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

Abstract

We consider the prospects for quantum simulation of condensed matter models exhibiting strong electronphonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally possesses 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.

Observation of Feshbach resonances between a single ion and ultracold atoms

“…This might provide deeper insight into the molecular structure at short-range, where additional interactions, such as SOC, shift and split resonances [46]. Furthermore, exploiting Feshbach resonances in a generic atomion ensemble might find application in many-body systems, such as polaron [26,27] and impurity physics [28] as well as experimental quantum simulations [29][30][31].…”

“…We tune the experimental parameters to probe different interaction processes -first, enhancing three-body reactions [21][22][23][24] and the related losses to identify the resonances, then making two-body interactions dominant to investigate the ion's sympathetic cooling [18] in the ultracold atomic bath. Our results provide deeper insights into atom-ion interactions, giving access to complex many-body systems [25][26][27][28] and applications in experimental quantum simulation [29][30][31].…”

Dynamics of a trapped ion in a quantum gas: effects of particle statistics

“…( 17) and it denotes the so-called Fröhlich model Hamiltonian in the context of the electron-phonon coupling in solid-state [51], while Ĥ(2) BS refers to the double sum over q, q ′ , which describes the so-called extended Fröhlich model [43]. Specifically for the ionic impurity, the coefficient c q is linked to the scattering amplitude (5) as…”

“…Indeed, such a compound system offers various fascinating perspectives both on fundamental quantum few-and many-body physics research and on technological applications that the two systems separately cannot afford. For instance, the exploration of novel polaronic states [1,2] and quantum simulation of the electron-phonon coupling [3][4][5]. For an extensive overview on atom-ion physics research, we refer to the review [6][7][8].…”

Spin-Holstein models in trapped-ion systems

“…As a tantalizing prospect, trapped-ion quantum simulators may help to gain new insights into the underlying physical mechanisms [6,7]. Their spin and motional degrees of freedom can be harnessed to realize a quantum-optics analogue of the electron-phonon system [8][9][10][11], which enables access to a variety of system observables. Moreover, their key parameters may be tuned in-situ to explore different regions of the phase diagram.…”