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.
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.
Motivated by the availability of optical lattices with tunable geometries in experiments, we compute different physical properties such as condensate fraction, fluctuation and depletion of the condensate density and quasi-particle velocity as a function of the interparticle interaction strength for bosons in different 2D optical potentials that correspond to square, triangular and honeycomb geometries. Our results demonstrate an interplay of these features with that of the coordination number and underlying lattice geometries. A triangular lattice, which has a coordination number z = 6, shows larger condensate fraction and fluctuation of the condensate density, along with a low depletion of the ground state occupancy. The other candidates, namely the square lattice (z = 4) and honeycomb lattice (z = 3) occupy second and third places, respectively, with regard to these properties. The quasi-particle velocities for these geometries follow a similar pattern as that of the condensate fraction data. The observations are explained by the behaviour of the low-energy quasi-particle density of states. Finally, to make the role of lattice geometry obvious, we include a discussion on a kagome lattice, which in spite of having the same coordination number as that of a square lattice, i.e. z = 4, yields a significantly low condensate fraction than that of the square lattice for all values of the interacting strength.
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.
The concept of spontaneous symmetry breaking and off-diagonal long-range order (ODLRO) are associated with Bose–Einstein condensation. However, as in the system of reduced dimension the effect of quantum fluctuation is dominating, the concept of ODLRO becomes more interesting, especially for the long-range interaction. In the present manuscript, we study the correlation dynamics triggered by lattice depth quench in a system of three dipolar bosons in a 1D triple-well optical lattice from the first principle using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). Our main motivation is to explore how ODLRO develops and decays with time when the system is brought out-of-equilibrium by a sudden change in the lattice depth. We compare results of dipolar bosons with contact interaction. For forward quench ( V f > V i ) , the system exhibits the collapse–revival dynamics in the time evolution of normalized first- and second-order Glauber’s correlation function, time evolution of Shannon information entropy both for the contact as well as for the dipolar interaction which is reminiscent of the one observed in Greiner’s experiment [Nature, 415 (2002)]. We define the collapse and revival time ratio as the figure of merit ( τ ) which can uniquely distinguish the timescale of dynamics for dipolar interaction from that of contact interaction. In the reverse quench process ( V i > V f ) , for dipolar interaction, the dynamics is complex and the system does not exhibit any definite time scale of evolution, whereas the system with contact interaction exhibits collapse–revival dynamics with a definite time-scale. The long-range repulsive tail in the dipolar interaction inhibits the spreading of correlation across the lattice sites.
Abstract The relaxation process of a few strongly interacting bosons in a triple well optical lattice is studied from the first principle using the multiconfigurational time-dependent Hartree method for bosons. We report the contrasting response of the system under two independent quench processes: an interaction quench and a lattice depth quench. We analyze the evolution of the reduced one-body density matrix, two-body density and the Shannon information entropy for a wide range of lattice depth and interaction strength parameters. For the strong interaction quench, we observe a very fast relaxation to the steady state. In contrast, for the lattice depth quench, we observe collapse–revival dynamics in all the key measures. We also provide the best fitting formulas for relaxation and revival time which follow power law decay.
Abstract Ultracold interacting atoms are an excellent tool to study correlation functions of many-body systems that are generally eluding detection and manipulation. Herein, we investigate the ground state of bosons in a tilted triple-well potential and characterize the many-body state by the eigenvalues of its reduced one-body density matrix and Glauber correlation functions. We unveil how the interplay between the interaction strength and the tilt can be used to control the number of correlated wells as well as the fragmentation, i.e. the number of macroscopic eigenvalues of the reduced one-body density matrix.
We explore the consequences of disorder on phase coherence in the Mott insulator phases in an optical lattice. Few bosons with contact interaction in small optical lattice can feature varieties of insulating phases---weakly interacting Mott in deep lattice, maximally fragmented and strongly interacting Mott in intermediate lattice, weak Mott with double filling and intrawell coherence, fermionized Mott with strong intrawell coherence. Utilization of the multiconfigurational time-dependent Hartree method for bosons to solve the many-boson Schr\"odinger equation, facilitates to understand the microscopic effect of disorder on the different kinds of Mott phases in the primary lattice. The many-body properties are analyzed by distinct measures of the reduced one-body density in real and momentum space, fragmentation, order parameter, variance of spatial single-shot measurements, compressibility, and the Glauber normalized correlation functions. We find very complex competition of localization due to disorder and Mott correlation. We observe distinct response of four different Mott phases in the disordered lattice. When the weakly interacting Mott exhibits the Bose glass phase, the strongly correlated and fully fragmented Mott exhibits leakage, melting and central localization. In contrast, weak Mott with double filling which is a spatially separated dimer in each site, exhibits only some dissociation of intrawell coherence and assist in the development of interwell coherence in the presence of strong disorder. For the fermionized Mott, when the density in each well is fragmented, strong disorder interferes with the intrawell correlation and the characteristic dip in each site starts to disappear leading to simple Mott localization with a pair of bosons.