b. Polarization

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Part I – Abstract

I.4. EXPERIMENTAL WORK

I.4.1. b. Polarization

As discussed in paragraph I3.2 where the laser set up is described, the radiation used for the polarization becomes available by taking a part of the repumper's light. This radiation, initially in resonance with the F = 3 → F' = 4 transition is shifted for ~350 MHz after passing twice an AOM in order to become resonant to the F = 3 → F' = 2 transition. A part of the radiation is polarized circularly and inserted vertically in the atomic trap region. A smaller part is linearly polarized and inserted in a horizontal direction. The intensity of the circularly polarized beam is ~800 µW/cm2 and the one of the linearly polarized beam ~10 times smaller.

Dividing the polarization beam in a strong circular and a weaker linear π component is necessary, since the circularly polarized light alone does not result for 100% atomic polarization.

The reason for this becomes clear when we see in Fig. I.4.4 we a diagram of the magnetic sublevels involved in the polarization process. As we see, the excitations induced by the circularly polarized light lead in an increase in the spin projection mF (σ+ light chosen for this example, where polarization to |F=3,mF=3> state considered). But for atoms occupying the |F=3,mF=2> state, such an excitation is impossible due to the lack of an exciting state with spin projection mF+1. This can lead to population trapping in this state and thus decrease of the polarization efficiency. This problem is confronted with the weak linear component which is able to pump atomic population out of the 'dark' |F=3,mF=2> state, and the combination of the two component results to almost 100%

population transfer in the desired |F=3,mF=3> state.

An important element of the polarization process is the small magnetic field bias. It is necessary in order to achieve and maintain polarization, but also it allow us to choose between the | F=3,mF=3> and the |F=3,mF=-3> states as the final states of our polarization scheme. Any atom possessing spin if subjected to magnetic field, performs Larmor oscillations around it. In the absence of this magnetic field bias, the polarized atoms will perform these oscillations around any stray magnetic field, resulting to a complete loss of their polarization. The energy shift between

Fig. I.4.4: Diagram of the magnetic sublevels involved in the polarization process. We see that the result of the circularly polarized light alone is accumulation to the |F=3,mF=2> 'dark' state, while polarization of

~100% in the |F = 3, mF = 3> state is achievable only after the insertion of the weak linearly polarized component.

magnetic sublevels shown in Fig. I.4.4 is caused by this magnetic field. More important, this field defines a direction upon which the whole geometry of the scheme is based. Inverting this field's direction results in the inversion of the target state, since the effect of the σ+ polarized light with the inverse magnetic field is the same as the effect of σ- radiation with the magnetic field direction as the one shown in the scheme.

The diagnostic applied in order to verify the performance of the polarization technique is the Stern-Gerlach separation. The separation is realized by letting the atoms fall in the presence of a strong magnetic field gradient. The force created by the interaction of the magnetic field gradient Fig. I.4.5: Experimental sequence used for the polarization of the Cs atoms, and the verification of the polarization performance via Stern-Gerlach separation.

with the atom's magnetic moment depends on the mF. Thus, the free fall of some atoms (low field seekers) is accelerated, while for others (low field seekers) is decelerated, resulting to spatial separation of the atoms according to their hyperfine state. In Fig. I.4.5 we see the experimental sequence used for the preparation of an ultracold Cs cloud, its polarization to the |F=3,mF=3> state the realization of the Stern-Gerlach separation and the detection of the atomic cloud via fluorescence imaging. Again the atoms are loaded from MOT 1 to MOT 2, are compressed in a C-MOT phase and cooled by molasses. Finally they are polarized and separated with the Stern-Gerlach magnetic field gradient. The magnetic field gradient is ~120 G/cm and it is provided by a single coil located ~4 cm lower than the atomic sample; in the schematic representation of figure 4.5 it is shown as if it was generated by the MOT fields (which is possible) for simplicity. After magnetically separated the atoms are detected via fluorescence imaging.

In Fig. I.4.6, we see fluorescence imaging detection of the atomic cloud. In part (a) the atoms have fallen freely and magnetic field gradient is not present. In part (b) the magnetic field gradient is turned on. We see that the atoms are separated to atomic clouds that correspond to states having mF equal to 1,2 and 3 while other states are not visible at these conditions. In part (c) we insert the circularly polarized light alone and we see a a clear difference in the atom's distribution on the magnetic sub-levels since most of them are found in the |F=3,mF=3> state and some of them in the |F=3,mF=2> state . Finally, in part (d), the linearly polarized component is also inserted and Fig. I.4.6: (a) Cs atoms falling under the influence of gravity. (b) The Stern-Gerlach separation magnetic field gradient is added and we see the appearance of separated atomic clouds corresponding to the

|F=3,mF=1>, |F=3,mF=2> and |F=3,mF=3> states. (c) The circularly polarized beam is inserted alone and most of the atomic population is found in the |F=3,mF=2> and |F=3,mF=3> states.(d) Inserting the linearly polarized component results to the accumulation of the atomic population in the |F=3,mF=3> state.

almost all atoms occupy the |F=3,mF=3> target state.

In Fig. I.4.6.b, we see that after the insertion of the Stern-Gerlach separation field gradient the atoms are spatially separated in atomic clouds that correspond to different hyperfine states. In those pictures only the states with mF = 1,2 and 3 are shown, while their relative distribution among them depends on the complicated optical pumping scheme involved in the MOT and molasses phase. A different method to verify the efficiency of the polarization scheme and to make sure that no atomic population is lying different states is to see the polarization effect on the magnetically trapped atoms. In Fig. I.4.7 we see three pictures of the magnetic trap realized with the use of the sequence shown in Fig. I.4.1 with the only differences in the polarization. In part (a), the polarization laser is blocked. In part (b) the polarization laser is on and the bias magnetic field is such that the atoms are polarized in the |F=3,mF=-3> state, so that the total number of atoms in the magnetic trap appears enhanced. In part (c) the direction of this field in making the |F=3,mF=3>

state the target state of the system. We see that the efficiency of the polarization scheme is close to 100% since almost no atoms are detected to be magnetically trapped.

I.4.1.c. Loading a crossed dipole trap from a magnetic trap

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