Atom-Light interaction: trapping vs heating

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General properties of Dysprosium

The early works on laser cooling techniques [62] opened the door for studying many-body physics with a high degree of control. Experiments mainly used alkalies species driven by the simplicity of their electronic configuration. However, implementing schemes with other species, such as the open-shell lanthanide atoms, can lead to the observation of a rich span of many-body phenomena, thanks to their peculiar features: large angular momenta, rich electronic excitation spectrum, etc. In our experiment, we use the highly magnetic Dysprosium atom. The group of B. Lev (Stanford) was the first to obtain a Bose-Einstein Condensate (BEC) in 2011 [36] and a Degenerate Fermi Gas (DFG) one year later [63], then followed by the group of T. Pfau (Stuttgart). Our experiment is the third to be built. Ever since more and more groups are using Dy or other atoms with similar properties like Erbium (Er) or Thulium (Tm), proving that the atomic elements of the lanthanide family open the door to new perspectives in the field. In our experiment, a particular interest is given to the interaction between the large spin of Dy and near resonant light.
The aim of this chapter is to introduce the properties of Dy and give the important parameters for its cooling and trapping.

Physical properties

Dysprosium was identified for the first time by a french chemist, Paul Émile Lecoq de Boisbaudran, in 1886 when he succeeded in separating this new element from a sample of Holmium. The origin of the appellation Dysprosium comes from Greek dusprositoc (dus-prósitos) which means hard to get as it was difficult to isolate from the Holmium. The first pure sample of Dy was obtained in 1950. Dysprosium belongs to the lanthanide family (cf.

Electronic configuration

Following the Madelung rule for filling the electronic orbitals, one gets that the ground state configuration is [Xe]4f106s2. The 4f shell has seven available orbitals (l = 3, jml j 3) for only 10 electrons. According to the Hund rule, the electronic configuration with the lowest energy is the one maximizing the orbital angular momentum L and the spin momentum S:
It results in an orbital angular momentum L = 6, a spin S = 2 and a total angular momentum J = L + S = 8. Fermionic isotopes have in addition a nuclear spin I = 5/2. This large angular momentum confers important characteristics on Dy, mainly an un-surpassed magnetic moment m ’ 10 mB with mB is the Bohr magneton (Dy magnetic moment is 10 times larger than the one for alkali atoms and it is the largest among neutral elements of the periodic table), hence Dy is a quantum dipolar gas suitable for studying dipolar interactions. It posesses a rich excitation spectrum (a fraction is presented in Fig. 1.2) offering several cooling schemes. In 1970, John Conway and Earl Worden gave a quite detailed description of the Dy spectrum in the University of California Radiation Laboratory Report UCRL-19944, where they listed more than 22000 lines between 230 nm and 900 nm for the neutral and singly-ionized Dysprosium DyI and DyII (cf. ref. [64] for more details). The values of the ground state angular momentum J and Landé’s factor g were determined experimentally by Cabezas et al. in 1961 [65]. These measurements are considered to be the first experimental proof that the ground state level is the 4f106s2 (5I8). Dy is also used in aeronautic and the production of permanent magnets. And from the fundamental physics point of view, Dy is a promising candidate for realizing P and P-T violation experiments, as it has a pair of almost degenerate levels with opposite-parity and the same angular momentum (J = 10) [66].
The complexity of the excitation spectrum can be overwhelming at first sight, but from a laser cooling point of view only two transitions are relevant: a broad transition at l = 421.290 nm that offers a significant cycling rate ideal for large capture velocities magneto-optical traps (MOTs), Zeeman slowing and imaging, and a relatively narrow transition at l = 626.082 nm suited for cold MOTs and atomic spin manipulation (see details in chapter 2). These two transitions result from the promotion of one electron from the outer shell 6s to the excited orbital 6p. For the 421 nm blue transition, the spin is conserved which gives a spectral term 4f10(5I8)6s6p(1Po1), while it is not for the red transition: 4f10(5I8)6s6p(3Po1). This latter is a singlet to triplet transition (forbidden) and therefore has a narrow linewidth (cf. Tab. 1.2). The coupling between the two angular momenta of the inner shell (J = 8) and the outer shell (J = 1), gives rise to three excited states with momenta J0 = 7, 8 and 9. A list of the different lines corresponding to these momenta is given in Tab. (1.3). The two excited states that we consider are those with a total angular momentum J = 9.

