Effective Dirac dynamics of ultracold atoms in bichromatic optical lattices

Abstract

We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e., a true crossing of two Bloch bands. The dynamics in the vicinity of such a crossing is described by the one-dimensional Dirac equation, which is rigorously shown beyond the tight-binding approximation. Within this framework we analyze the effects of an external potential and demonstrate numerically that it is possible to demonstrate Klein tunneling with current experimental setups

Klein tunneling of two correlated bosons

“…(10), the energy difference 2σ between adjacent lattice sites being determined by the unbalance (U − V ) of on-site and nearest-neighbor site interaction in the original problem. As discussed in several previous works (see, for instance, [15,18,22,48,49]), a Dirac-like behavior is found for a non-relativistic particle hopping on a binary superlattice in one dimension, including the analogue of KT in the presence of a potential barrier. In our case, since Eqs.…”

“…The observation of KT for a relativistic particle is very challenging, because it would require an ultrastrong field, of the order of the critical field for e − e + pair production in vacuum [2,3], which is not currently available. In recent years, there has been an increased interest in simulating KT in diverse and experimentally accessible physical systems (see, for instance, [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] and references therein). A remarkable example is provided by electronic transport in graphene, a carbon mono layer of honeycomb shape, where the energy dispersion relation near a Dirac point resembles the dispersion of relativistic electrons [23].…”

Veselago lensing with ultracold atoms in an optical lattice

“…The band structure of the variable lattice along with the energy splitting between the lowest two excited Bloch bands can be calculated as follows, see Salger et al 11 , Witthaut et al 18 and Ritt et al 25 for details. The atomic evolution in the Fourier-synthesized lattice potential is determined by the Hamiltonian…”

“…Further, c eff ¼ 2 hk/m is an effective light speed, which for rubidium atoms and a 783 nm lattice laser wavelength is 1.1 cm s À 1 , ten orders of magnitude smaller than the speed of light in vacuum. The dynamics of atoms in the bichromatic lattice near the crossing is well described by a one-dimensional Dirac equation, which allows us to study relativistic wave equation predictions with ultracold atoms 18 . By tuning of the splitting DE, moreover different projections of a two-dimensional Dirac cone can be realized.…”

Staggered grid leap-frog scheme for the Dirac equation

“…Layered high-T c systems may be seen as an example in the wider sense [15]. Optical lattices also constitute a rich play ground for the engineering of 2D physics with the possibility of tuning various parameters and therewith controlling atom localization and effective many-body interactions [17][18][19]. Surfaces of solids in general provide a natural environment for the study of (quasi-) 2D phenomena, with a remarkable recent example provided by the topologically protected 2D metallic surface states of TIs.…”