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Chinese Optics Letters

Spin dynamics of high-spin fermions in optical superlattices

Shaobing Zhu, Jun Qian Jun Qian, Yuzhu Wang Yuzhu Wang

Published Jan 1, 2017• 1 citation
Publisher

Abstract

We investigate the spin dynamics, starting from the initial band-insulating state, of fermionic high-spin atoms in optical superlattices. Through numerical simulations and analytical calculations, we determine the time evolution behavior of the system. When the spin-changing strength and tunneling strength are comparable, the spin dynamics feature a spin-changing oscillation with the amplitude modulated by the superexchange interaction. When the double-well potential is very shallow, the spin dynamics feature a simple harmonic oscillation with the oscillation frequencies related only to the spin-changing strength, which can be properly explained with the perturbation model.

DOI
10.3788/col201715.060202

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We investigate the spin dynamics, starting from the initial band-insulating state, of fermionic high-spin atoms in optical superlattices. Through numerical simulations and analytical calculations, we determine the time evolution behavior of the system. When the spin-changing strength and tunneling strength are comparable, the spin dynamics feature a spin-changing oscillation with the amplitude modulated by the superexchange interaction. When the double-well potential is very shallow, the spin dynamics feature a simple harmonic oscillation with the oscillation frequencies related only to the spin-changing strength, which can be properly explained with the perturbation model.
We show that fermionic high-spin systems with spin-changing collisions allow one to monitor superexchange processes in optical superlattices with large amplitudes and strong spin fluctuations. By investigating the non-equilibrium dynamics, we find a superexchange dominated regime at weak interactions. The underlying mechanism is driven by an emerging tunneling-energy gap in shallow few-well potentials. As a consequence, the interaction-energy gap that is expected to occur only for strong interactions in deep lattices is re-established. By tuning the optical lattice depth, a crossover between two regimes with negligible particle number fluctuations is found: firstly, the common regime with vanishing spin-fluctuations in deep lattices and, secondly, a novel regime with strong spin fluctuations in shallow lattices. We discuss the possible experimental realization with ultracold 40 K atoms and observable quantities in double wells and two-dimensional plaquettes.
We study the time-dependent dynamical properties of two-component ultracold fermions in a one-dimensional optical superlattice by applying the adaptive time-dependent density matrix renormalization group to a repulsive Hubbard model with an alternating superlattice potential. We clarify how the time evolution of local quantities occurs when the superlattice potential is suddenly changed to a normal one. For a Mott-type insulating state at quarter filling, the time evolution exhibits a profile similar to that expected for bosonic atoms, where correlation effects are less important. On the other hand, for a band-type insulating state at half filling, the strong repulsive interaction induces an unusual pairing of fermions, resulting in some striking properties in time evolution, such as a paired fermion co-tunneling process and the suppression of local spin moments. We further address the effect of a confining potential, which causes spatial confinement of the paired fermions.
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 report on the experimental implementation of a spin pump with ultracold bosonic atoms in an optical superlattice. In the limit of isolated double wells, it represents a 1D dynamical version of the quantum spin Hall effect. Starting from an antiferromagnetically ordered spin chain, we periodically vary the underlying spin-dependent Hamiltonian and observe a spin current without charge transport. We demonstrate a novel detection method to measure spin currents in optical lattices via superexchange oscillations emerging after a projection onto static double wells. Furthermore, we directly verify spin transport through in situ measurements of the spins' center-of-mass displacement.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
The dynamic response of ultracold Bose gases in one-dimensional optical lattices and superlattices is investigated based on exact numerical time evolutions in the framework of the Bose–Hubbard model. The system is excited by a temporal amplitude modulation of the lattice potential, as it was done in recent experiments. For regular lattice potentials, the dynamic signatures of the superfluid to Mott-insulator transition are studied and the position and the fine-structure of the resonances is explained by a linear response analysis. Using direct simulations and the perturbative analysis it is shown that in the presence of a two-colour superlattice the excitation spectrum changes significantly when going from the homogeneous Mott-insulator to the quasi-Bose-glass phase. A characteristic and experimentally accessible signature for the quasi-Bose-glass is the appearance of low-lying resonances and a suppression of the dominant resonance of the Mott-insulator phase.