SO(3) “Nuclear Physics” with ultracold Gases

Abstract

An ab initio calculation of nuclear physics from Quantum Chromodynamics (QCD), the fundamental SU (3) gauge theory of the strong interaction, remains an outstanding challenge. Here, we discuss the emergence of key elements of nuclear physics using an SO(3) lattice gauge theory as a toy model for QCD.We show that this model is accessible to state-of-the-art quantum simulation experiments with ultracold atoms in an optical lattice. First, we demonstrate that our model shares characteristic many-body features with QCD, such as the spontaneous breakdown of chiral symmetry, its restoration at finite baryon density, as well as the existence of few-body bound states. Then we show that in the one-dimensional case, the dynamics in the gauge invariant sector can be encoded as a spin S = 3 2 Heisenberg model, i.e., as quantum magnetism, which has a natural realization with bosonic mixtures in optical lattices, and thus sheds light on the connection between non-Abelian gauge theories and quantum magnetism.

Digital quantum simulation of lattice gauge theories in three spatial dimensions

“…On the one hand, we have Trotter errors coming from the digitization which can be estimated by specifying the general error bounds given in section 3 to the case of three dimension and gauge group D 3 . We obtain for the fist order formula (see (44)): We stress again that the digitization error does not break gauge invariance, because all steps of the sequence individually respect the right symmetry. Therefore, the Trotter expansion can only give rise to quantitative deviations, but not to qualitative changes.…”

“…Here we just report the bounds on the Trotter error that can be computed following the discussion in section 3.3. In three dimensions and for the gauge group  N , we obtain the first order formula (see (44)) :…”

“…There are also differences in the proposed simulation scheme: the first one is the analogue approach, where not only the degrees of freedom of the simulated system are mapped to those of the simulating one: by appropriately tailoring the interactions of the simulator, its Hamiltonian is exactly or approximately mapped to the desired one (which can be adiabatically changed). Quantum simulations of this type have been proposed, mostly using ultracold atoms [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], as well as trapped ions [45,46] and superconducting qubits [47,48]. Another approach-the digital one-is based on an idea of Feynman [49], to use a quantum computer (i.e.…”

Effective multi-body SU(N)-symmetric interactions of ultracold fermionic atoms on a 3D lattice

“…In addition to illuminating open questions in our understanding of the fractional quantum Hall effect and unconventional superconductivity [25][26][27], the CSL can support non-Abelian excitations which allow for universal topological quantum computation [23,28]. Harnessing the SU(N)-symmetric interactions of AEAs might also enable the simulation of various lattice gauge theories [29,30], some of which share important qualitative features with quantum chromodynamics such as few-body bound states and confinement [31,32]. These direct, quantum simulations have an extraordinary potential to provide novel insights by circumventing e.g.severe sign problems which plague classical simulations of strongly interacting fermionic systems [29,33].…”

Scattering-Based Geometric Shaping of Photon-Photon Interactions

“…They are widely used in the study of quantum dynamics such as spin frustration [10] and thermalization and localization transitions [11,12]. Recently more applications of lattice gauge theories have been proposed, appealing to simulations of high energy physics [13][14][15]. While these fascinating quantum simulators offer unprecedented glimpse into nonequilibrium dynamics, upscaling the number of qubits is just as challenging.…”