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arXiv:1504.00128 · New Journal of Physics

Interaction-dependent photon-assisted tunneling in optical lattices: a quantum simulator of strongly-correlated electrons and dynamical Gauge fields

Alejandro Bermudez, Diego Porras

Published Oct 12, 2015• 45 citations
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Abstract

We introduce a scheme that combines photon-assisted tunneling (PAT) 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 allowed by standard single-band Hubbard Hamiltonians in the strong-repulsion limit. We finally show that, by generalizing the PAT 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.

DOI
10.1088/1367-2630/17/10/103021

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We introduce a scheme that combines photon-assisted tunneling (PAT) 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 allowed by standard single-band Hubbard Hamiltonians in the strong-repulsion limit. We finally show that, by generalizing the PAT 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.
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.
We describe a versatile toolbox for the quantum simulation of many-body lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder and strong on-site interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quantized vibrational modes of the ions can be described by a quantum lattice model. We present a detailed theoretical proposal for a quantum simulator in that experimental setup, and show that it is possible to explore phases of matter that range from the fractional quantum Hall effect, to exotic strongly correlated glasses or flux-lattice models decorated with arbitrary patterns of localized defects.
Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large on-site repulsion UUU, the model is shown to reproduce the ttt-JJJ Hamiltonian, in which the JJJ coefficient of the Heisenberg term depends on the particle-assisted tunneling rate ggg: explicitly, J=4g2/UJ=4{g}^{2}/UJ=4g2/U. At half-filling, ggg drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms (g=0g=0g=0) to the antiferromagnetic Mott insulator of the standard Hubbard case (g=tg=tg=t). This is observed already in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of ggg.
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.
We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions, which can be identified with an effective tunneling potential and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site and bond-charge interactions. We derive an extended occupation-dependent Hubbard model with multi-orbitally renormalized processes and compute the corresponding phase diagram. It substantially deviates from the single-band Bose–Hubbard model and predicts strong changes of the superfluid-to-Mott-insulator transition. In general, the presented beyond-Hubbard physics plays an essential role in bosonic lattice systems and has an observable influence on experiments with tunable interactions.
Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterize these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunable effects such as long-range density-density interactions, perfectly correlated atomic tunneling, superexchange, and effective pair processes. We further show that this provides a framework for enhancing quantum simulations to include such long-range and correlated processes, including reservoir models and dynamical global gauge fields.