Summary form only given. Experiments on dilute alkali vapor condensates with internal degrees of freedom have opened up new areas in the study of Bose-Einstein condensation. In particular, the realization of an optically confined condensate has prompted much interest in the study of the spinor condensate-a condensate with the spin orientation as a new degree of freedom. A key feature of this system is the presence of the spin-exchange interactions that cause spin mixing within the condensate. Therefore, it is interesting to study how the spins are organized in the ground state and what is the nature of the dynamics of the spin-mixing process. These are the questions we want to answer in the context of an f=1 spinor condensate.
Summary form only given. Experiments on dilute alkali vapor condensates with internal degrees of freedom have opened up new areas in the study of Bose-Einstein condensation. In particular, the realization of an optically confined condensate has prompted much interest in the study of the spinor condensate-a condensate with the spin orientation as a new degree of freedom. A key feature of this system is the presence of the spin-exchange interactions that cause spin mixing within the condensate. Therefore, it is interesting to study how the spins are organized in the ground state and what is the nature of the dynamics of the spin-mixing process. These are the questions we want to answer in the context of an f=1 spinor condensate.
Summary form only given. The optical trapping of sodium Bose condensates has opened the possibility to study spinor condensates which have their hyperfine spin as a new degree of freedom. They represent a superfluid system with a vector order parameter. A host of novel phenomena have been predicted. A spinor condensate such as the one realized by Stamper-Kurn et al. involves all three hyperfine states in the lowest energy f=1 manifold and thus poses challenges towards the understanding of the low energy properties and dynamics of such systems. We consider a Bose condensate which contains atoms with three internal spins in a cigar-shaped trap and approximate the wavefunction of the spin state.
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.
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.
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.
The magnetism of Fermi gases and local magnetic moments has long been a key research topic in condensed matter physics,while that of Bose gases has historically been less studied. The reason for this may be due to the fact that He-4,the prototypical Bose system studied in earlier years,is a system of scalar particles and does not display magnetism at all. The realization of Bose-Einstein condensation in alkali atoms opens up a way to study magnetism in spinor bosons,because these constituent atoms usually have a hyperfine spin degree of freedom. This paper will review our current understanding of magnetism in Bose gases,especially focusing on new results obtained regarding ferromagnetic transitions in spinor bosons and the spin dynamics of spinor condensates.
Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we