Proposed in the 1970s [1], Doppler cooling of neutral atoms is a simple theoretical model which initiated a nowadays immense field of ultracold atoms [2]. The model was developed for a two level atom (one ground state and one excited state, but no degeneracy) and one of its main predictions is the minimal achievable temperature called the Doppler limit. It quickly turned out that it cannot be verified experimentally. This is due to the fact that real atoms are multilevel for which other cooling mechanisms exist (due to the degenerate level structure) allowing sub-Doppler temperatures without having to make any changes in the experimental setup.

Among "traditional" laser cooled atoms two species, metastable Helium and Lithium, seem to be good candidates for the study of Doppler cooling because their capture velocity for sub-Doppler cooling is below the Doppler limit. Indeed, recently [3] the Doppler limit was verified in metastable He-4. But for the other candidate (Li-7) temperatures of about twice the Doppler limit have been observed [4,5]. Moreover, we have recently observed that a finite and low steady state temperature is achieved for vanishing detuning although the standard Doppler theory predicts no cooling for δ=0. At δ=0 we find a temperature of T≈3.5 T_D. Only as we go to δ≈+0.3Γ (blue detuned,  Γ is the natural linewidth of the Lithium atoms excited state) the temperature diverges. For these measurements, we used a locking feedback system wired directly to the driving current of the diode laser. We report a typical laser bandwidth of <100kHz. This corresponds to an accuracy of 0.01Γ.

To understand this surprising result we build a full (24 level) semi-classical model of Li-7 subject to a one dimensional σ⁺-σ^- laser light configuration. The force and diffusion coefficient are found as a function of velocity. While the diffusion coefficient is more or less constant for all relevant velocities the force has favorable features which can explain, in particular, the low temperature at δ=0. In addition, we can make an estimation for the steady state temperature by carefully analyzing the force and the diffusion coefficient.

We find good qualitative agreement between the experimental results and the numerical simulations.  However, several discrepancies with the model will be discussed.

[1] T.W. Haensch and A.L. Schawlow: Cooling of gases by laser radiation, Opt. Com. 13, 68 (1975)

[2] C. Cohen-Tannoudji and D. Guery-Odelin: Advances in Atomic Physics: An Overview, World Scientific (2011)

[3] R. Chang et.al: Three-dimensional laser cooling at the Doppler limit, Phys. Rev. A 90, 063407 (2014)

[4] U. Schuenemann et.al: Magneto-optic trapping of lithium using semiconductor lasers, Opt. Com. 158, 263 (1998)

[5] N. Gross and L. Khaykovich: All-optical production of Li-7 Bose-Einstein condensation using Feshbach resonances, Phys. Rev. A 77, 023604 (2008)