Part I – Abstract
I.1.2. b. Evaporating Cooling
As mentioned above, laser cooling itself cannot lead to the production of a BEC. Perhaps the most serious limitation comes from the fact that for very high densities, like the ones that one needs to obtain a BEC, light that is scattered from one atom is very likely to be absorbed by another causing the atoms to repel each other. An additional reason for which laser cooling cannot lead to the production of BEC, is the fact that in a laser cooled sample, there are always excited atoms, which can collide with ground state atoms in an inelastic and thus exothermic collision.
The technique that carries the second half of the road to condensation is evaporating cooling.
It consists of the selective removal of the most energetic (hottest) atoms from the atomic sample and thus lowering the overall temperature, and relies upon elastic collisions in order to bring the system to a new equilibrium.
Evaporation can be realized in any conservative trap. We can choose as example the very simple case of a quadrupole magnetic trap, which is realized with two coils in an anti-Helmholtz configuration, as the ones used to produce the magnetic field of the MOT described in the previous paragraph. Simple quadrupole traps are rarely used in condensation experiments. The reason is that in the center of such a trap, the field becomes zero, which results to spin flipping and atom loss (the so called Majorana losses). Usually in BEC experiments more complicated traps are used, like the Ioffe-Pritchard trap or the Time Averaged Potential (TOP) traps, which manage to create trapping potentials without areas of zero field, and thus without Majorana losses.
Spin flips lead to atom loss, since not all the angular momentum species can be trapped by a magnetic potential. Such a potential can trap only atoms in particular angular momentum projection states, while which state is trapped and which not depends on the atomic species. The condition is that the particular state has to increase its energy with increasing magnetic field, to be a 'low-field seeker'. For the cesium 6S1/2 electronic state in particular, such states are the states with negative m.
High-field seekers like the absolute ground state F = 3, MF = 3 of Cs, cannot be magnetically trapped [Wing84]. Such atoms decrease their energy with increasing magnetic field, and thus would be repelled by a local minimum of magnetic field. Thus, if one can trap Cs atoms their F = 3, MF = - 3 low-field seeking state, he can remove them by exciting them to the high-field seeking F = 3, MF
Fig.I.1.7: Schematic representation of the evaporating cooling process. As the trapping barrier is lowered the hottest atoms escape the trap leaving the sample to re-thermalize in a lower temperature.
= 3, for example by means of RF fields. Furthermore, as the coldest atoms are closer to the trap’s center, and in lower magnetic field, their energy levels lie somehow lower than the ones of the hottest atoms. Thus, in different RF frequencies, atoms of different temperature can be excited and removed from the trap. Such a technique is often called as an 'RF knife', which one can use to 'cut' the hottest part of the atomic sample’s temperature distribution schematically viewed in Fig.I.1.7.
This technique has been used for the realization of the pioneering BEC experiments and remains today the most commonly used.
Evaporation can be realized in more types of traps, like the optical dipole traps. Dipole traps are becoming very popular, since they can reduce considerably the loading time. Additionally, dipole traps can be used to trap high field seekers if necessary since, contrary to magnetic traps, they are not state selective. As a consequence, RF knifes can not be used with dipole traps and evaporation can be achieved simply by lowering the trapping potential, which for the case of dipole traps means to lower the power of the trapping laser. However, lowering the power of a dipole laser modifies the trapping potential making it less confining, which effects (slows down) the evaporation process. That’s why it is better to hold in mind the magnetic trap picture for the discussion of the evaporation cooling in this paragraph; we will return to evaporation in dipole traps in the chapter I.2. where our approach to evaporation is discussed.
I.1.3. The cesium atom: characteristics and particular interest
Cesium is one of the most studied elements in atomic physics, especially because the SI standard for the definition of the second is based in one of its transitions. The isotope 133Cs, is the only one that is stable, and it is the heaviest stable alkali atom. The structure of the first electronic states, between which the transitions that are used in the laser cooling are performed, are shown in the Fig.I.1.8. The transition from the ground 62S1/2 state and the 62P3/2 (D2 line) is employed for laser cooling and has a natural line width of 5.22 MHz. while the transition between the ground state and the 62P1/2 (D1 line) has a line width of 4.56 MHz. The hyperfine splitting of its ground state, which is used for the definition of the second, equals to 9.2 GHz, while the hyperfine splitting of the 62P3/2 state is 150-250 MHz [Steck02]. Cs was considered to be one of the primer candidates for the achievement of BEC, since its large weight resulted to vary small corresponding temperature for the one photon recoil limit (~200 nK), thus making it very suitable for laser cooling. Another reason for its popularity was the fact that the transitions that are needed for Cs cooling and repumping lies in the infrared region (~852 nm), and can be addressed with cost effective diode lasers.
