Three-dimensional laser cooling at the Doppler limit R. Chang, A. L. Hoendervanger, Q. Bouton, Y. Fang, T. Klafka, K. Audo, Alain Aspect, C. I. Westbrook, D. Clément To cite this version: R. Chang, A. L. Hoendervanger, Q. Bouton, Y. Fang, T. Klafka, et al.. Three-dimensional laser cooling at the Doppler limit. Physical Review A, American Physical Society, 2014, 90 (6), pp.063407. 10.1103/PhysRevA.90.063407. hal-01068704 HAL Id: hal-01068704 https://hal.archives-ouvertes.fr/hal-01068704 Submitted on 22 Feb 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Copyright Three-Dimensional Laser Cooling at the Doppler limit R. Chang,1 A. L. Hoendervanger,1 Q. Bouton,1 Y. Fang,1, 2 T. Klafka,1 K. Audo,1 A. Aspect,1 C. I. Westbrook,1 and D. Cl´ement1 1Laboratoire Charles Fabry, Institut d'Optique, CNRS, Univ. Paris Sud, 2 Avenue Augustin Fresnel 91127 PALAISEAU cedex, France 2Quantum Institute for Light and Atoms, Department of Physics, State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, 200241, China Many predictions of Doppler cooling theory of two-level atoms have never been verified in a three- dimensional geometry, including the celebrated minimum achievable temperature ~Γ=2kB , where Γ is the transition linewidth. Here, we show that, despite their degenerate level structure, we can use Helium-4 atoms to achieve a situation in which these predictions can be verified. We make measurements of atomic temperatures, magneto-optical trap sizes, and the sensitivity of optical molasses to a power imbalance in the laser beams, finding excellent agreement with Doppler theory. We show that the special properties of Helium, particularly its small mass and narrow transition linewidth, prevent effective sub-Doppler cooling with red-detuned optical molasses. I. INTRODUCTION 35 30 The seminal proposals for Doppler cooling in 1975 [1,2] 25 prompted the realization of the first optical molasses in D the 1980's [3], a major landmark in the field of laser cool- [ T ] 20 ing and trapping of atoms [4{6]. The physical concepts behind the Doppler cooling mechanism are both simple 15 10 MOT temperature and elegant, and predict the achievement of very low tem- Temperature peratures. They remain to this day the starting point of Molasses temperature Doppler theory I=I most courses on laser cooling and degenerate gases [7]. It 5 MOT Doppler theory I=IMOL is thus ironic that not only, to our knowledge, quantita- 0 tive predictions of this simple model have not been exper- -30 -25 -20 -15 -10 -5 0 Detuning [ Γ ] imentally validated, but moreover, experimental studies have found results quantitatively and even qualitatively 4.0 different from the predictions of the model [8{11]. Today, it is well known that for most atoms with a 3.5 degenerate ground state manifold, the complex multi- D 3.0 level structure gives rise to new mechanisms which come [ T ] to dominate the cooling process, yielding ultimate tem- 2.5 peratures far below those predicted by Doppler theory [7, 12, 13]. Accounting for these sub-Doppler mecha- 2.0 nisms allows one to understand the qualitative and quan- Temperature titative experimental observations. In contrast, three- 1.5 dimensional laser cooling of an atomic sample in agree- 1.0 ment with the celebrated Doppler model is still lack- -2.0 -1.5 -1.0 -0.5 0.0 ing [14]. Recent work with alkaline-earth and rare-earth Detuning [ Γ ] atoms, which exhibit a non-degenerate ground state, have provided natural candidates to study cooling in a purely FIG. 1. Temperature in magneto-optical trap and optical Doppler regime. Yet, to our knowledge, all experiments molasses as a function of the detuning of the laser cooling with these atoms have found temperatures above the ex- beams. Temperatures are extracted from monitoring time-of- pected Doppler limit in magneto-optical traps (MOTs) flight expansion of the gas. Error bars (one standard de- [16{28]. This discrepancy has been attributed to the viation) reflect the error from fitting. The total intensity presence of additional heating mechanism [29, 30]. (sum of the six beams) used in the experiment are respec- Here we report the three-dimensional laser cooling of tively IMOT = 100 Isat and IMOL = Isat=10. The lines are the metastable Helium-4 gases in the Doppler regime. We results of Doppler theory of Eq.7, for intensities IMOT (solid line) and I (dashed line). monitor the temperature of the gas as a function of MOL the laser detuning δ, as shown in Fig.1, finding excel- lent agreement with Doppler theory. The temperature reaches a minimum for a detuning δ = −Γ=2 (where Γ is the transition linewidth), while increasing with jδj at val- ues jδj Γ, in contrast with sub-Doppler molasses. In 2 addition, the drift velocities of optical molasses with un- the temperature of a 3D molasses formed by three or- balanced power between counter-propagating beams are thogonal pairs of counter-propagating laser beams is, far larger than those expected of sub-Doppler molasses 3 3 Γ 1 + I =I + (2δ=Γ)2 [9]. We use the 2 S1 ! 