In this thesis, we present some experiments realized with ultracold gases of sodium atoms, trapped at the intersect between two laser beams. At very low temperature, the discretization of energy and the indistinguishability of particles, lead to a new state of matter, a Bose-Einstein condensate. This remarkable phenomenon was initially introduced to describe an ideal gas, that is to say with no interactions between its constituents. Here, we are interested in the effects of the interactions between the atoms. More precisely, our atoms carry a spin 1, and we focus on the collective spin state, in a regime where the spatial degrees of freedom are frozen. Two important results that we present were obtained by embedding the condensate in a nearly vanishing magnetic field. In that regime, interactions dominate and favor the emergence of strongly correlated states. In a first series of experiment, the magnetic field is suddenly decreased to bring the system out-of-equilibrium. The ensuing relaxation dynamics leads to a stationnary state that can be well described by a Gibbs ensemble. In a second experiment, the field is slowly reduced, in order to follow the ground state of the system. We thereby produce a fragmented condensate, which possesses the remarkable feature of being invariant upon spin rotations. The restoration of this symmetry, always broken by single (i.e. nonfragmented) condensates, is driven by the pairing of atoms in singlet states.
In this thesis, we present some experiments realized with ultracold gases of sodium atoms, trapped at the intersect between two laser beams. At very low temperature, the discretization of energy and the indistinguishability of particles, lead to a new state of matter, a Bose-Einstein condensate. This remarkable phenomenon was initially introduced to describe an ideal gas, that is to say with no interactions between its constituents. Here, we are interested in the effects of the interactions between the atoms. More precisely, our atoms carry a spin 1, and we focus on the collective spin state, in a regime where the spatial degrees of freedom are frozen. Two important results that we present were obtained by embedding the condensate in a nearly vanishing magnetic field. In that regime, interactions dominate and favor the emergence of strongly correlated states. In a first series of experiment, the magnetic field is suddenly decreased to bring the system out-of-equilibrium. The ensuing relaxation dynamics leads to a stationnary state that can be well described by a Gibbs ensemble. In a second experiment, the field is slowly reduced, in order to follow the ground state of the system. We thereby produce a fragmented condensate, which possesses the remarkable feature of being invariant upon spin rotations. The restoration of this symmetry, always broken by single (i.e. nonfragmented) condensates, is driven by the pairing of atoms in singlet states.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
Dynamique cohérente, relaxation et fragmentation d'un condensat de Bose-Einstein spinoriel Dans cette thèse, nous présentons des expériences réalisées avec des gaz d'atome de sodium ultrafroids, piégés à l'intersection de deux faisceaux laser. À très basse température, discrétisation de l’énergie et indiscernabilité des particules conduisent à un nouvel état de la matière, un condensat de Bose-Einstein. Ce phénomène remarquable a d'abords été décrit pour un gaz idéal, c'est-à-dire sans interaction entre ses constituants. Ici, nous nous intéressons aux effets des interactions entre atomes. Plus précisément, nos atomes possèdent un spin 1, et nous nous interessont à l'état spinoriel collectif, dans un régime ou les degrées de liberté spatiaux sont gelés. Deux résultats importants que nous présentons ont été obtenus en plongeant le condensat dans un champ magnétique quasi-nul. Dans ce régime, les interactions dominent et favorisent l'émergence d'états fortement corrélés. Dans une première série d'expériences, le champ est soudainement réduit, et le système se retrouve horséquilibre. Il s'ensuit une dynamique de relaxation, qui mène à un état stationnaire bien décrit par un ensemble de Gibbs. Dans une seconde expérience, le champ est progressivement réduit, de façon à suivre l'état fondamental du système. Nous réalisons ainsi un condensat fragmenté, dont une remarquable propriété est l'invariance sous rotations des spins. La restauration de cette symétrie, toujours brisée par les condensat “simple" (i.e. non-fragmenté), se fait grâce à l'appariement des atomes en état singulet.
In this thesis, we study theoretically and in experimentally the properties of spin-1 Bose-Einstein condensates with antiferromagnetic interactions realized in the ultra-cold sodium gases confined in optical dipole traps. We present in detail how to realize, diagnose and control the spinor Bose-Einstein condensates in our experiment. In order to describe the condensate, a mean-field theory is first adopted. This theory predicts a phase transition when changing the magnetic field B. The predictions of the mean-field theory agree very well with most of our experimental results, including the values of the critical magnetic field Bc, asymptotic values of n0 (relative atom number in mF=0 state) at large B and the phase diagram of n0. However, for small magnetization and small magnetic fields, we find abnormally large fluctuations (super-Poissonian) of n0. In order to describe these large fluctuations, we develop a full quantum statistical description for the spinor condensate at finite temperature. To describe uncondensed thermal atoms (also present in the same trap), we use the ``semi-ideal" Hartree-Fock approximation to deal with the interactions between the condensate atoms and the thermal ones. The experimental results lead us to introduce two kinds of temperatures, the ``spin temperature" Ts and the ``kinetic temperature" Tk with Ts≪Tk, characterizing respectively the fluctuaitons of the condensate spin and the thermal gas. We conclude that the system is reaching a quasi-equilibrium states, where different degrees of freedom reach equilibrium by separate mechanisms but where the mutual thermalization does not occur over the lifetime of the cloud.
