Tunable Gauge Potential for Neutral and Spinless Particles in Driven Optical Lattices

Abstract

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated by applying a suitable periodic inertial force such that the method does not rely on any internal structure of the particles. We experimentally demonstrate the realization of such artificial potentials, which generate ground state superfluids at arbitrary non-zero quasi-momentum. We furthermore investigate possible implementations of this scheme to create tuneable magnetic fluxes, going towards model systems for strong-field physics.First introduced in electromagnetism, gauge fields play a central role in the description of interactions in physics, from particle physics to condensed matter. Currently there is a large interest to introduce gauge fields into model systems in order to study fundamental aspects of physics [1]. Especially the emulation of synthetic electric and magnetic fields for of ultracold atomic systems is crucial in order to extend their proven quantum simulation abilities further, e.g. to quantum Hall physics or topological insulators. In this context, the analogy between inertial and Lorentz forces triggered the simulation of homogeneous artificial magnetic fields using rapidly rotating trapped ultracold gases [2]. Recently, several proposals ([3, 4] and references therein) and experimental realizations focused on the simulation of a gauge vector potential A either in a bulk system [5,6] or in optical lattices [7,8]. The realized schemes exploit the Berry phase which arises when the atomic ground state is split in several space-dependent sublevels, as in the presence of an electromagnetic field. Hence they rely on the coupling between internal and external degrees of freedom induced by laser fields. Here we demonstrate the generation of artificial gauge potentials for neutral atoms in an optical lattice without any requirements on the specific internal structure. As the realized scheme only relies on the trapability of the particle, it can be very widely applied to many atomic systems, in principle also to molecules and other complex particles. It is particularly interesting for fermionic systems, where in a many-body state governed by Pauli principle, the use of internal degrees of freedom often lead to conflicts with the creation of gauge potentials. As an important additional benefit, the internal degrees of freedom of the particles can be addressed independently, e.g. by real magnetic fields or microwave excitations. In general, the presence of a gauge vector potential modifies the kinetic part of the Hamiltonian describing the system. In a lattice, an artificial field can then be simulated by engineering a complex tunneling parameter J = |J| · e iθ , where θ is the Peierls phase. The central approach here is to control this phase via a suitable forcing of the lattice potential, acting at the single-particle level. We describe the general scheme for the...

Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions

“…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]. The backaction of the atoms on the value of a synthetic gauge field is expected to lead to interesting physics, including statistically induced phase transitions and anyons in 1D lattices [32], and chiral solitons in Bose-Einstein condensates [33].Periodically modulated optical lattices open interesting possibilities for the engineering of lattice gases [16][17][18][34][35][36][37][38][39][40]. In particular, periodic lattice shaking results in a modified hopping rate [34][35][36], which has been employed to drive the superfluid (SF) to Mott insulator (MI) transition [37], to simulate frustrated classical magnetism [38], and to create tunable gauge potentials [16].…”

Looking for Hofstadter’s Butterfly in Cold Atoms

“…Recently, staggered magnetic fields in optical lattices were achieved using laser-induced tunneling in superlattice potentials [12] or through dynamical shaking [13]. In one dimension, tunable gauge fields have been implemented in an effective ''Zeeman lattice' ' [14] and using periodic driving [15]. Furthermore, the free-space spin Hall effect was observed using Raman dressing [16].…”

Dynamically Induced Topological Properties in Two-Dimensional Optical Lattices

“…Therefore these effective interactions are absent when the interactions and the timedependent term in the Hamiltonian commute. For example, if we consider a (Bose or Fermi) Hubbard model with a time-dependent on-site potential term, effective interactions do not appear since the onsite potential and on-site interactions commute with each other (this case corresponds to the "hopping renormalization" phenomena which are studied in several articles [15,16]). After some calculation on our model (14)- (17), we obtain…”