Trap losses due to binary collisions
The development of optical cooling and trapping techniques revived the interest in the study of collisions in atomic gases. The lower temperature regime presents two main differences with respect to thermal collisions:
• a long de Broglie wavelength, typically hundred times the chemical bond.
• a long interaction time with respect to the spontaneous emission lifetime. Multiple photons can be exchanged during the collision.
The intensive studies of cold and ultracold collisions, starting from 1986 , were motivated by various questions, for example:
• how do collisions affect densities in atomic traps?
• how can the outcome channel of a collision be modified by an optical field?
• what is the quantum nature of the scattering process?
• Is it possible to reach quantum degeneracy with laser cooling techniques?
In this section, I will focus on light-assisted inelastic collisions in MOTs. I will start by giving an overview of the developed models and main experimental investigations of atomic trap loss due to binary collisions [71, 89]. Then, I will present our experimental study of two-body losses in a Dy MOT for different light parameters, and conclude with the MOT parameters leading to an optimal loading of the optical dipole trap.
Light-assisted collisions: models and limits
During an exothermic collision, the internal atomic energy (e.g. fine or hyperfine structure splitting energy) converts into kinetic energy shared by the atomic pair, which as a consequence heats the atomic sample. If the acquired energy is sufficiently high for the atoms to escape the trap, the collision results solely in atom losses. A simplified collisional scheme is presented in Fig. 2.8. Two atoms in the ground state interact through the attractive C6/R6 potential with R being the internuclear separation (shown as the S + S potential in Fig. 2.8). In the presence of an optical field, one or both atoms of the pair can absorb a photon and get promoted to an excited state. In this case, the interaction is mediated by the resonant dipole-dipole force and the atomic pair approaches along attractive or repulsive C3/R3 potential depending on the light detuning with respect to the asymptotic resonance. The three possible excitation configurations are presented by the numbers 1, 2 and 3 in Fig. 2.8:
1. a resonant excitation with respect to the asymptotic resonance frequency w0, defined as Ve(R) Vg(R) = h¯w0 in the asymptotic regime (i.e. for a large internuclear separation R) with Ve and Vg being the excited-state and ground-state potentials respectively.
2. If the laser field has a frequency w1 detuned to the blue with respect to the asymptotic resonance, then the repulsive C3/R3 potential will prevent the atomic pair from shrinking and thus 2-body collisions get prohibited. This mechanism is called optical shielding .
3. The third case corresponds to the situation where the laser field frequency is red detuned with respect to the asymptotic resonance. The absorption of a photon excites the atomic pair around the Condon point Rc and forms a quasimolecule. This process is called photoassociation [91, 92]. After the excitation, the quasimolecule vibrates within the potential and can be ionized in the presence of a second laser field of a frequency w2 or decay to the ground state accompanied by the emission of a photon. The photoassociation technique is used to perform precision spectroscopy measurements that give an insight into the properties of the scattering process (molecular potentials, radiative lifetimes, etc) [93, 94].
Figure 2.8 – A simplified schematic of excited-state binary collisions: 1) laser field resonant with the excited molecular potential, 2) blue detuned laser field and 3) red detuned laser field.
We now focus on the first case. It is possible to divide collisions in two categories:
• ground-state collisions: two atoms in the ground state interact through the S + S potential for which the encounter pair could undergo an elastic collision (not exothermic) or a hyperfine-structure changing collision (HCC). The latter corre-sponds to the transition to a lower molecular hyperfine level during the collision and the released energy is equal to the Zeeman energy difference between the initial and final hyperfine levels. Since the released energy is relatively small (few GHz), the HCC mechanism dominates for low intensity optical fields as the trap becomes shallow and the needed energy for an atom to escape the trap decreases.
• excited-state collisions: atoms can absorb a MOT beam photon and this light-assisted collision occurs on an excited state. The two atoms approach each other along the attractive C3/R3 potential (here we consider only attractive potentials since repulsive potentials do not contribute to collisions that result in atom losses) and during this time, the pair can undergo a fine-structure changing collision (FCC) or a radiative escape (RE). The former mechanism is comparable to the HCC mechanism but taking place between two fine-structure levels. The latter mechanism describes a spontaneous emission occurring during the approach and the quasimolecule relaxes to the ground state. The gained kinetic energy can be sufficient for the pair to escape the trap.
The Gallagher-Pritchard model
In 1989, Gallagher and Pritchard developped a semi-classical model  motivated by the experimental observation of trap atom losses due to exothermic collisions in a cold sample of Cs atoms . They calculated the FCC and RE rates for a Na MOT and predict that the FCC is the dominant collisional mechanism. The scheme for the FCC and RE mechanisms is shown in Fig. 2.9. The absorption of a photon at a frequency w excites the population to the S + P3/2 state (for the Na example). If the quasimolecule incurs a crossing to the S + P1/2 potential, the collision leads to an energy transfer of DFS/2 for each atom (DFS is the fine-structure splitting). If a spontaneous emission takes place before reaching the potentials crossing, then the energy transferred to each atom is 2h¯ (w w0) with w0 being the frequency of the emitted photon.
where DM = wL w(R0) is the laser detuning with respect to the resonance frequency taken at an internuclear separation R0 (distance at which the excitation occurs). This latter is given by w (R0) = wA C3/¯hR30, with wA being the atomic resonant frequency. GM is the molecular spontaneous decay rate and s is the photoabsorption cross section taking into account all attractive molecular potentials.
Table of contents :
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
2.1 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
Conclusion and perspectives