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arXiv:1512.04550 · Physical Review A

First-order superfluid-to-Mott-insulator phase transitions in spinor condensates

Jie Jiang, Lichao Zhao, Sheng-Tao Wang, Z. Chen, Tao Tang, L.-M. Duan, Yingmei Liu

Published Jun 7, 2016• 24 citations
arXivHTMLPDF

Abstract

We observe evidence of first-order superfluid-to-Mott-insulator quantum phase transitions in a lattice-confined antiferromagnetic spinor Bose-Einstein condensate. The observed signatures include the hysteresis effect, significant heatings across the phase transitions, and changes in spin populations due to the formation of spin singlets in the Mott-insulator phase. The nature of the phase transitions is found to strongly depend on the ratio of the quadratic Zeeman energy to the spin-dependent interaction. Our observations are qualitatively understood by the mean field theory and suggest tuning the quadratic Zeeman energy is a new approach to realize superfluid-to-Mott-insulator phase transitions.

DOI
10.1103/physreva.93.063607

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We observe evidence of first-order superfluid-to-Mott-insulator quantum phase transitions in a lattice-confined antiferromagnetic spinor Bose-Einstein condensate. The observed signatures include the hysteresis effect, significant heatings across the phase transitions, and changes in spin populations due to the formation of spin singlets in the Mott-insulator phase. The nature of the phase transitions is found to strongly depend on the ratio of the quadratic Zeeman energy to the spin-dependent interaction. Our observations are qualitatively understood by the mean field theory and suggest tuning the quadratic Zeeman energy is a new approach to realize superfluid-to-Mott-insulator phase transitions.
We study the superfluid--Mott insulator (SF-MI) transition of spin-1 bosons interacting antiferromagnetically in an optical lattice. Starting from a Bose-Hubbard tight-binding model for spin-1 bosons, we obtain the zero-temperature phase diagram by a mean-field approximation. We find that the MI phase with an even number of atoms per site is a spin singlet state, while the MI phase with an odd number of atoms per site has spin 1 at each site in the limit of t=0t=0t=0, where ttt is the hopping matrix element. We also show that the superfluid phase is a polar state as in the case for a spin-1 Bose condensate in a harmonic trap. It is found that the MI phase is strongly stabilized against the SF-MI transition when the number of atoms per site is even, due to the formation of singlet pairs. We derive the effective spin Hamiltonian for the MI phase with one atom per site and briefly discuss the spin order in the MI phase.
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.
We study the ground-state phase diagram of spinless and spin-1 bosons in optical superlattices using a Bose-Hubbard Hamiltonian that includes spin-dependent interactions. We decouple the unit cells of the superlattice via a mean-field approach and take into account the dynamics within the unit cell exactly. 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. Finally, we show that an energy offset between the two sites of the unit cell induces a staircase of single-atom tunneling resonances, which surprisingly survives well into the superfluid regime.
We present an experimental study on nonequilibrium dynamics of a spinor condensate after it is quenched across a superfluid to Mott insulator (MI) phase transition in cubic lattices. Intricate dynamics consisting of spin-mixing oscillations at multiple frequencies are observed in time evolutions of the spinor condensate localized in deep lattices after the quantum quench. Similar spin dynamics also appear after spinor gases in the MI phase are suddenly moved away from their ground states via quenching magnetic fields. We confirm these observed spectra of spin-mixing dynamics can be utilized to reveal atom number distributions of an inhomogeneous system, and to study transitions from two-body to many-body dynamics. Our data also imply the nonequilibrium dynamics depend weakly on the quench speed but strongly on the lattice potential. This enables precise measurements of the spin-dependent interaction, a key parameter determining the spinor physics.
We analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons in the presence of an external magnetic field, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. In particular at zero temperature, we determine both the Mott and the superfluid phases for the competition between the anti-ferromagnetic interaction and the linear Zeeman effect within the validity range of the Ginzburg-Landau theory. Moreover, we find that the phase transition between the superfluid and Mott insulator phases is of second order and that the transitions between the respective superfluid phases for anti-ferromagnetic interaction can be both of first and second order.