Landau Levels in Strained Optical Lattices

Abstract

We propose a hexagonal optical lattice system with spatial variations in the hopping matrix elements. Just like in the valley Hall effect in strained graphene, for atoms near the Dirac points the variations in the hopping matrix elements can be described by a pseudomagnetic field and result in the formation of Landau levels. We show that the pseudomagnetic field leads to measurable experimental signatures in momentum resolved Bragg spectroscopy, Bloch oscillations, cyclotron motion, and quantization of in situ densities. Our proposal can be realized by a slight modification of existing experiments. In contrast to previous methods, pseudomagnetic fields are realized in a completely static system avoiding common heating effects and therefore opening the door to studying interaction effects in Landau levels with cold atoms. DOI: 10.1103/PhysRevLett.115.236803 PACS numbers: 73.22.Pr, 37.10.Jk, 67.85.-d, 73.43.-f The Lorentz force, which acts on charged particles moving in a magnetic field, results in a number of fundamental phenomena in condensed matter systems including the Hall effect in metals, Abrikosov lattices in superconductors, and the integer and fractional quantum Hall effects in ultrapure two-dimensional electron gases. While phenomena, such as the quantized conductance plateaus of the integer and fractional quantum Hall effects have been both observed experimentally and described theoretically [1], many properties, such as the non-Abelian nature of excitations in the fractional quantum Hall effects [2-4], remain subjects of active research.These problems are difficult-they involve strongly interacting systems that are resistant to conventional theoretical and numerical tools. The current theoretical state of the art involves comparisons of trial wave functions and numerical calculations on small systems using exact diagonalization and the density matrix renormalization group (DMRG) [3,4]. Ultracold atom experiments offer an alternative route, in which, potentially, the interplay of gauge fields, band structure, interactions, and disorder can be studied by engineering and controlling these effects independently [5]. Moreover, by engineering these properties one could generate novel phases that have not yet been observed in condensed matter systems [6,7].Various groups have recently experimentally demonstrated "synthetic gauge fields"-methods for driving neutral atoms using laser beams in such a way that they behave as if they were charged particles moving in a magnetic field [8][9][10][11][12]. A number of effects, such as Abrikosov lattice formation [13], Hall deflection [11,14,15], and chiral currents [16], have been observed. However, an important limitation of these methods, that use either periodic lattice modulations or Raman transitions, seems to be significant heating of the atom clouds. For optical lattice experiments, this limits the time scale in which experiments can be performed to several tens of milliseconds [17], in contrast to experiments in static lattices which allow for several hun...

Electronic and optical properties of strained graphene and other strained 2D materials: a review

“…For comparison, (pulsed) magnetic fields of up to 100 Tesla can only be obtained in state-of-the-art experimental facilities. Subsequently, many experimental confirmations of the pseudomagnetic fields in graphene have been reported under other strain configurations [260][261][262][263][264][265][266][267][268] and in various graphene-like systems such as molecular graphene [203], photonic crystals [269], and optical lattices [270]. Beyond graphene, strain-induced gauge fields have been also characterized on bilayer graphene [271][272][273], borophene [274], topological insulators [275], transition metal dichalcogenides [9,276,277] and on three-dimensional Dirac and Weyl semimetals [166,243,[278][279][280].…”

Pseudo-Landau levels of Bogoliubov quasiparticles in strained nodal superconductors

“…There have been theoretical studies of Josephson coupling through pseudo-LLs 22,23 , and interaction effects which can lead to exotic correlated states 24,25 . Strain effects have also been generalized to 3D Dirac and Weyl semimetals [26][27][28][29] , Kitaev spin liquids 30 , and atoms in optical lattices 31,32 .…”

Two-dimensional optical quasicrystal potentials for ultracold atom experiments

“…In our application, however, the microscope needs to be bi-telecentric, such that the distance between the principle planes of the lenses is equal to the sum of their focal lengths, to ensure that the phase relationships, and therefore the interference pattern, of the light projected onto the atoms' plane matches those where the beams from the fibers initially intersect. Otherwise, additional distortion and field curvature aberrations will deform the potential, creating unwanted effective strain in the QC lattice [59,60]. For maximal interference contrast, all of the beams must have the same polarization.…”