A disordered insulator in an optical lattice

Localization of correlated fermions in optical lattices with speckle disorder

“…In contrast, for a localized state the spectrum is given by a dense distribution of poles in the allowed energy interval on the real ω-axis. The residues approach a finite value, but some will dominate the sum in equation (17). If their values were sorted by value, their contribution would decrease exponentially for spatially localized states.…”

“…[15][16][17]39,40 A statistical analysis of the scattering process 41 shows that the probability distribution function (PDF) of the resulting light intensity pattern obeys p I (I) = Θ(I) exp(−I/ I )/ I , where I is the averaged light intensity and Θ(x) denotes the Heaviside function. By superimposing the speckle light pattern onto the optical lattice, the atoms are subjected to a random optical dipole potential V D (r) ∝ I(r), 40 which is attractive for red-detuned laser light or repulsive for blue-detuned laser light.…”

“…11,12 Thereby a binary disorder potential is realized due to the interatomic interaction; ii) by superimposing two laser beams with incommensurate frequencies, 13,14 thereby generating a stationary quasiperiodic lattice; iii) by using an optical speckle field 15 superimposed onto an optical lattice. 16,17 In general, particles in a disordered lattice are exposed to an on-site potential varying from site to site, which already gives rise to localization due to coherent backscattering. 1 In tight-binding lattice models this randomness is termed diagonal disorder.…”

Excitations in disordered bosonic optical lattices

“…While optical lattices provide a very clean experimental realization of strongly correlated lattice bosons, they can be used to study disordered systems on a very high level of control as well. Disorder can be added to the regular optical lattice by several techniques, such as by superposing additional optical lattices with shifted wavelength and beam angles [9][10][11][12][13][14], laser speckle fields [15][16][17][18], or including atoms of a different species acting as impurities [19].The disordered BH model has been widely investigated in the literature. Most of the work has been devoted to study the phase transitions occurring in the disordered BH model [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

“…While optical lattices provide a very clean experimental realization of strongly correlated lattice bosons, they can be used to study disordered systems on a very high level of control as well. Disorder can be added to the regular optical lattice by several techniques, such as by superposing additional optical lattices with shifted wavelength and beam angles [9][10][11][12][13][14], laser speckle fields [15][16][17][18], or including atoms of a different species acting as impurities [19].…”