We investigate the transport properties in out-of-equilibrium dynamics of strongly correlated dipolar fermions initially localized in one-dimensional inhomogeneous optical lattice. The dynamics is studied by experimentally measurable dynamical variables such as one-body density, pair-correlation function and size of the expanding cloud. In the noninteracting limit, we trace the usual fingerprints of ballistic expansion in the short time dynamics. However, dynamics is strongly affected by system size due to Pauli principle. The dynamics also exhibits significant dependence on the sign of the interactions. We observe that strong repulsive dipolar interaction gives rise to many-body features in the dynamics, while strong attractive dipolar interaction leads to stabilized cluster states. Intermediate dipolar interaction are found to hinder expansion of correlations, while very strong dipolar interaction favors expansion of the cloud. Our work show the effect of dipolar interaction in the transport properties of interacting fermions, that can be studied in on-going experiments with ultracold dipolar fermions.
We investigate the transport properties in out-of-equilibrium dynamics of strongly correlated dipolar fermions initially localized in one-dimensional inhomogeneous optical lattice. The dynamics is studied by experimentally measurable dynamical variables such as one-body density, pair-correlation function and size of the expanding cloud. In the noninteracting limit, we trace the usual fingerprints of ballistic expansion in the short time dynamics. However, dynamics is strongly affected by system size due to Pauli principle. The dynamics also exhibits significant dependence on the sign of the interactions. We observe that strong repulsive dipolar interaction gives rise to many-body features in the dynamics, while strong attractive dipolar interaction leads to stabilized cluster states. Intermediate dipolar interaction are found to hinder expansion of correlations, while very strong dipolar interaction favors expansion of the cloud. Our work show the effect of dipolar interaction in the transport properties of interacting fermions, that can be studied in on-going experiments with ultracold dipolar fermions.
Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases under these long-range interactions. In this work, we study repulsive ultracold dipolar fermions in a quasiperiodic optical lattice to characterize the behavior of interacting quasicrystals. We simulate the full time evolution of the typical experimental protocols used to probe quasicrystalline order and localization properties. We extract experimentally measurable dynamical observables and correlation functions to characterize the three phases observed in the noninteracting setting: localized, intermediate, and extended. We then study the stability of such phases to repulsive dipolar interactions. We find that dipolar interactions can completely alter the shape of the phase diagram by stabilizing the intermediate phase, mostly at the expense of the extended phase. Moreover, in the strongly interacting regime, a resonance-like behavior characterized by density oscillations appears. Remarkably, strong dipolar repulsions can also localize particles even in the absence of quasiperiodicity if the primary lattice is sufficiently deep. Our work shows that dipolar interactions in a quasiperiodic potential can give rise to a complex, tunable coexistence of localized and extended quantum states.
We theoretically investigate the thermodynamics of an interacting inhomogeneous two-component Fermi gas in an optical lattice. Motivated by a recent experiment by L. Hackermüller et al., Science 327, 1621 (2010), we study the effect of the interplay between thermodynamics and strong correlations on the size of the fermionic cloud. We use dynamical mean-field theory to compute the cloud size, which in the experiment shows an anomalous expansion behavior upon increasing attractive interaction. We confirm this qualitative effect but, assuming adiabaticity, we find quantitative agreement only for weak interactions. For strong interactions we observe significant nonequilibrium effects which we attribute to a dynamical arrest of the particles due to increasing correlations.
We experimentally and numerically investigate the expansion of initially localized ultracold bosons in homogeneous one- and two-dimensional optical lattices. We find that both dimensionality and interaction strength crucially influence these nonequilibrium dynamics. While the atoms expand ballistically in all integrable limits, deviations from these limits dramatically suppress the expansion and lead to the appearance of almost bimodal cloud shapes, indicating diffusive dynamics in the center surrounded by ballistic wings. For strongly interacting bosons, we observe a dimensional crossover of the dynamics from ballistic in the one-dimensional hard-core case to diffusive in two dimensions, as well as a similar crossover when higher occupancies are introduced into the system.
Using the time-dependent density-matrix renormalization-group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass when the interaction strength is increased. This unique feature can be considered as a dynamical signature for the emergence of a Mott plateau for an interacting trapped Fermi gas in an optical lattice.
Transport properties and nonequilibrium dynamics in strongly correlated materials are \ntypically difficult to calculate. This holds true even for minimalistic model Hamiltonians \nof these systems, such as the fermionic Hubbard model. \nUltracold atoms in optical lattices enable an alternative realization of the Hubbard \nmodel and have the advantage of being free of additional complications such as phonons, \nlattice defects or impurities. This way, cold atoms can be used as quantum simulators of \nstrongly interacting materials. Being thermally isolated systems, however, we show that \ncold atoms in optical lattices can also behave very differently from solids and can show a \nplethora of novel dynamic effects. \nIn this thesis, several out-of equilibrium processes involving interacting fermionic atoms \nin optical lattices are presented. We first analyze the expansion dynamics of an initially \nconfined atomic cloud in the lowest band of an optical lattice. While non-interacting atoms \nexpand ballistically, the cloud expands with a dramatically reduced velocity in the presence \nof interactions. Most prominently, the expansion velocity is independent of the attractive \nor repulsive character of the interactions, highlighting a novel dynamic symmetry of the \nHubbard model. \nIn a second project, we discuss the possibility of realizing negative absolute temperatures in optical lattices. Negative absolute temperatures characterize equilibrium states \nwith an inverted occupation of energy levels. Here, we propose a dynamical process to realize equilibrated Fermions at negative temperatures and analyze the time scales of global \nrelaxation to equilibrium, which are associated with a redistribution of energy and particles \nby slow diffusive processes. \nWe show that energy conservation has a major impact on the dynamics of an interacting \ncloud in an optical lattice, which is exposed to an additional weak linear (gravitational) \npotential. Instead of ‘falling downwards‘, the cloud diffuses symmetrically upwards and \ndownwards in the gravitational potential. Furthermore, we show analytically that the \nradius R grows with the time t according to R ∼ t^1/3, consistent with numerical simulations \nof the Boltzmann equation. \nFinally, we analyze the damping of Bloch oscillations by interactions. For a homogeneous system, we discuss the possibility of mapping the dynamics of the particle current to \na classical damped harmonic oscillator equation, thereby giving an analytic explanation for \nthe transition from weakly damped to over-damped Bloch oscillations. We show that the \ndynamics of a strongly Bloch oscillating and weakly interacting atomic cloud can be discribed in terms of a novel effective “stroboscopic” diffusion equation. In this approximation, \nthe cloud’s radius R grows asymptotically in time t according to R ∼ t^1/5 .
Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson–boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator and a Tonks–Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 [ 33 ]). Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as a function of the dipolar interaction strength. We then analyze the real- and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.