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arXiv:1201.6674 · Physical Review A

Dynamics of correlations in shallow optical lattices

Stefan S. Natu, Erich J. Mueller

Published Jun 17, 2013• 14 citations
arXivHTMLPDF

Abstract

We explore the time evolution of correlations in a homogeneous gas of lattice bosons with filling factor ${n}_{0}$, following a sudden reduction in the lattice depth to a regime where the interactions are weak. In the limit of vanishing interactions, we find a simple closed-form expression for the static structure factor. The corresponding real-space density-density correlation function shows multiple spatial oscillations which disperse linearly in time. By perturbatively including the effect of interactions, we study the evolution of boson quasimomentum distribution following the quench. In one dimension, the quasimomentum distribution develops peaks at finite momentum which disperse towards $q=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. In two dimensions, the momentum occupation rapidly approaches a steady-state distribution characterized by a broad peak at $q=0$. Quasi-long-range order is never found at finite time. Our studies provide insight into the dynamics of isolated quantum systems.

DOI
10.1103/physreva.87.063616

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We explore the time evolution of correlations in a homogeneous gas of lattice bosons with filling factor n0{n}_{0}n0​, following a sudden reduction in the lattice depth to a regime where the interactions are weak. In the limit of vanishing interactions, we find a simple closed-form expression for the static structure factor. The corresponding real-space density-density correlation function shows multiple spatial oscillations which disperse linearly in time. By perturbatively including the effect of interactions, we study the evolution of boson quasimomentum distribution following the quench. In one dimension, the quasimomentum distribution develops peaks at finite momentum which disperse towards q=\ifmmode±\else\textpm\fi\ensuremathπ/2q=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2q=\ifmmode±\else\textpm\fi\ensuremathπ/2. In two dimensions, the momentum occupation rapidly approaches a steady-state distribution characterized by a broad peak at q=0q=0q=0. Quasi-long-range order is never found at finite time. Our studies provide insight into the dynamics of isolated quantum systems.
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.
Long-range order in quantum many-body systems is usually associated with equilibrium situations.Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case.We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d.After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice.Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta Æðπ=2Þðℏ=dÞ in the momentum distribution function.
Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta ±(π/2)(ℏ/d) in the momentum distribution function.
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.
We explore the nonequilibrium dynamics of a density-ordered dipolar Bose gas in a finite one-dimensional optical lattice following a negative interaction quench, using the numerically exact multiconfigurational time-dependent Hartree method for bosons. The interaction sign reversal, effectively driving a crossover from long-range to short-range interactions, generates rich intra- and interwell tunneling dynamics spanning superfluid, Mott-insulating, and fragmented regimes. A striking finding is the robustness of the underlying crystal-state correlations against the quench, despite the strong dynamical response. We identify emergent excitation modes, including local breathing and dipole-like oscillations, via real- and momentum-space observables, and quantify tunneling through site-resolved position variance. One- and two-body Glauber correlation functions further uncover a direct connection between tunneling and correlation dynamics. Moreover, we show that combining interaction quenches with lattice-depth ramping enables controllable dynamical engineering, establishing dipolar lattice systems as a promising platform for nonequilibrium quantum simulation.
We study the evolution of correlations in a quasi-two-dimensional dipolar gas driven out of equilibrium by a sudden ramp of the interactions. On short time scales, rotonlike excitations coherently oscillate in and out of the condensate, giving rise to pronounced features in the time evolution of the momentum distribution, excited fraction, and the density-density correlation function. The evolution of these correlation functions following a quench can thus be used to probe the spectrum of the dipolar gas. We also find that density fluctuations induced by the presence of rotons following the quench, dramatically slows down the rate of spreading of correlations in the system: Near the roton instability, correlations take infinitely long to build up and show deviations from light-cone-like behavior.