Summary form only given. The experimental discovery of Bose-Einstein condensation in dilute alkali atomic gases has revolutionized the field of macroscopic quantum coherence. Further, fundamental issues like symmetry breaking, collapse and revival of macroscopic wavefunctions can perhaps now be tested in an experimentally controllable way. A further step in the control and study of Bose-Einstein condensates (BEC) has been the creation of spinor condensates-BEC in different spin states-through optical confinement and has led to considerable theoretical activity.
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 paper we discuss Bose-Einstein spinor condensates for
F=1 atoms in the context of
87Rb, as studied experimentally by the Stamper-Kurn group [L. E. Sadler et al., Nature (London) 443, 312 (2006)]. The dynamical quantum fluctuations of a sample that starts as a condensate of
N atoms in a pure
F=1,
mF=0 state are described in analogy to the two-mode squeezing of quantum optics in terms of an
su(1,1) algebra. In this system the initial
mF=0 condensate acts as a source (pump) for the creation pairs of ${m}_{F}=1,\ensuremath{-}1$ atoms. We show that even though the system as a whole is described by a pure state with zero entropy, the reduced density matrix for the
mF=+1 degree of freedom, obtained by tracing out the ${m}_{F}=\ensuremath{-}1,0$ degrees of freedom, corresponds to a thermal state. Furthermore, these quantum fluctuations of the initial dynamics of the system provide the seeds for the formation of domains of ferromagnetically aligned spins.
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.
We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a
F=1 87Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.
We develop theory for fluctuations in atom number and spin within finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a model of measurements that can be performed in current experiments using finite resolution in situ imaging. We develop analytic results for quantum and thermodynamic limits of the fluctuations and apply our theory to the four equilibrium phases of a spin-1 condensate. We then validate these limits and examine the behavior over a wide parameter regime using numerical calculations specialized to the case of a spinor condensate confined to be quasi-two-dimensional.