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arXiv:1104.1833 · Physical Review Letters

Controlling Correlated Tunneling and Superexchange Interactions with ac-Driven Optical Lattices

Yu-Ao Chen, Sylvain Nascimbène, Monika Aidelsburger, Marcos Atala, Stefan Trotzky, Immanuel Bloch

Published Nov 18, 2011• 169 citations
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Abstract

The dynamical control of tunneling processes of single particles plays a major role in science ranging from Shapiro steps in Josephson junctions to the control of chemical reactions via light in molecules. Here we show how such control can be extended to the regime of correlated tunneling of strongly interacting particles. Through a periodic modulation of a biased tunnel contact, we have been able to coherently control single-particle and correlated two-particle hopping processes. We have furthermore been able to extend this control to superexchange spin interactions in the presence of a magnetic-field gradient. Such photon-assisted superexchange processes constitute a novel approach to realize arbitrary XXZ spin models in ultracold quantum gases, where transverse and Ising-type spin couplings can be fully controlled in magnitude and sign.

DOI
10.1103/physrevlett.107.210405

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The dynamical control of tunneling processes of single particles plays a major role in science ranging from Shapiro steps in Josephson junctions to the control of chemical reactions via light in molecules. Here we show how such control can be extended to the regime of correlated tunneling of strongly interacting particles. Through a periodic modulation of a biased tunnel contact, we have been able to coherently control single-particle and correlated two-particle hopping processes. We have furthermore been able to extend this control to superexchange spin interactions in the presence of a magnetic-field gradient. Such photon-assisted superexchange processes constitute a novel approach to realize arbitrary XXZ spin models in ultracold quantum gases, where transverse and Ising-type spin couplings can be fully controlled in magnitude and sign.
Quantum mechanical superexchange interactions form the basis of quantum magnetism in strongly correlated electronic media. We report on the direct measurement of superexchange interactions with ultracold atoms in optical lattices. After preparing a spin-mixture of ultracold atoms in an antiferromagnetically ordered state, we measured coherent superexchange-mediated spin dynamics with coupling energies from 5 hertz up to 1 kilohertz. By dynamically modifying the potential bias between neighboring lattice sites, the magnitude and sign of the superexchange interaction can be controlled, thus allowing the system to be switched between antiferromagnetic and ferromagnetic spin interactions. We compare our findings to predictions of a two-site Bose-Hubbard model and find very good agreement, but are also able to identify corrections that can be explained by the inclusion of direct nearest-neighbor interactions.
The correlated atoms in a tilted optical lattice driven by an ac field are studied within the Hubbard model. By making use of both photon-assisted tunneling and coherent destructive tunneling effects, we can move a pair of strongly correlated atoms in the lattice via manipulating the global amplitude of the driving field. We propose a scheme for creating entanglement between the particle pair and a single particle through interacting oscillations. Our model may provide a new building block for investigating quantum computing and quantum information processing with ultracold atoms in optical lattices.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.
The interplay of magnetic exchange interactions and tunneling underlies many complex quantum phenomena observed in real materials. We study nonequilibrium magnetization dynamics in an extended two-dimensional (2D) system by loading effective spin-1/2 bosons into a spin-dependent optical lattice and use the lattice to separately control the resonance conditions for tunneling and superexchange. After preparing a nonequilibrium antiferromagnetically ordered state, we observe relaxation dynamics governed by two well-separated rates, which scale with the parameters associated with superexchange and tunneling. With tunneling off-resonantly suppressed, we observe superexchange-dominated dynamics over two orders of magnitude in magnetic coupling strength. Our experiment will serve as a benchmark for future theoretical work as the detailed dynamics of this 2D, strongly correlated, and far-from-equilibrium quantum system remain out of reach of current computational techniques.
We introduce a scheme that combines photon-assisted tunneling by a moving optical lattice with strong Hubbard interactions, and allows for the quantum simulation of paradigmatic quantum many-body models. We show that, in a certain regime, this quantum simulator yields an effective Hubbard Hamiltonian with tunable bond-charge interactions, a model studied in the context of strongly-correlated electrons. In a different regime, we show how to exploit a correlated destruction of tunneling to explore Nagaoka ferromagnetism at finite Hubbard repulsion. By changing the photon-assisted tunneling parameters, we can also obtain a t-J model with independently controllable tunneling t, super-exchange interaction J, and even a Heisenberg-Ising anisotropy. Hence, the full phase diagram of this paradigmatic model becomes accessible to cold-atom experiments, departing from the region t _ J allowed by standard single-band Hubbard Hamiltonians in the strong-repulsion limit. We finally show that, by generalizing the photon-assisted tunneling scheme, the quantum simulator yields models of dynamical Gauge fields, where atoms of a given electronic state dress the tunneling of the atoms with a different internal state, leading to Peierls phases that mimic a dynamical magnetic field.
The resonant tunneling of correlated bosons in optical lattices is investigated in the presence of doubly modulated AC-fields. The effective hopping coefficients are density-dependent. We can make use of this property to control the migration of a pair of strongly interacting particles in one- or two-dimensional uniform lattices via properly manipulating the phases, frequencies and amplitudes of the driven fields. We design a bifurcating quantum motion of the pair in contrast to the coherent quantum walk of the correlated pair in the absence of external fields.