Recently, experiments on Bose\|Einstein condensates (BECs) confined in an optical lattice have made breakthroughs. A research group in Munich has demonstrated for the first time the quantum phase transition of a superfluid state to the Mott insulator state of a BEC confined in a 3D optical lattice. Such a quantum phase transition is not only fundamentally profound, but also provides new access to applications of BECs. This paper reports our recent theoretical work on the spin dynamics and magnetism of BECs confined in an optical lattice, and explores their possible applications in atomic magnetic sensors and quantum computation.
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.
Abstract Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations.
Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. In this work we evaluated the phase boundary between the Mott insulator and the superfluid phase by means of the density matrix renormalization group. Furthermore, we studied the properties of the insulating phase for odd fillings. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S = 1 Heisenberg model with biquadratic interaction.
We study the ground-state magnetic properties of ferromagnetic spinor Bose-Einstein condensates confined in deep optical lattices. In the Mott-insulator regime, the ``minicondensates'' at each lattice site behave as mesoscopic spin magnets that can interact with neighboring sites through both the static magnetic dipolar interaction and the light-induced dipolar interaction. We show that such an array of spin magnets can undergo a ferromagnetic or antiferromagnetic phase transition under the magnetic dipolar interaction depending on the dimension of the confining optical lattice. The ground-state spin configurations and related magnetic properties are investigated in detail.