2 P2 transition of Helium-4, ~ tot sat kBT2level = ; (3) which allows in principle for sub-Doppler cooling, and 2 4jδj=Γ yet our results show no evidence for such effects. We where the I = 6I is the total intensity resulting from present a physical argument showing that the special tot all six laser beams. In the Doppler regime, the minimum properties of metastable Helium (4He*) strongly inhibit possible temperature is achieved for a detuning δ = −Γ=2 sub-Doppler cooling in the experimental configuration we and vanishing intensity. This minimum is commonly re- probe. ferred to as the Doppler limit, TD = ~Γ=2kB . We now turn the discussion to an atom with sev- II. THEORETICAL CONSIDERATIONS eral ground-state levels where sub-Doppler mechanisms of cooling may be involved [9, 10, 12]. For this discussion we restrict ourselves to the atomic structure of the 4He* A. Laser cooling mechanisms 3 3 atom on the 2 S1 ! 2 P2 transition (see Fig.2a), and the laser configuration used in the experiment: counter- Laser cooling of an atomic gas relies upon the ex- propagating laser beams with opposite circular polariza- change of momentum between the atoms and the near- tion (configuration σ+ −σ−) along three orthogonal axes. resonant light field, resulting in a mechanical force F on Consider first a single axis of the system. Following the atoms. For small velocities, the equilibrium temper- the derivation from [31] an explicit formulation of the ature T of these cooling schemes is given by the ratio of a semi-classical force F on a moving atom can be obtained. momentum-space diffusion constant D (given by the fluc- This approach takes into account atomic coherence ef- tuations of the force) to the velocity-damping coefficient fects up to second-order in absorption-emission processes. α. In the following we will first recall the main theoreti- In Fig.2 we plot this force F along with that exerted on cal results for laser Doppler cooling of a two-level atom, a two-level atom F2level. In the low-velocity region (see then proceeding to discuss a multi-level atom where sub- Fig.2c) the cooling force on the multi-level atom ex- Doppler mechanisms may appear. hibits a sharp feature with an associated damping coeffi- The mechanical interaction of a near-resonant light cient α significantly larger than that of a two-level atom. beam (frequency !) with a two-level atom (atomic reso- This feature arises from the presence of atomic coher- nance frequency !0) is dominated by the radiation pres- ences and two-photon processes, and is the signature of sure effect and its associated force [9]. This light-matter sub-Doppler cooling mechanisms. Since the momentum- interaction is characterised by the laser detuning from space diffusion coefficient hardly changes, the new damp- resonance δ = ! − !0, the laser intensity I, the natural ing coefficient would lead one to expect sub-Doppler cool- linewidth of the transition Γ, and the saturation intensity ing. of the transition Isat. A convenient physical quantity is In this configuration, the additional cooling results the generalized saturation parameter from a motion-induced population difference between the s ground-state levels, and is referred to as σ+ − σ− polar- s = 0 ; (1) 1 + 4δ2=Γ2 ization gradient cooling. In a 3D configuration, it is well known that Sisyphus cooling can also occur due to spa- which characterizes the excited state population in a 2- tially dependent light shifts of the atomic ground-state 2 2 level atom, s=2(1 + s). Here s0 = I=Isat = 2Ω =Γ is the levels. The electric field from laser beams along orthog- on-resonance saturation parameter, and Ω is the Rabi onal axes interfere, resulting in a modulation of the in- frequency. tensity, which in turn may lead to Sisyphus cooling as At low saturation of the atomic transition s 1 and in a one-dimensional lin ? lin configuration. Within the small velocities jkvj jδj, the average force acting on parameter range of interest (jδj ∼ Γ), both sub-Doppler a two-level atom moving at velocity v takes the form effects result in similar velocity capture ranges and equi- F2level = −α2levelv with librium temperatures [9, 10, 12].