Isotope shift

The charge distribution of the atomic nucleus gets slightly modified for different isotopes. This effect results in an energy shift of the excitation spectrum [67]. The total shift is the sum of a field shift and a mass shift. The first is due to the influence of the nuclear charge distribution on the binding energy of electrons and the second comes from the influence of the nuclear recoil energy. For Dy bosonic isotopes, we measure a shift of Dn = f476, 491g MHz/[m.a.u], for the blue and red transitions, respectively.

Interactions in dipolar quantum gases

Scattering phenomena play a fundamental role in the study of quantum gases, it is thus important to understand and characterize the different interaction processes. In this section, I will present the main interaction potentials to be considered for a Dy gas: the Van der Waals and the dipole-dipole potentials. We neglect higher order interactions like the electric quadrupole-quadrupole potential as it was shown that it is much weaker than the other two [68]. In the second part of this section, I will recall the expressions of the scattering cross sections for both types of interaction as it will be needed to calculate the collision rate (cf. chapter 4).

The anisotropic dispersion interaction

The dispersion potential, also known as the Van der Waals (VdW) potential, arises from the interaction between induced electric dipoles of two atoms and has the following form: UVdW(r) = C6  where r is separation between two interacting atoms and C6 is called the Van de Waals coefficient. This potential is short-ranged and has a spherical symmetry for alkali atoms. For atoms with a strong magnetic character like Dy, the C6 coefficients depend on the projection of the total angular momentum onto the internuclear axis. The exact calculation of this potential is very challenging for Dy due to the complex electronic configuration, nevertheless numerical simulations have been performed for interacting Dy atoms in their ground states (see refs. [69, 68]).
Let’s consider two colliding atoms in their ground states with angular momenta J1 = J2 = 8. The total angular momentum of the pair is then J = J1 + J2, and we define W to be its projection along the internuclear axis. We consider a weak interaction such that both atoms remain in the J1 = J2 = 8 manifold after the collision. The matrix elements of the VdW potential are given by [70, 68]: where r is the internuclear separation. J1, J2 are angular momenta of the two incoming states and M1, M2 are their projections along the internuclear axis such that W = M1 + M2. M10 and M20 are the corresponding projections of the outgoing states after the interaction. One has to sum over all electronic states jna Ja Ma, nb Jb Mb of atoms a and b excluding states with energies equal to the ground states energies E1 and E2. Ja, Jb are the intermediate angular momenta for atoms a and b respectively, Ma and Mb are their respective projections along the internuclear axis and na, nb account for the remaining state parameters. Vˆdd corresponds to the electric dipole-dipole interaction operator. As we can see from eq. (1.2), the C6 coefficients depend on the values of M1, M2, M10 and M20, thus the interaction energy depends on the relative orientation of the atoms. This effect finds its origin in the anisotropic coupling of the unpaired electrons of the 4f shell. The general expression of the C6 coefficients can be written as [68]

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Experiment

Lanthanide atoms have a complex electronic structure with respect to alkali species but cooling schemes still relatively simple [78, 79, 80, 81]. In our experiment, only two optical transitions are used: the broad transition at l = 421 nm that has a natural linewidth G = 2p 32 MHz, and the narrow-line transition at l = 626 nm, with a natural linewidth G = 2p 136 kHz. The first transition is used for the Zeeman slower (ZS), the transverse cooling and for the imaging, and the latter is used for the magneto-optical trap (MOT) and further atomic spin manipulation.
This chapter sets forth the different cooling stages in our setup. In the first section, I will give a short summary of the general features of the experimental apparatus and cooling lasers as well as the experimental sequence. A more detailed description of the experimental setup can be found in Davide Dreon’s Ph.D. thesis [82]. The study carried on light-assisted collisions in the MOT will be discussed in the second part of this chapter. In the last part, I will detail the procedure for trapping and transporting atoms by mean of an optical dipole trap (ODT).

