Appendix A - Correspondence between parameters of the statistical models and atomic and laser parameters

Summary

We establish here the correspondence between the statistical models introduced in Chapter 3 and the quantum evolution of atoms undergoing subrecoil laser cooling. This enables us to establish analytical expressions connecting the parameters of the statistical models (τ₀, p₀, p_D, Δ_p, p_max, τ_b and) to atomic and laser parameters relevant to subrecoil laser cooling.

Such a ‘dictionary’ is useful for the numerical estimation of the results derived in this book (see Chapter 8). It also leads to analytical relations between τ_b and, which are used for cooling optimization (see Chapter 9).

We first treat in detail Velocity Selective Coherent Population Trapping in Section A.1. Analytical expressions are given for the statistical parameters. Special attention is given to the p-dependences of the jump rates both for small p and for large p, because they control the asymptotic behaviours of the trapping and recycling times. It is thus important to include these p-dependences correctly in the simplified jump rates in order to ensure the validity of the statistical model. Raman cooling is then briefly treated in Section A.2.

We only consider here the limit of small laser intensities (and a null detuning for VSCPT) but it is clear that the calculations can easily be generalized if needed.

Velocity Selective Coherent Population Trapping

We first present the quantum optics treatment of one-dimensional σ₊/σ₋ VSCPT (Section A.1.1).