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arXiv:1912.10028 · Physical Review A

Dynamics of rotated spin states and magnetic ordering with two-component bosonic atoms in optical lattices

Araceli Venegas‐Gomez, Anton S. Buyskikh, Johannes Schachenmayer, Wolfgang Ketterle, Andrew J. Daley

Published Aug 20, 2020• 8 citations
arXivHTMLPDF

Abstract

The microscopic control available over cold atoms in optical lattices has opened new opportunities to study the properties of quantum spin models. While a lot of attention is focused on experimentally realizing ground or thermal states via adiabatic loading, it would often be more straightforward to prepare specific simple product states and to probe the properties of interacting spins by observing their dynamics. We explore this possibility for spin-1/2 and spin-1 models that can be realized with bosons in optical lattices, and which exhibit $\mathit{XY}$-ferromagnetic (or counterflow spin-superfluid) phases. We consider the dynamics of initial spin-rotated states corresponding to a mean-field version of the phases of interest. Using matrix product state methods in one dimension, we compute both nonequilibrium dynamics and ground and thermal states for these systems. We compare and contrast their behavior in terms of correlation functions and induced spin currents, which should be directly observable with current experimental techniques. We find that although spin correlations decay substantially at large distances and on long timescales, for induction of spin currents, the rotated states behave similarly to the ground states on experimentally observable timescales.

DOI
10.1103/physreva.102.023321

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The microscopic control available over cold atoms in optical lattices has opened new opportunities to study the properties of quantum spin models. While a lot of attention is focused on experimentally realizing ground or thermal states via adiabatic loading, it would often be more straightforward to prepare specific simple product states and to probe the properties of interacting spins by observing their dynamics. We explore this possibility for spin-1/2 and spin-1 models that can be realized with bosons in optical lattices, and which exhibit XY\mathit{XY}XY-ferromagnetic (or counterflow spin-superfluid) phases. We consider the dynamics of initial spin-rotated states corresponding to a mean-field version of the phases of interest. Using matrix product state methods in one dimension, we compute both nonequilibrium dynamics and ground and thermal states for these systems. We compare and contrast their behavior in terms of correlation functions and induced spin currents, which should be directly observable with current experimental techniques. We find that although spin correlations decay substantially at large distances and on long timescales, for induction of spin currents, the rotated states behave similarly to the ground states on experimentally observable timescales.
We suggest and analyze a scheme to adiabatically cool bosonic atoms to picokelvin temperatures which should allow the observation of magnetic ordering via superexchange in optical lattices. The starting point is a gapped phase called the spin Mott phase, where each site is occupied by one spin-up and one spin-down atom. An adiabatic ramp leads to an xyxyxy-ferromagnetic phase. We show that the combination of time-dependent density matrix renormalization group methods with quantum trajectories can be used to fully address possible experimental limitations due to decoherence, and demonstrate that the magnetic correlations are robust for experimentally realizable ramp speeds. Using a microscopic master equation treatment of light scattering in the many-particle system, we test the robustness of adiabatic state preparation against decoherence. Due to different ground-state symmetries, we also find a metastable state with xyxyxy-ferromagnetic order if the ramp crosses to regimes where the ground state is a zzz ferromagnet. The bosonic spin Mott phase as the initial gapped state for adiabatic cooling has many features in common with a fermionic band insulator, but the use of bosons should enable experiments with substantially lower initial entropies.
We investigate spin-order of ultracold bosons in an optical lattice by means of dynamical mean-field theory. A rich phase diagram with anisotropic magnetic order is found, both for the ground state and at finite temperatures. Within the Mott insulator, a ferromagnetic to antiferromagnetic transition can be tuned using a spin-dependent optical lattice. In addition we find a supersolid phase, in which superfluidity coexists with antiferromagnetic spin order. We present detailed phase diagrams at finite temperature for the experimentally realized heteronuclear 87Rb-41K^{87}\text{R}\text{b-}^{41}\text{K}87Rb-41K mixture in a three-dimensional optical lattice.
Abstract We analyze a scheme for preparation of magnetically ordered states of two-component bosonic atoms in optical lattices. We compute the dynamics during adiabatic and optimized time-dependent ramps to produce ground states of effective spin Hamiltonians, and determine the robustness to decoherence for realistic experimental system sizes and timescales. Ramping parameters near a phase transition point in both effective spin-1/2 and spin-1 models produces entangled spin-symmetric states that have potential future applications in quantum enhanced measurement. The preparation of these states and their robustness to decoherence is quantified by computing the quantum Fisher information (QFI) of final states. We identify that the generation of useful entanglement should in general be more robust to heating than it would be implied by the state fidelity, with corresponding implications for practical applications.
A major focus in condensed matter physics is to study the origin of exotic quantum phases such as coexistent and inhomogeneous phases, quantum criticality, and secondary ordered phases close to quantum critical points. Exotic phenomena in strongly correlated systems occur due to competing complex interactions of spin, charge, lattice, and orbital degrees of freedom. Complex quantum phases in strongly correlated systems are challenging, but they might be very useful due to their possible functionality to make advance devices. In order to understand, utilize, and optimize such behaviors, we need to improve our understanding of these systems. Studies in cold atom systems are of interest since cold atom experiments provide a control on model parameters. In this thesis, we use novel analytical and computational techniques to treat strongly interacting bosonic systems. Taking advantage of the very versatile quantum Monte Carlo Stochastic Green Function algorithm, we studied several interesting problems. First, we explore a recently developed new confining method for cold atoms on optical lattices. Atoms are confined via a hopping integral that decreases as a function of the distance from the center of the lattice. This method might lead to lower temperatures than existing diagonal confinement methods. Next, we study the ground state phase diagram of interacting bosons on a ring-shape lattice with a region of weak hopping integrals. The model, an extension of the well known Bose-Hubbard model, develops a novel local Mott phase in addition to the usual Mott and superfluid phases in the homogeneous system. This might provide a new insight to the description of atomtronics applications. Finally, we study the two species Bose Hubbard model in a two-dimensional lattice. This model presents novel phases due to the complexity associated with multiple species. Its phase diagram shows ordered and coexistence phases including a ferromagnetic phase separated phase with high entropy. This phase might be accessible experimentally. The novel phases found from our studies are linked to experiments on ultra-cold atoms trapped by laser beams.
Cold atoms in optical lattices offer an exciting new laboratory where quantum many-body phenomena can be realized in a highly controlled way. They can even serve as quantum simulators for notoriously difficult problems like high-temperature superconductivity. This review is focussed on the recent developments and new results in multi-component systems. Fermionic atoms with SU(N) symmetry have exotic superfluid and flavor-ordered ground states. We discuss symmetry breaking, collective modes, and detection issues, e.g. in Bragg scattering. On the other hand, bosonic multiflavor ensembles allow for engineering of spin Hamiltonians which are interesting from a quantum computation point of view. Finally, we address the role of disorder in optical lattices. Fermionic atoms experience Anderson localization at sufficiently strong disorder. Interactions among the atoms induce a competing tendency towards delocalization. We present a complete phase diagram obtained within dynamical mean-field theory and discuss experimental observability of the Mott and Anderson phases.
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 . . . . . . . . .