Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Interference induced anisotropy in a two-dimensional dark state optical lattice



Ian Spielman, Gediminas Juzeliūnas, Edvinas Gvozdiovas


We describe a two-dimensional optical lattice for ultracold atoms with spatial structure below the diffraction limit created by a bichromatic optical standing wave. At every point in space these fields couple the internal atomic states in a three-level Lambda coupling configuration. Adiabatically following the local wavefunction of the resulting dark state yields a spatially uniform Born-Oppenheimer potential which is augmented by geometric scalar and vector potentials appearing due to spatially rapid changes of the wavefunction. Depending on system parameters, we find that the geometric scalar potential can interpolate from a 2D analogue of the Kronig-Penney lattice, to an array of tubes with a zig-zag shaped barrier. The geometric vector potential induces a spatially periodic effective magnetic field (the Berry's curvature) that can be tuned to cause destructive interference between neighboring tubes, thereby decoupling them at a critical point in parameter space. We numerically investigate the energy spectrum including decay from the excited state, and find that the adiabatic approximation is sound for strong coupling strengths, leading to negligible loss in the dark state manifold. Furthermore, the spectrum is well-described by a non-Hermitian tight binding model with on-site losses, and hopping characterized by both loss and, surprisingly, gain.
Physical Review A


non-Hermitian, Bose-Einstein condensate, lattice, subwavelength


Spielman, I. , Juzeliunas, G. and Gvozdiovas, E. (2023), Interference induced anisotropy in a two-dimensional dark state optical lattice, Physical Review A, [online], (Accessed April 18, 2024)
Created March 27, 2023, Updated May 12, 2023