theory for non-fluctuating lasers. This implies an additional heating mechanism exists due to the laser fluctuations. Furthermore, our numerical analysis shows that the effect of laser power stability on reducing the number of trapped atoms in a magneto-optical trap is more substantial than the effect of laser linewidth.
The influence of laser linewidth Γ 1 on laser cooling of atoms was investigated theoretically by using a diffusing phase model. The final temperature which can be achieved by Doppler cooling or sub-Doppler cooling in phase fluctuating laser field is presented. It was found that the natural linewidth Γ n of the transition used for cooling the atoms is an important quantity in evaluating the influence of Γ 1 under Doppler cooling mechanism, and the laser linewidth has little effect on the final temperature under sub-Doppler cooling mechanism because the laser detuning is very large in this case.
We analyze the influence of an arbitrarily directed uniform magnetic field on the laser sub-Doppler cooling of atoms. The analysis is done for a (3+5)-level atom excited by a ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ laser field configuration. Our analysis shows that the effects of the magnetic field depend strongly on the direction of the magnetic field. In an arbitrarily directed magnetic field the laser cooling configuration produces both the main resonance existing already at zero magnetic field and additional sub-Doppler resonances caused by two-photon and higher-order multiphoton processes. These sub-Doppler resonances are, however, well separated on the velocity scale if the Zeeman shift exceeds the widths of the resonances. This allows one to use the main sub-Doppler resonance for an effective laser cooling of atoms even in the presence of the magnetic field. The effective temperature of the atomic ensemble at the velocity of the main resonance is found to be almost the same as in the absence of the magnetic field. The defined structure of the multiphoton resonances may be of importance for the sub-Doppler laser cooling of atoms, atomic extraction from magneto-optical traps, and applications related to the control of atomic motion.
We present a simple review of the basic physical processes allowing one to control, with laser beams, the velocity and the position of neutral atoms. The control of the velocity corresponds to a cooling of atoms, that is, a reduction of the atomic velocity spread around a given value. The control of the position means a trapping of atoms in real space. The best present performances will be given, in terms of the lowest temperatures and the highest densities. The corresponding highest quantum degeneracy will also be estimated. It is imposed by fundamental limits, which will be described briefly. We also give the general trends in this field of research and outline the new directions which look promising for observing quantum statistical effects in laser cooled atomic samples, but which are for the moment restricted by unsolved problems. Introducing the Simple Schemes The radiative forces acting on atoms in a light field can be split into two parts, a reactive one and a dissipative one. The dissipative force (radiation pressure), which basically involves scattering processes, is velocity dependent. We will see that this dependence leads to the Doppler cooling scheme and to the concept of optical molasses, and we will give the corresponding minimal achievable temperature. The dissipative force can be made position dependent, through a gradient of the magnetic field, so that the atoms are also trapped in the so-called magneto-optical trap.
We theoretically investigate the damping and trapping forces in a three-dimensional magneto-optical trap (MOT), by numerically solving the optical Bloch equations.We focus on the case where there are dark states because the atom is driven on a 'type-II' system where the angular momentum of the excited state, F¢, is less than or equal to that of the ground state, F. For these systems we find that the force in a three-dimensional light field has very different behaviour to its one dimensional counterpart.This differs from the more commonly used 'type-I' systems (F F 1 ¢ = + ) where the 1D and 3D behaviours are similar.Unlike type-I systems where, for red-detuned light, both Doppler and sub-Doppler forces damp the atomic motion towards zero velocity, in type-II systems in 3D, the Doppler force and polarization gradient force have opposite signs.As a result, the atom is driven towards a non-zero equilibrium velocity, v 0 , where the two forces cancel.We find that v 0 2 scales linearly with the intensity of the light and is fairly insensitive to the detuning from resonance.We also discover a new magneto-optical force that alters the normal MOT force at low magnetic fields and whose influence is greatest in the type-II systems.We discuss the implications of these findings for the laser cooling and magneto-optical trapping of molecules where type-II transitions are unavoidable in realising closed optical cycling transitions.
We report on the observation of a new laser trap for neutral atoms. It uses three orthogonal pairs of counterpropagating laser beams having linear polarizations at 45° and a quadrupole magnetic field. 10 8 cesium atoms were thus confined in a 0.15 mm 3 volume at a temperature of 60 μK, a factor of 2 below the Doppler cooling limit. We interpret this trapping as being due to the new magneto-optical force recently observed by Grimm et al. and which is essentially a dipole force rectified by the magnetic field. This trap opens new possibilities for increasing the phase-space density of laser-cooled atoms.
We report a frequency stabilization technique of a diode laser in a Doppler-free atomic transition used for obtaining the magneto-optical trapping of Rb atoms. This technique, based on side locking to an atomic transition using a servo controller, is very simple and can be implemented straightforwardly to lock the laser at the red detuned frequency position required for laser cooling experiments. The number of trapped atoms and the temperature of the cold cloud have been determined. The effect of trapping the magnetic field on the cloud radius has also been analyzed.