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Chinese Physics Letters

Calculation of the Spin-Dependent Optical Lattice in Rubidium Bose—Einstein Condensation

Mingtao Cao, Liang Han, Yue-Rong Qi, Shougang Zhang, Hong Gao, Fuli Li

Published Mar 1, 2012• 3 citations
Publisher

Abstract

We provide a theoretical study to calculate the spin-dependent optical lattice with rubidium Bose—Einstein condensation (BEC) in a steady magnetic field. The optical dipole potential variation at different Zeeman levels are obtained. We also show that atoms can be transported in three dimensions by changing the polarization of the trapping field. An explanation of this transportation process in an atomic coordinate is presented.

DOI
10.1088/0256-307x/29/3/034201

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We provide a theoretical study to calculate the spin-dependent optical lattice with rubidium Bose—Einstein condensation (BEC) in a steady magnetic field. The optical dipole potential variation at different Zeeman levels are obtained. We also show that atoms can be transported in three dimensions by changing the polarization of the trapping field. An explanation of this transportation process in an atomic coordinate is presented.
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Abstract We investigate a Bose–Einstein condensate of F = 187Rb atoms in a 2D spin-dependent optical lattice generated by intersecting laser beams with a superposition of polarizations. For 87Rb the effective interaction of an atom with the electromagnetic field contains scalar and vector (called a fictitious magnetic field, B fic) potentials. The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic rotational motion angular momentum and the hyperfine spin. The ground state of the QR is affected upon applying an external magnetic field, B ext, perpendicular to the plane of QR motion and a sudden change of its topology occurs as the ratio B ext/B fic exceeds a critical value. It is shown that the change of topology of the QR ground state is a result of combined action of Zeeman and Einstein–de Haas effects. The first transfers atoms to the largest hyperfine component to polarize the sample along the field as the external magnetic field is increased. The second sweeps spin to rotational angular momentum, modifying the kinetic energy of the atoms.
The final stage in the creation of a Bose-Einstein condensate (BEC) is trapping and compressing in a strong magnetic trap. When the spin of an atom changes, it is lost from this magnetic trap. To be able to do experiments with varying atom spin, one can use an optical dipole trap, which traps atoms independent of their spin. This thesis presents a far red-detuned optical dipole trap, which is characterized by trapping BEC's. Furthermore, an approach to rapidly scan this trap is presented, creating a 'quasi-2D' potential. With this potential we attempt to create a horizontal sheet of condensed atoms, where the depth of the sheet of atoms is smaller than the range of the spin dynamics. This would enable a unique visualization of the spin dynamics using spin-dependent imaging.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.
The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. This article offers a short survey on mathematical models and theories as well as numerical methods for BEC based on the mean field theory. We start with the Gross-Pitaevskii equation (GPE) in three dimensions (3D) for modeling one-component BEC of the weakly interacting bosons, scale it to obtain a three-parameter model and show how to reduce it to two dimensions (2D) and one dimension (1D) GPEs in certain limiting regimes. Mathematical theories and numerical methods for ground states and dynamics of BEC are provided. Extensions to GPE with an angular momentum rotation term for a rotating BEC, to GPE with long-range anisotropic dipole-dipole interaction for a dipolar BEC and to coupled GPEs for spin-orbit coupled BECs are discussed. Finally, some conclusions are drawn and future research perspectives are discussed.
We investigate the properties of a Bose-Einstein condensate (BEC) of F=1F=1F=1 87^{87}87Rb atoms in a 2D spin-dependent optical lattice potential generated by intersecting laser beams with a superposition of polarizations. For 87^{87}87Rb, where the total electronic angular momentum is J=1/2J = 1/2J=1/2, the effective interaction of an atom with the electromagnetic field contains a scalar potential VVV and a vector potential (often called fictitious magnetic field). The Rb atoms behave as a quantum rotor (QR) with angular momentum given by the sum of the atomic motion rotational angular momentum around the lattice minima and the atomic hyperfine spin FFF. Properties of the QR are strongly affected when an external magnetic field perpendicular to the plane of QR motion is applied. A topological phase transition occurs as the ratio of the external transverse magnetic field to fictitious magnetic field exceeds critical value. At such a quantum phase transition the symmetry of the ground state changes and is expressed in the change of the spin texture.