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Acta Physica Sinica

Ultracold spin-1 atoms in three-well optical superlattice under a weak magnetic field

Qin Shuai-Feng, Gong-Ping Zheng, Xiao Ma, Haiyan Li, Tong Jing-Jing, Bo Yang

Published Jan 1, 2013• 1 citation
Publisher

Abstract

Ultracold atoms trapped in an optical lattice of double-well potential, the so-called optical superlattice, have received much attention in the field of cold atoms. A protocol generalized to three-well optical superlattice is suggested in this paper. The ground-state diagrams of ultracold spin-1 atoms trapped in a symmetric three-well optical superlattice in a weak magnetic field are studied based on the exact diagonalization. It is shown that the ground-state diagrams are remarkably different for the ferromagnetic and antiferromagnetic atoms. There does not exist the type of ground state for the antiferromagnetic interaction atoms, where the magnetic quantum number of the total spin of the system along the external magnetic field are ±2. But for the ferromagnetic interaction atoms, there do exist. In addition, there exist only the fully polarized ground-states for the ferromagnetic atoms in the negative quadratic-Zeeman-energy region. The physicsal origin of the dependence of the ground states on the controllable parameters are analyzed. These quantum spin-states can be controlled easily and exactly by modulating the external magnetic field and the height of the optical barrier, which may be a tool for the study of spin-entanglement.

