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.
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.
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.
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.
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.
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.
In this thesis we investigate the static, dynamic, and thermodynamic properties\nof atomic spin-1 Bose gases in external magnetic fields. At low magnetic fields\nthe properties of single-component, or scalar condensates, are essentially\nunaffected but can become significantly altered for spinor Bose condensates as\nshown by our studies.\n\nWe first study the Bose-Einstein condensation of trapped spin-1 Bose gases by\nemploying the Hartree-Fock approximation and the two-fluid model within a mean\nfield approximation. Our detailed investigation reveals that the\nferromagnetically interacting spin-1 condensates exhibit triple condensations\nwhile the antiferromagnetically interacting ones show double condensations.\n\nThe ground state structure of homogeneous and trapped spin-1 Bose condensates\nwith ferromagnetic and antiferromagnetic interactions at zero temperature in\nmagnetic fields are then investigated systematically. We further illuminate the\nimportant effect of quadratic Zeeman shift which causes a preferred occupation\nof the $|m_F=0\nangle$ state through spin exchange collisions, $2|m_F=0\nangle\nleftrightarrow |m_F=1\nangle + |m_F=-1\nangle$.\n\nWe also present detailed studies of the off-equilibrium coherent dynamics of\nspin-1 Bose condensates in magnetic fields within the single spatial mode\napproximation. Dynamical instabilities of the off-equilibrium oscillations are\nshown to be responsible for the formation of multiple domains as recently\nobserved in several 87Rb experiments.\n\nFinally, we discuss briefly excited condensate states, or soliton-like states,\nin cigar-shaped spin-1 Bose condensates with an effective quasi-1D description,\nusing the developed nonpolynomial Schr"odinger equation.
We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.