This paper reviews our current understanding of the dynamics of a laser-cooled trapped particle in the Lamb–Dicke regime, where the quantum structure of the energy levels cannot be ignored. The derivation and validity of a master equation are surveyed, and its physical interpretation is discussed in some detail. The structure and physical nature of the ultimate steady state are discussed. Using a generating function method, we can solve for both the complete eigenvalue spectrum and the general time-dependent solution of the master equation. These results are derived and interpreted physically. They have earlier been scattered in our various publications and are presented here in a coherent way for the first time. Also included are some new results and a physical discussion of the situation. The paper concludes with a discussion of the validity and limitations of the model as treated so far.
© 1985 Optical Society of America
Original Manuscript: April 8, 1985
Manuscript Accepted: July 2, 1985
Published: November 1, 1985
Stig Stenholm, "Dynamics of trapped particle cooling in the Lamb–Dicke limit," J. Opt. Soc. Am. B 2, 1743-1750 (1985)