DOI
10.7498/aps.62.110304

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Ultracold atoms trapped in an optical lattice of double-well potential, the so-called optical superlattice, have received much attention in the field of cold atoms. A protocol generalized to three-well optical superlattice is suggested in this paper. The ground-state diagrams of ultracold spin-1 atoms trapped in a symmetric three-well optical superlattice in a weak magnetic field are studied based on the exact diagonalization. It is shown that the ground-state diagrams are remarkably different for the ferromagnetic and antiferromagnetic atoms. There does not exist the type of ground state for the antiferromagnetic interaction atoms, where the magnetic quantum number of the total spin of the system along the external magnetic field are ±2. But for the ferromagnetic interaction atoms, there do exist. In addition, there exist only the fully polarized ground-states for the ferromagnetic atoms in the negative quadratic-Zeeman-energy region. The physicsal origin of the dependence of the ground states on the controllable parameters are analyzed. These quantum spin-states can be controlled easily and exactly by modulating the external magnetic field and the height of the optical barrier, which may be a tool for the study of spin-entanglement.
The ground states of the ultracold spin-1 atoms trapped in a deep one-dimensional double-well optical superlattice in a weak magnetic field are obtained. It is shown that the ground-state diagrams of the reduced double-well model are remarkably different for the antiferromagnetic and ferromagnetic condensates. The transition between the singlet state and nematic state is observed for the antiferromagnetic interaction atoms, which can be realized by modulating the tunneling parameter or the quadratic Zeeman energy. An experiment to distinguish the different spin states is suggested.
We discuss a model with ultra-cold atoms confined in optical superlattices. In particular, we study the ground-state properties of two spin-1 bosons trapped in a double-well potential. Depending on the external magnetic field and biquadratic interactions different phases of magnetic order are realized. Applying von Neumann entropy and number of relevant orbitals, we quantify the bipartite entanglement between particles. Changing the values of the parameters determining superlattices, we can switch the system between differently entangled states.
In this thesis we study various aspects of spinor Bose-Einstein condensates in optical superlattices using a Bose-Hubbard Hamiltonian that takes spin effects into account. We decouple the unit cells of the superlattice via a mean-field approach and take into account the dynamics within the unit cell exactly. In this way we derive the ground-state phase diagram of spinor bosons in superlattices. The system supports Mott-insulating as well as superfluid phases. The transitions between these phases are second-order for spinless bosons and second- or first-order for spin-1 bosons. Antiferromagnetic interactions energetically penalize high-spin configurations and elongate all Mott lobes, especially the ones corresponding to an even atom number on each lattice site. We find that the quadratic Zeeman effect lifts the degeneracy between different polar superfluid phases leading to additional metastable phases and first-order phase transitions. A change of magnetic fields can drive quantum phase transitions in the same way as a change in the tunneling amplitude does. Furthermore we study the physics of spin-1 atoms in superlattices deep in the Mott insulating phase when the superlattice decomposes into isolated double-well potentials. Assuming that a small number of spin-1 bosons is loaded in an optical double-well potential, we study single-particle tunneling that occurs when one lattice site is ramped up relative to a neighboring site. Spin-dependent effects modify the tunneling events in a qualitative and quantitative way. Depending on the asymmetry of the double well different types of magnetic order occur, making the system of spin-1 bosons in an optical superlattice a model for mesoscopic magnetism with an unprecedented control of the parameters. Homogeneous and inhomogeneous magnetic fields are applied and the effects of the linear and the quadratic Zeeman shifts are examined. We generalize the concept of bosonic staircases to connected double-well potentials. We show that an energy offset between the two sites of the unit cell in an extended superlattice induces a staircase of single-atom resonances in \nthe same way as in isolated double well. We also examine single-atom resonances in the superfluid regime and find clear fingerprints of them in the superfluid density. We also investigate the bipartite entanglement between the sites and construct states of maximal entanglement. The entanglement in our system is due to both orbital and spin degrees of freedom. We calculate the contribution of orbital and \nspin entanglement and show that the sum of these two terms gives a lower bound for the total entanglement.
Since the experimental realization of Bose-Einstein condensation in 1995, the field of ultracold atoms has expanded rapidly, and has become an important arena for exploring diverse quantum many-body physics, as highlighted by the experimental observation of quantum phase transitions in the system of bosons in a periodic potential, which is described by the Bose-Hubbard model.Recently, ultracold atoms with spin degrees of freedom are actively studied because the coupling between the internal spin degrees of freedom and the spatial degrees of freedom can give rise to novel and interesting physics.A minimal model for studying such physics is the spin-1 Bose-Hubbard model, which describes spin-1 bosons in a periodic potential.The model has a spin-dependent interaction, which can be ferromagnetic or antiferromagnetic, and it is known that although the ferromagnetic model resembles the spinless counterpart, the antiferromagnetic model exhibits totally different features, which make the model much more intensively studied compared with the ferromagnetic one.However, the presence of an external magnetic field can change the situation, because the positive quadratic Zeeman energy competes with the ferromagnetic interaction, which can give rise to rich phases.In this thesis, we explore the ground-state and nonzero-temperature phase diagrams of the spin-1 Bose-Hubbard model under an external magnetic field.To analyze the model, we use an approximation method called the decoupling approximation, or equivalently, the Gutzwiller variational ansatz.It is shown that, in addition to the Mott insulator phase, the model possesses two superfluid phases.Moreover, for large values of a spin-dependent interaction, the phase transitions between the two superfluid phases can be discontinuous.Such discontinuous phase transitions are shown to survive at nonzero but sufficiently low temperature.The discontinuous phase transitions are in clear contrast to the mean-field theory of weakly interacting spin-1 bosons without a lattice, which predicts that the corresponding phase transition is continuous, signifying the importance of the effect of strong interactions on the interplay between the spatial and spinor degrees of freedom. 4.1.2The grand Hamiltonian . . . . . . . . .
We examine spinor Bose-Einstein condensates in optical superlattices theoretically using a Bose-Hubbard Hamiltonian that takes spin effects into account. Assuming that a small number of spin-1 bosons is loaded in an optical potential, we study single-particle tunneling that occurs when one lattice site is ramped up relative to a neighboring site. Spin-dependent effects modify the tunneling events in a qualitative and quantitative way. Depending on the asymmetry of the double well, different types of magnetic order occur, making the system of spin-1 bosons in an optical superlattice a model for mesoscopic magnetism. We use a double-well potential as a unit cell for a one-dimensional superlattice. Homogeneous and inhomogeneous magnetic fields are applied, and the effects of the linear and the quadratic Zeeman shifts are examined. We also investigate the bipartite entanglement between the sites and construct states of maximal entanglement. The entanglement in our system is due to both orbital and spin degrees of freedom. We calculate the contribution of orbital and spin entanglements and show that the sum of these two terms gives a lower bound for the total entanglement.