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arXiv:2005.08635 · Physical Review Research

Quantum simulation of extended polaron models using compound atom-ion systems

Krzysztof Jachymski, Antonio Negretti

Published Aug 28, 2020• 15 citations
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Abstract

We consider the prospects for quantum simulation of condensed matter models exhibiting strong electron-phonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally posesses a phonon structure, in contrast to the standard optical lattice scenarios usually employed with ultracold atoms in which the lattice is generated by laser light and thus it remains static. We derive the effective Hamiltonian describing the general system and discuss the arising energy scales, relating the results to commonly employed extended Hubbard-Holstein models. Although for a typical experimentally realistic system the coupling to phonons turns out to be small, we provide the means to enhance its role and reach interesting regimes with competing orders. Extended Lang-Firsov transformation reveals the emergence of phonon-induced long-range interactions between the atoms, which can give rise to both localized and extended bipolaron states with low effective mass, indicating the possibility of fermion pairing.

DOI
10.1103/physrevresearch.2.033326

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We consider the prospects for quantum simulation of condensed matter models exhibiting strong electron-phonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally posesses a phonon structure, in contrast to the standard optical lattice scenarios usually employed with ultracold atoms in which the lattice is generated by laser light and thus it remains static. We derive the effective Hamiltonian describing the general system and discuss the arising energy scales, relating the results to commonly employed extended Hubbard-Holstein models. Although for a typical experimentally realistic system the coupling to phonons turns out to be small, we provide the means to enhance its role and reach interesting regimes with competing orders. Extended Lang-Firsov transformation reveals the emergence of phonon-induced long-range interactions between the atoms, which can give rise to both localized and extended bipolaron states with low effective mass, indicating the possibility of fermion pairing.
State-of-the-art experiments using Rydberg atoms can now operate with large numbers of trapped particles with tunable geometry and long coherence time. We propose a way to utilize this in a hybrid setup involving neutral ground-state atoms to efficiently simulate condensed-matter models featuring electron-phonon coupling. Such implementation should allow for controlling the coupling strength and range as well as the band structure of both the phonons and atoms, paving the way towards studying both static and dynamic properties of extended Hubbard-Holstein models.
We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian, including the atomic band structure, and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.
We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time possess properties of systems with both short- and long-range interactions. This opens perspectives for novel quantum simulators of finite-range interacting systems, even though the light-induced interaction is global (i.e., infinitely long range). This is achieved by spatial structuring of the global light-matter coupling at a microscopic scale. Such simulators can directly benefit from the collective enhancement of the global light-matter interaction and constitute an alternative to standard approaches using Rydberg atoms or polar molecules. The system in the steady state of light induces effective many-body interactions that change the landscape of the phase diagram of the typical Bose-Hubbard model. Therefore, the system can support nontrivial superfluid states, bosonic dimer, trimer, etc., states, and supersolid phases depending on the choice of the wavelength and pattern of the light with respect to the classical optical lattice potential. We find that by carefully choosing the system parameters one can investigate diverse strongly correlated physics with the same setup, i.e., modifying the geometry of light beams. In particular, we present the interplay between the density and bond (or matter-wave coherence) interactions. We show how to tune the effective interaction length in such a hybrid system with both short-range and global interactions.
We have investigated bipolaron formation in the Holstein-Hubbard and the Fr\"ohlich-Hubbard model on a discrete one-dimensional lattice. Phonon enriched basis has been generated by exploiting the idea of the Lang-Firsov transformation, which results in better convergence in the strong coupling regime. The incorporation of the finite-range electron-phonon (e-ph) interaction reduces the bipolaron effective mass. We systematically increase the spatial extent of the e-ph interaction to study the effect of the long-range tail of the Fr\"ohlich model. The electron-electron (e-e) interaction also plays a crucial role in lowering the effective mass for both the Holstein and the Fr\"ohlich bipolarons. In the presence of the extended e-e interaction, the intersite S1 Holstein bipolaron becomes unstable, while the effective mass of the Fr\"ohlich bipolaron becomes significantly reduced for both the spin singlet and triplet cases.
We show how bond order emerges due to light mediated synthetic interactions in ultracold atoms in optical lattices in an optical cavity. This is a consequence of the competition between both short- and long-range interactions designed by choosing the optical geometry. Light induces effective many-body interactions that modify the landscape of quantum phases supported by the typical Bose–Hubbard model. Using exact diagonalization of small system sizes in one-dimension, we present the many-body quantum phases the system can support via the interplay between the density and bond (or matter–wave coherence) interactions. We find numerical evidence to support that dimer phases due to bond order are analogous to valence bond states. Different possibilities of light-induced atomic interactions are considered that go beyond the typical atomic system with dipolar and other intrinsic interactions. This will broaden the Hamiltonian toolbox available for quantum simulation of condensed matter physics via atomic systems.
Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high- T c superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.