Influence of the quadratic Doppler effect on the absorption line profile of particles captured by a trap

It is found that allowance for the quadratic Doppler effect broadens and changes the resonance absorption line profile of particles trapped in an oscillator potential comprising a periodic lattice of resonances having an envelope in the form of a conventional Doppler profile, if the particle oscillation frequency is greater than the homogeneous line width. When the quadratic Doppler shift is small compared with the homogeneous line width, its influence is reduced to a shift of the resonances. A new possibility for eliminating thermal broadening of individual resonances is discussed.