Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

Abstract

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

“…As L increases, the three curves C(c 3 ) seem to vary systematically as expected by Eq. (14). In Fig.…”

“…Stimulated by the enormous progress made in experimental ultra-cold atomic systems, theoretical proposals have been made for quantum simulations of various physical systems and associated phenomena [2,3]. One such proposal is atomic quantum simulation of lattice gauge theories (LGTs) [4][5][6][7][8][9][10][11][12][13][14][15][16].…”

“…(14). Then we obtain the expectation value E n x,i by letting the partial derivative (−i∂/∂J x,i ) n act on Z GH [J].…”

Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions

“…Synthetic fields may be generated as well in optical lattices, and recent experiments have created artificial staggered [14][15][16] and uniform [17,18] magnetic fields. These fields are, however, static, as they are not influenced by the atoms.The dynamical feedback between matter and gauge fields plays an important role in various areas of physics, ranging from condensed matter [19] to quantum chromodynamics [20], and its realization in cold lattice gases is attracting growing attention [21]. Schemes have been recently proposed for multicomponent lattice gases, such that the low-energy description of these systems is that of relevant quantum field theories [22][23][24][25][26][27][28][29][30][31].…”

Proposal for the Quantum Simulation of the CP(2) Model on Optical Lattices

“…analog quantum computing -could overcome the notorious sign problem that usually occurs if the Euclidean action is complex; in this approach, the phase factor is naturally incorporated (for recent reviews, see Refs. [1]). A prominent long-term goal of this concept is the exploration of the QCD phase diagram at finite baryon density, or a finite vacuum angle θ .…”