We study several problems in Bose-Einstein condensates with internal degrees of freedom, and we find that this kind of condensates, which are usually referred to as spinor condensates, exhibit several phenomena that are qualitatively different from scalar (i.e. spinless) condensates. We analyze the ground state of a condensate with the constraint of maintaining a constant value of the total spin, and we find a number of different structures depending on the value of the total spin and the applied external magnetic field. We also study a certain type of measurement on spinor condensates in an attempt to distinguish between the so-called coherent and singlet states. We find that this kind of measurement cannot distinguish between the two states in question. We then consider a different experiment based on the interference between spinor condensate. It turns out that interference experiments cannot be used to distinguish between coherent and singlet states either. One of the interesting results regarding interference between two spinor condensates is that both the offset and visibility of the interference fringes vary from shot to shot, even if the initial conditions are identical in all the runs of the experiment. We then turn to the problem of condensing a gas of effectively spin 1/2 atoms. We argue that if spin relaxation mechanisms are slow enough, the condensate displays the phenomenon of fragmentation. The main difference of the fragmented state that we study and other fragmented states discussed in the literature is that this one is not caused by interatomic interactions, but rather by the constraint on the total spin of the system. We investigate the consequences of performing the experiment in a toroidal trap, and we find that, under certain conditions, the system spontaneously builds up a macroscopic value of orbital angular momentum. We finally discuss several problems related to the external Josephson effect. We derive simple equations of motion for the case of a two-component condensate that are identical to the extensively analyzed Bloch equations. We also find equilibrium points of the motion that are unstable in the spinless case.
Weakly interacting Bose gases usually form Bose-Einstein condensates in which most particles occupy the same single-particle state. However, when this state cannot realize a continuous symmetry of the many-body Hamiltonian, a fragmented condensate exhibiting the expected symmetry may emerge. Here, we produced a three-fragment condensate for a mesoscopic spin-1 gas of about 100 atoms, with anti-ferromagnetic interactions and vanishing collective spin. Using a spin-resolved detection approaching single-atom resolution, we show that the reconstructed state is close to the expected many-body ground state, whereas one-body observables are the same as for a completely mixed state. Our results highlight how the interplay between symmetry and interactions generates entanglement in a mesoscopic quantum system.
Optical trapping as a viable means of exploring the physics of ultracold dilute atomic gases has revealed a new spectrum of physical phenomena. In particular, macroscopic and sudden occupation of the ground state below a critical temperature—-a phenomenon known as Bose-Einstein condensation—-has become an even richer system for the study of quantum mechanics, ultracold collisions, and many-body physics in general. Optical trapping liberates the spin degree of the BEC, making the order parameter vectorial (‘spinor BEC’), as opposed to the scalar order of traditional magnetically trapped condensates. The work described within is divided into two main efforts. The first encompasses the all-optical creation of a Bose-Einstein condensate in rubidium vapor. An all-optical path to spinor BEC (as opposed to transfer to an optical trap from a magnetic-trap condensate) was desired both for the simplicity of the experimental setup and also for the potential gains in speed of creation; evaporative cooling, the only known path to dilute-gas condensation, works only as efficiently as the rate of elastic collisions in the gas, a rate that starts out much higher in optical traps. The first all-optical BEC was formed elsewhere in 2001; the years following saw many groups worldwide seeking to create their own version. Our own all-optical spinor BEC, made with a single-beam dipole trap formed by a focused CO₂ laser, is described here, with particular attention paid to trap loading, measurement of trap parameters, and the use of a novel 780 nm high-power laser system. The second part describes initial experiments performed with the nascent condensate. The spinor properties of the condensate are documented, and a measurement is made of the density-dependent rate of spin mixing in the condensate. In addition, we demonstrate a novel dual-beam atom laser formed by outcoupling oppositely polarized components of the condensate, whose populations have been coherently evolved through spin dynamics. We drive coherent spin-mixing evolution through adiabatic compression of the initially weak trap. Such dual beams, nominally number-correlated through the angular momentum-conserving collision m=0 + m=0 ⇌ m=+1 + m=-1 have been proposed as tools to explore entanglement and squeezing in Bose-Einstein condensates.