Artificial Quantum Spin Systems from Atomic Physics – ArtiQ

This theory project is devoted to the quantum simulation of fundamental models of quantum magnetism with competing interactions (frustrated quantum spin models) in the context of current experiments in atomic physics. Frustrated quantum spin systems are among the most complex quantum many-body systems, and their behavior features equilibrium states dominated by quantum fluctuations, whose description has defied condensed-matter theory for more than half a century. Ongoing and upcoming experiments using trapped ions and neutral atoms have the ability to realize artificial frustrated quantum spin models with unprecedented control, and with several, fundamental differences compared to more conventional solid-state magnetic materials: 1) the Hamiltonian is in principle known a priori, and its parameters are tunable in a controlled way so as to explore entire phase diagrams in Hamiltonian space; 2) the models realized in atomic physics feature highly anisotropic spin-spin interactions, involving one-spin component only (quantum Ising models) or two spin components (quantum XY models), which are not found in magnetic materials; 3) remarkably, quantum Ising models and (in some particular regime) quantum XY models lend themselves to a quantitative theoretical treatment using state-of-the-art numerical approaches, and they allow for a direct theoretical validation of their experimental quantum simulation; 4) the most interesting equilibrium states realized by frustrated quantum spins – the so-called “quantum spin liquids” – might look completely featureless to conventional observables in solid-state magnetism – such as two-point correlation functions and response functions – while their possible realization in atomic physics allows for novel probes (such as local fluctuations and correlation functions of arbitrary order) which might unveil their unique forms of correlation, including the so-called topological quantum order.
This project has the ambitious goal of paving the way towards the first experimental realizations of complex quantum spin states in the context of frustrated trapped ions and frustrated bosons in optical lattices. a) In the case of trapped ions, we propose a thorough investigation of two-dimensional frustrated quantum Ising models to be realized via ions in micro-trap arrays. In these models a transverse field coherently mixes up the exponentially degenerate ground-state manifold of the classical spins, potentially giving rise to ordered states due to quantum effects, or to non-classical states, either with short-range entanglement and crystalline order (valence-bond crystals), or with long-range entanglement and absence of any symmetry breaking (spin liquids). b) In the case of frustrated bosons in the presence of artificial gauge fields, we will investigate the regime of large filling of the lattice, realizing the physics of frustrated quantum rotors, whose low-temperature state features complex ordered or quasi-ordered phases (spiraling states), which are turned into quantum paramagnetic phases (corresponding to Mott insulators) for an increasing strength of the repulsion, passing through unconventional quantum phase transitions. Moreover we will investigate the regime of low filling, realizing the physics of quantum S=1/2 XY spins; this regime potentially harbors spin-liquid phases, connected with the physics of the fractional quantum Hall states of bosons. In both cases of trapped ions and lattice bosons, we will dedicate a special effort to the ab-initio derivation of the spin Hamiltonians starting from the relevant experimental setup, and to the proposal of optimization schemes of current experimental setups, in order to reach the parameter regimes and low-temperature regimes necessary for the observation of the above-cited phases.