Doppler cooling force

For small ion velocities the Doppler cooling force in Equations 10.11 and 10.12 can be approximated by a viscous damping force that is proportional to velocity, Pooppd =. where Y is a constant that depends on the laser wavelength, inten-... 

In this section, various effects that can limit the accuracy of the SCSI-MS technique are considered. In particular, deviations from the idealized case considered in Section 10.3.4, due to finite size motional amplitudes and the effects of the Doppler cooling force will be discussed. 

The effects of anharmonic terms have been sought experimentally by measuring the COM mode frequency at different amplitudes for two " Ca ions. Because the non-linearity of the Coulomb force does not affect the oscillation frequency in this case, any amplitude dependence should be due to either anharmonicity or the nonlinear velocity dependence of the Doppler cooling force as discussed in Section 10.5.1. As shown in Figure 10.7, at amplitudes between 15 pm and 35 pm, the measured COM frequencies near 95.625 kHz differ by less than 20 Hz and are equal within the error bars. Hence, at least at the level of 2 x 10" anharmonic effects can be ignored. Furthermore, if anharmonic effects were significant, a frequencypulling effect should have been apparent, but no such effect was observed. 

This expression shows diat if die detuning Acuj is negative (i.e. red detuned from resonance), dieii die cooling force will oppose die motion and be proportional to die atomic velocity. The one-diniensional motion of die atom, subject to an opposing force proportional to its velocity, is described by a damped haniionic oscillator. The Doppler damping or friction coefficient is die proportionality factor. 

The value of the temperature in eqn (5.3) is nowadays referred to as the Doppler temperature or Doppler cooling limit. At a typical value of the natural hnewidth of an allowed transition 2y = 27t X 10 MHz, the temperature To is of the order of 100 pK. Because of the great promise that laser cooling and subsequent laser trapping of atoms held for laser spectroscopy, researchers at the Institute of Spectroscopy in Troitsk, Russia, launched experiments in this field. By the time the first successful experiment was conducted (Andreyev et al. 1981, 1982), the first theoretical work, summarized in a review of the manipulation of atoms by the light pressure force of a resonant laser (Letokhov and Minogin 1981a), had already been completed. 

Wab Equation (13.20) expresses the differences in the probabilities of recoil momentum transfer for atoms with k v < 0 and k y > 0. The numerator in (13.20) can take positive and negative values depending on w. If the Doppler shift kv becomes smaller than the natural linewidth y, the positive and negative contributions nearly cancel and the cooling force becomes exceedingly small. 

Not only can the radiation pressure force lead to ion cooling through the Doppler-effect, but it can be used further to exert a periodic force on the atomic ions. By modulating the intensity of one of the two laser-cooling beams propagating along... 

Doppler laser-cooling is an essential ingredient in the SCSI-MS technique. First, it provides the necessary damping force to cool directly and sympathetically the atomic and molecular ions, respectively, such that a cold and strongly-coupled two-ion system is formed. Second, it gives rise to the fluorescence photons used in the detection process. Third, the radiation pressure force can be modulated to excite the common motion of the ions. 

In ID laser cooling the force on the atoms is Fiaser = —Ev, where the velocity dependence arises from the Doppler shift of the atom and the laser detuning, such that the faster the atom moves the more resonant the cooling light, the more photons the atom scatters, the larger the force is on the atom. Metcalf shows that in this system the phase space density evolves according to dp(p,r,t)/dt = rp p,r,t). This result shows that the phase space density of this system increases in time, thereby cooling the system. 

S has several safety systems active, passive, and inherent (IAEA, 2003) (see Fig. 20.22). Active shutdown systems are (1) inserting reflectors by using gravitational force and (2) inserting black control rods. The passive safety system of 4S uses natural circulation in RVACS and Intermediate Reactor Auxiliary Cooling System (IRACS). In addition, inherent safety system uses Doppler effect via metallic fuel and large inventory of coolant. 

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