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Diagnosing Optical Lattices With Momentum Boosts

Tarek A. Elsayed, Alexej I. Streltsov

Published May 29, 2017• 0 citations
OpenAlex

Abstract

We present a novel technique to diagnose the condensate fraction in an optical lattice of weakly-interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the Multi-Configuration Time Dependent Hartree method for Bosons (MCTDHB) that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt depends directly on the amount of phase coherence between the lattice sites which in turn depends on the condensate fraction. The potential of using the relation between the frequency of the induced current and the amount of momentum boost imparted to the system in magnetic field gradiometery is also discussed.

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We present a novel technique to diagnose the condensate fraction in an optical lattice of weakly-interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the Multi-Configuration Time Dependent Hartree method for Bosons (MCTDHB) that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt depends directly on the amount of phase coherence between the lattice sites which in turn depends on the condensate fraction. The potential of using the relation between the frequency of the induced current and the amount of momentum boost imparted to the system in magnetic field gradiometery is also discussed.
We present a technique to diagnose the condensate fraction in a one-dimensional optical lattice of weakly interacting bosons based on the dynamics of the trapped atoms under the influence of a momentum kick. It is shown using the multi-configuration time-dependent Hartree method for bosons that the two extreme cases of the superfluid and Mott insulator states exhibit different behaviors when the lattice is briefly tilted. The current induced by the momentum boost caused by the tilt which depends directly on the amount of phase coherence between the lattice sites is linearly proportional to the condensate fraction. The atom-atom interactions only change the slope of the linear relationship. We discuss the applications of this scheme in magnetic field gradiometery.
We propose a method to probe states in the Mott insulator regime produced from a condensate in an optical lattice. We consider a system in which we create time-dependent number fluctuations in a given site by turning off the atomic interactions and lowering the potential barriers on a nearly pure Mott state to allow the atoms to tunnel between sites. We calculate the expected interference pattern and number fluctuations from such a system and show that one can potentially observe a deviation from a pure Mott state. We also discuss a method in which to detect these number fluctuations using time-of-flight imaging.
In this work we study the properties of interacting bosons in a tilted triple well optical lattice potential. A tilted optical lattice is possible to create in an experiment with charged bosons in presence of an electric field. The ground state energy, occupation densities in each well and first order correlation function of occupation densities as a function of the tilt parameter for N = 90 bosons using recently developed Multiconfigurational time-dependent Hartree method for bosons (MCTDHB) are studied. The ground state energy falls off with the tilt parameter for a given value of the barrier height and interparticle interaction. Also the tilt parameter is observed to restrict the fragmentation of the occupation densities in each well and thus promote condensation. Further the correlation between the bosons in different wells enhances with the tilt parameter and at large values the bosons in the first and the third wells are correlated apart from the correlation among the bosons in the same well, while the occupancy in the middle one seems to be uncorrelated with the other two. Such correlation between different wells is not observed in absence of the tilt effect for the same barrier height of the potential and interparticle interaction strength.
We experimentally probe the properties of the disordered Bose-Hubbard model using an atomic Bose-Einstein condensate trapped in a 3D disordered optical lattice. Controllable disorder is introduced using a fine-grained optical speckle field with features comparable in size to the lattice spacing along every lattice direction. A precision measurement of the disordering potential is used to compute the single-particle parameters of the system. To constrain theories of the disordered Bose Hubbard model, we have measured the change in condensate fraction as a function of disorder strength for several different ratios of tunneling to interaction energy. We observe disorder-induced, reversible suppression of condensate fraction for superfluid and coexisting superfluid-Mott-insulator phases.
Motivated by the recent advancements in experimental techniques in the cold atomic systems, we study the dependence of the conductivity on momentum in a system of strongly interacting bosons in an optical lattice. By employing the quantum rotor approach to the Bose-Hubbard model we calculate the current-current correlation function and subsequently obtain the analytic formula for the momentum-dependent longitudinal conductivity. We analyze the behavior of the conductivity for the square and cubic lattices in both, the superfluid and Mott insulator phases. As a consequence of the particle-hole symmetry, the conductivity for a uniformly filled lattice in the superfluid phase exhibits a linear dependence for a surprisingly wide range of momenta around k=0\mathbf{k}=0k=0. This allows us to predict the value of the group velocity of the particle excitations. We also consider the impact of finite temperature and discover that it leads to an additional conductivity channel, which is aligned along the direction of the probe field and located within the energy gap.
Interacting bosons with two ``spin'' states in a lattice show superfluid-insulator phase transitions in the presence of spin-orbit coupling. Depending on the parameter regime, bosons in the superfluid phase can condense to either a zero-momentum state or to one or multiple states with finite momentum, leading to an unconventional superfluid phase. We study the response of such a system to modulation of the optical lattice potential. We show that the change in momentum distribution after lattice modulation shows distinct patterns in the Mott and the superfluid phase and these patterns can be used to detect these phases and the quantum phase transition between them. Further, the momentum-resolved optical modulation spectroscopy can identify both the gapless (Goldstone) and gapped amplitude (Higgs) mode of the superfluid phase and clearly distinguish between the superfluid phases with a zero-momentum condensate and a twisted superfluid phase by looking at the location of these modes in the Brillouin zone. We discuss experiments which can test our theory.