For our group, as well as for many others, the particular interest on ultra-cold Cs, was due to the fact that this atom is suitable for the study of cold molecules. Indeed some of the first cold [Fio98] and ultra-cold [Herb03] molecule formation where reported with Cs dimers, and prepared with photoassociation and magneto-association respectively.
Photoassociation is the process in which two atoms are colliding in the presence of a laser field. This laser can bring the atoms into resonance with a long range, but bound molecular state.
Because the free-state thermal energy spread is negligibly small, this process leads to a well resolved free-bound absorption spectrum. This "photoassociation spectroscopy" is proving to be a powerful tool for the analysis of atomic interactions at long ranges. It has also shown that these long range molecules can relax to more closely bound states, thus leading to stable cold molecule formation [Fio99]. In our laboratory molecules have also being used to load a magnetic [Vanh02] or a dipole trap [Zahz06]. In a recent development that resulted the efforts of the experimental group of cold molecules in LAC, Cs dimers were optically pumped to their ground vibrational state [Vit08] with the use of shaped femtosecond lasers. Photoassociation is furtherly discussed in the
second half of this thesis, were I describe the experiments for the creation and the manipulation of cold Cs molecules.
Cold molecules can be formed in ultra cold temperature with the use of magnetic field ramps exploiting the phenomenon known as Feshbach resonance [Ties93, Inou98]. The situation in which a Feshbach resonance occurs is schematically represented in Fig. I.1.9. The Feshbach resonance is the result of the coupling between a molecular state in an inter-atomic potential with the threshold of another. Out of the two molecular potentials shown in a), the one which has a threshold close to the collision energy of the free atoms is called the open channel; this potential would not support a bound state for these colliding atoms. A second molecular potential, called the closed channel, has a bind state in the vicinity of the threshold as well. As shown in b), these two molecular states are tuned differently with respect to external magnetic fields, a fact that can lead to the crossing of the two levels and to the production of bound molecular states for particular magnetic field values [Ing07].
Fig.I.1.8: Diagram of the transitions of Cs atoms which are used for laser cooling and trapping.
In the vicinity of a Feshbach resonance, the elastic collision cross section takes its extreme values, and moreover the scattering length diverges, as shown in Fig.I.1.10. When the scattering length takes positive values, the inter-atomic interactions are repulsive, and when it takes negative values they are attractive. This fact makes the Feshbach resonance useful not only for the creation of molecules, but for the tuning of the scattering length to values that are convenient for evaporation and for the production of a BEC. The ability to tune the interactions with the magnetic field, can lead to molecule formation under certain conditions [Herb03] and thus can change the nature of the trapped gas from fermionic to bosonic in the case of fermionic atoms [Zwie05].
Magneto-association can result to the production of triatomic molecules, since three colliding atoms can be brought to resonance to a bound trimer state, a case of which are the so-called Efimov states. Such a state has an infinite number of energy levels and exists in the absence of corresponding two-body bound states [Efi70, Niel99]. This particularity is schematically presented in Fig. I.1.11, where the binding energy of the trimer states is plotted against the inverse of the scattering length value. The shaded area corresponds to the scattering continuum for free atoms for negative scattering wave values, while it represents an atom and a dimer state for positive scattering length values. In 2006, evidence of Efimov state production where observed, again in Fig. I.1.9: a) Feshbach resonances is the result of the interaction between a molecular state in an inter-atomic potential with the threshold of another. b) The bare molecular state of the closed channel tunes differently with a magnetic field than the open channel threshold, a fact that can lead to a crossing of the two levels.
Internuclear separation R open channel
magnetic field B
Fig.I.1.10: Dependence of the elastic scattering cross section, the scattering length and the energy of the emerging bound states for the case of Cs atoms. Image takes from [Chin01].
ultra-cold cesium atoms [Krae06]. This evidence consisted of a giant recombination loss in conditions where the strength of the two body interaction was varied.
However, these results raised a vivid discussion as a number of groups argued against this interpretation. The argumentation upon which this critics was based, was that the three body recombination rate that was the observable of this experiment does not depend to the magnetic field only by the dependence of the scattering upon the magnetic field, but also through the strongly varying properties of the comparatively tightly bound diatomic molecules [Lee07]. This exciting scientific dialog took place in a period when our team was preparing the BEC experiment in LAC.
The fact that in the same period it was proposed theoretically that excited trimer states of Cs can be prepared in the vicinity of 800G [Lee07], contributed to our motivation.