Experimental setup

The vacuum and laser systems

Our vacuum system (shown in Fig. 2.1) can be decomposed in two sections separated by a differential pumping stage: the high vacuum part (HV) which pressure is on the order of 10 8 mbar, and the ultra-high vacuum part (UHV) with a pressure two orders of magnitude lower.
• The HV section comprises the oven and spectroscopy chambers. Our oven is a commercial double effusion cell. We refill the crucible with 10 g of metallic Dy crumbs every six months approximatively. The sample is heated to 1050 C in order to obtain an atomic jet (the melting point of Dy is 1412 C at atmospheric pressure). The oven is shielded and water cooled in order to keep it at room temperature during operation.
After exiting the oven, atoms enter a cubic chamber where we perform spectroscopy on the red, l = 626 nm narrow transition. We use a technique based on the fluores-cence Lamb-dip to lock the MOT laser. We have a 40 L ion pump connected to this chamber. Then atoms cross an octagonal chamber where we carry out spectroscopy on the blue transition l = 421 nm. We use a modulation transfer spectroscopy technique to lock the laser, which allows us to reach a stability of 1 MHz on the blue line. In this chamber we implement also transverse cooling of the atomic beam.
• There are three main parts in the UHV section: the Zeeman slower, the MOT chamber and finally the science cell. We installed a gate valve at the entrance of the ZS that offers the possibility to open and refill the oven without affecting the vacuum in the UHV section. We have also a mechanical shutter that permits to block the atomic jet if needed. At the same level, we implemented a second ion pump. Typical pressure in this region is 5 10 9 mbar. At the exit of the 50 cm long ZS, atoms enter the MOT chamber. It is a cubic piece with CF60 windows on the facets and CF16 connections on the vertices. A third ion pump is connected to this chamber, and the typical pressure is 4 10 10 mbar. The final piece of our vacuum system is the glass cell. It is connected to the MOT chamber through a custom T-shape piece. At the level of this piece we have a hybrid ion-getter pump that assures a pressure below 10 11 mbar. The glass cell has parallelepiped shape with 6 cm long, 2.5 cm large and 5 mm thick, with no coating.
The used lasers are: a commercial Toptica lasera for the blue transition and a home made laser for the red transition. This latter is obtained by a sum-frequency generation of l1 = 1050 nm and l2 = 1550 nm using a non-linear crystal.

Table of contents :

Introduction
1 General properties of Dysprosium
1.1 Physical properties
1.1.1 Electronic conguration
1.1.2 Cooling scheme
1.1.3 Isotope shift
1.2 Interactions in dipolar quantum gases
1.2.1 The anisotropic dispersion interaction
1.2.2 The dipole-dipole interaction
1.2.3 Scattering properties for a cold dipolar gas
2 Experiment
2.1 Experimental setup
2.1.1 The vacuum and laser systems
2.1.2 Typical experimental sequence
2.2 Trap losses due to binary collisions
2.2.1 Light-assisted collisions: models and limits
2.2.2 Experimental investigation of 2-body losses in a Dy MOT
2.3 Optical dipole trap
2.3.1 Experimental setup
2.3.2 Measurement of oscillation frequencies
2.3.3 Loading the ODT
2.4 Optical transport of a thermal cloud
2.4.1 Harmonic case
2.4.2 The real trap
3 Atom-Light interaction: trapping vs heating
3.1 Optical light shift and photon-scattering rate
3.2 Lifetime and heating in a dipole trap at l = 1070 nm
3.2.1 Case of a circular polarization
3.2.2 Case of a linear polarization
3.3 Lifetime and heating in a dipole trap at l = 626 nm
3.4 Dipolar relaxation
3.4.1 Theoretical derivation of the two-body loss rate and its dependence on the B-eld
3.4.2 Experimental investigation of the dipolar relaxation in a thermal gas
4 Interactions between Dysprosium atoms and evaporative cooling 
4.1 Forced evaporation in a single far detuned optical beam
4.2 Crossed dipole trap
4.2.1 Characterization of the crossed dipole trap
4.2.2 Optimizing the loading into the cross dipole trap
4.3 Controlling the interactions via Feshbach resonances
4.3.1 Nature of Dy Feshbach spectrum
4.3.2 Characterization of a Feshbach resonance
4.4 Forced evaporation in the cross dipole trap
4.4.1 Evaporation model
4.4.2 Gravity eects on the evaporation eciency
4.4.3 Interaction eects on the evaporation eciency
4.5 Heating in the cODT
5 Manipulating the atomic spin with light
5.1 Spin-dependent light-shift
5.2 Calibration of the coupling strength
5.3 Eective magnetic eld 98
Conclusion and perspectives
A Design of the transport acceleration prole
B Article: Optical cooling and trapping of highly magnetic atoms: the benets of a spontaneous spin polarization
Bibliography

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