Bidimensional gas of cold bosons (new experimental system of Bose-Einstein condensation)

Allen L. Wasserman

From a certain temperature on, the molecules “condense” without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there also some truth to it? Albert Einstein, Letter to Ehrenfest (Dec. 1924). Abraham Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein , Oxford University Press, New York (1982) Introduction For over 50 years the low-temperature liquid state of uncharged, spinless He 4 was the only system in which a Bose–Einstein (BE) condensation was considered experimentally realized. In that case, cold (<2.19K) liquid He 4 passes into an extraordinary phase of matter called a superfluid , in which the liquid's viscosity and entropy become zero. With advances in atomic cooling (to ≈ 10 –9 K) the number of Bose systems which demonstrably pass into a condensate has considerably increased. These include several isotopes of alkali gas atoms as well as fermionic atoms that pair into integerspin (boson) composites. Although an ideal Bose gas does exhibit a low-temperature critical instability, the ideal BE gas theory is not, on its own, able to describe the BE condensate wave state. In order for a theory of bosons to account for a condensate wave state, interactions between the bosons must be included. Nevertheless, considerable interesting physics is contained in the ideal Bose gas model.

Robert Seiringer

Edwin Pedrozo-Peñafiel

In this work we constructed an experimental system to realize a BEC of sodium atoms. In the first part of the work, we study two atomic sources in order to choose the most suitable for our system. The comparison between a Zeeman slower and a bidimensional magnetooptical trap (2D-MOT) was performed to evaluate the capacity of producing an appropiate flux of atoms in order to load a tridimensional magneto-optical trap (3D-MOT). The experimental results show that the 2D-MOT is as efficient as the Zeeman slower with the advantage of being more compact and easier to operate, and for these reasons we choose it as our source of cold atoms. After this, the experimental apparatus to produce a Bose-Einstein condensate was constructed and characterized. With this experimental system we realized all the required stages to achieve the Bose-Einstein condensation (BEC). Initially, we characterized and compared the performance between the Bright-MOT and Dark-SPOT MOT of sodium atoms, observing the great advantages this last configuration offers. Afterward, we implemented the experimental sequence for the achivement of the BEC of sodium atoms. After the optical molasses process, the atoms are tranferred to an optically plugged quadrupole trap (OPT) where the process of evaporative cooling is performed. With this setup, we achive a sodium BEC with ∼ 5×105 atoms and a critical temperature of ∼ 1.1 μK. Finally, with the constructed and characterized machine, we started to perform experiments of cooperative absorption of two photons by two trapped atoms. With the new system, we wanted to take advantage of the higher densities in the magnetic trap and BEC to explore some features of this phenomenon in the classical and quantum regimes. We were interested in exploring some features of this nonlinear light-matter interaction effect. The idea of having two or more photons interacting with two or more atoms is the beginning of a new possible class of phenomena that we could call many photons-many body intercation. In this new possibity, photons and atoms will be fully correlated, introducing new aspects of interactions.

Fabrizio Tafuri, C. A. Perroni, G. De Filippis

Pierre Jouve

This thesis reports on a study of the molecular Bose-Einstein condensation (mBEC) of the 6Li. More specifically, using model the Hartree-Fock (HF) model to fit the spatial density of the cloud, we demonstrate that the thermal cloud deplete the condensate, therefore a lower temperature is needed to condense the atoms in the ground state. Moreover the inter-atomic interactions can be controlled via Feshbach resonance (see section 2.2), allowing us to study the effects of the interactions on the thermodynamics properties of a mBEC, especially the critical temperature of the BEC that decreases when we increase the inter-atomic interactions. The description starts from the experimental procedure to produce a mBEC to its physical analysis. We draw a list describing the different chapters presented in the thesis: Chapter 1 Introduction: We present the fundamental difference between fermions and bosons, and we give some example of realisations of Bose-Einstein condensation and degenerate Fermi gas. Chapter 2 Interactions in an ultracold gas: We discuss the role of interactions depending on the type of particles, either fermions or bosons, and the phenomena of Feshbach resonance which is a powerful tool to change the interaction strength between particles. Chapter 3 Degenerate quantum gas: A brief historical section gives the fundamental ideas that initiate the long story of the Bose-Einstein condensation phenomena. We then discuss the mathematical description of a BEC without interactions, which is the starting point of the theoretical analysis used in the chapter 3 where we study the influence of the interactions. Then, we describe the statistics of Fermi gas and the different states that can be reached using Feshbach resonances, in particular the creation of the Feshbach molecules. Chapter 4 Basics of Cold atoms physics: A toolbox of the necessary knowledge to understand the underlying phenomena and concepts used in a cold atoms experiment. We describe the kind of atoms used, how these atoms interact with a magnetic and an electromagnetic field. Chapter 5 Guideline to making a 6Li BEC: This chapter describes the experimental methods used in our laboratory to cool down atoms to the regime of ultra-cold temperature T < 1µK. This section gives details about atomic beams production, the Zeemann slower (radiation force cooling), the magnetooptical trap (MOT) (cooling b molasses), optical dipole trap (evaporative cooling). Also we present the methods used to probe atomic clouds, such as in situ imaging methods. My contribution to this section has been to improve the stability of the evaporative cooling sequence (see section 5.4.4) and to optimize the shape of the the evaporative cooling ramp (see section 5.4.1) in order to maximise the phase space density (PSD), to reach Bose-Einstein condensation. Then, to make precise simulations and measurements to extract values of the trapping frequencies (see section 5.4.5) and scattering length (see section 5.5.4), the latter gives us the interaction strength of the system. These parameter are then used in the next chapter to extract thermodynamics properties of the system. Moreover, I developed the sequence for in situ absorption imaging (see section 5.5.3). Chapter 6 Study of an interacting 6Li mBEC: This chapter discusses the theory to understand the thermodynamics properties of an interacting Bose6 Einstein condensate. It is accomplished by fitting the spatial atomic density profiles with different models, the ideal gas (IG) model, the semi-Ideal (SI) gas model and the Hartree-Fock (HF) model. These three models vary in complexity from the most simple one the IG model to most elaborated one the HF model. The HF model requires a lot more of computational power than the other methods, therefore we present a new numerical method requiring less computational power proposed by Nathan Welch, and demonstrate experimentally through a statistical analysis that the HF model used to determine the thermodynamics properties of a BEC is more accurate to describe utracold atomic gas near the transition. Then, we present the results of the influence of the scattering length on the transition temperature and the chemical potential. My contribution to this section has been to develop tools to analyse the in situ atomic density profiles and improve the fitting program of Nathan (see section 6.3). Also, after taking the measurement of the in situ atomic density profiles, I developed and used the tools for the analysis of the thermodynamics properties of the mBEC (see section 6.4). I also adapted the models described in [1] to our experiment to extract the value of the radius of the condensate (see section 6.5). Finally, with N.Welch we present method based on energy conservation to verify the validity of the different model, my principal contribution to this was to modify the experiment to use this method (see section 6.7). Chapter 7 Initial work: Double well with 6Li molecules: This chapter presents the initial work to produce a double well potential to trap cold atoms and create a Josephson Junction. We present the state of the art of the different effects that have been observed, and discuss future measurements that would be achievable in our laboratory, in particular we would like to use a second specie 133Cs as impurities and observe the influence on Josephson oscillations of 6Li molecules. An experimental description of the double well trapping potential has been implemented and is also described. My contribution to this section was to design and implement the double well trapping potential.