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arXiv:1112.5013 · Physical Review A

Entangling many-body bound states with propagative modes in Bose-Hubbard systems

Mario Collura, Helge Aufderheide, Guillaume Roux, Dragi Karevski

Published Jul 12, 2012• 45 citations
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Abstract

The quantum evolution of a cloud of bosons initially localized on part of a one-dimensional optical lattice and suddenly subjected to a linear ramp is studied, realizing a quantum analog of the ``Galileo ramp'' experiment. The main remarkable effects of this realistic setup are revealed using analytical and numerical methods. Only part of the particles are ejected for a high enough ramp, while the others remain self-trapped. Then, the trapped density profile displays rich dynamics with Josephson-type oscillations around a plateau. This setup, by coupling bound states to propagative modes, creates two diverging condensates for which the entanglement is computed and related to the equilibrium one. Further, we address the role of integrability on the entanglement and on the damping and thermalization of simple observables.

DOI
10.1103/physreva.86.013615

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The quantum evolution of a cloud of bosons initially localized on part of a one-dimensional optical lattice and suddenly subjected to a linear ramp is studied, realizing a quantum analog of the ``Galileo ramp'' experiment. The main remarkable effects of this realistic setup are revealed using analytical and numerical methods. Only part of the particles are ejected for a high enough ramp, while the others remain self-trapped. Then, the trapped density profile displays rich dynamics with Josephson-type oscillations around a plateau. This setup, by coupling bound states to propagative modes, creates two diverging condensates for which the entanglement is computed and related to the equilibrium one. Further, we address the role of integrability on the entanglement and on the damping and thermalization of simple observables.
The quantum evolution of a cloud of bosons initially localized on part of a one dimensional optical lattice and suddenly subjected to a linear ramp is studied. The main remarkable effects of this realistic setup are revealed using analytical and numerical methods. Only part of the particles are ejected for a high enough ramp, while the others remain self-trapped. Then, the trapped density profile displays rich dynamics with Josephson-like oscillations around a plateau. This setup, by coupling bound states to propagative modes, creates two diverging condensates for which the entanglement is computed and related to the equilibrium one. Further, we address the role of integrability on the entanglement and the damping and thermalization of simple observables.
We study the quantum evolution of a cloud of hard-core bosons loaded on a one-dimensional optical lattice after its sudden release from a harmonic trap. Just after the trap has been removed, a linear ramp potential is applied, mimicking the so-called Galileo ramp experiment. The nonequilibrium expansion of the bosonic cloud is elucidated through a hydrodynamical description which is compared to the exact numerical evolution obtained by exact diagonalization on finite lattice sizes. The system is found to exhibit a rich behavior, showing, in particular, Bloch oscillations of a self-trapped condensate and an ejected particle density leading to two diverging entangled condensates. Depending on the initial density of the gas different regimes of Josephson-like oscillations are observed. At low densities, the trapped part of the cloud is in a superfluid phase that oscillates in time as a whole. At higher densities, the trapped condensate is in a mixed superfluid--Mott-insulator phase that show a breathing regime for steep enough potential ramps.
We study the temporal expansion of an ultracold Bose gas in two-dimensional square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical [Bose-Einstein condensate (BEC)] part and quantum mechanical fluctuations. After a quench, i.e., after a sudden switch of the lattice nearest-neighbor hopping, the expanding bosonic cloud separates spatially into a fast ballistic forerunner and a slowly expanding central part controlled by self-trapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.
We study the temporal expansion of an ultracold Bose gas in two-dimensional, square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical (BEC) part and quantum mechanical fluctuations. After a quench, i.e. after a sudden switch of the lattice nearest-neighbor hopping, the expanding, bosonic cloud separates spatially into a fast, ballistic forerunner and a slowly expanding central part controlled by selftrapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.
We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.
We analyze the effect of a linear time-variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible onsite particle distribution are studied as a function of the ramp time using time-dependent exact diagonalization and density-matrix renormalization group techniques. We find that the dynamics of a trapped system typically display two regimes: for long ramp times, the dynamics are governed by density redistribution, while at short ramp times, local dynamics dominate as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the non-trivial scaling of the energy absorbed with the ramp time.