An optical-lattice-based quantum simulator for relativistic field theories and topological insulators

Abstract

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from noninteracting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize a majority of phases in the periodic table of topological insulators.

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

“…A detailed discussion of the simulation of non-Abelian SU(2) potentials with alkaline atoms can be found in Ref. [26]. There, the spin degree of freedom is coded in two hyperfine levels of 40 K. Zeeman splitting allows for independent addressing of the transitions between different spin states, thus creating the desired spin-dependent hopping amplitude.…”

“…[25], which associates non-trivial phases to the tunneling amplitudes between nearest-neighbor and next-nearest neighbor-sites through the interaction of two atomic hyperfine species with counter-propagating Raman beams. These setups can efficiently reproduce spin-orbit terms to simulate topological insulators [17,26]. Experimental results along this line have been recently obtained: a tunable effective magnetic field for ultracold atoms was implemented using Raman-assisted tunneling in an optical superlattice [27], while a one-dimensional chain with complex tunneling matrix elements was obtained from a combination of Raman coupling and radio-frequency magnetic fields [28].…”

Towards quantum simulating QCD

“…Proposals for quantum simulator constructions already exist for some simple bosonic [26,27,28] and fermionic [29,30,31,32] field theories. Hence it is natural to ask whether our understanding of strongly coupled systems in nuclear and particle physics may benefit from quantum simulation.…”

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

“…A promising and challenging application of synthetic gauge fields is to the tunable experimental realization of systems relevant for high energy physics and quantum gauge theories [24][25][26][27][28][29][30][31][32][33][34][35]: in perspective new developments could permit to study in a controllable experimental set-up part of the phase diagrams of gauge theories even strongly coupled, like QCD [36] [34] . Clearly gauge fields are a basic ingredient to realize this task: up to now only static gauge fields have been experimentally simulated, but there are recent proposals for dynamical fields [31][32][33][34][35].…”