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arXiv:1302.5083 · Physical Review A

Hydrodynamic description of hard-core bosons on a Galileo ramp

Pierre Wendenbaum, Mario Collura, Dragi Karevski

Published Feb 19, 2013• 26 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.023624

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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.
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.
Abstract We consider the unitary time evolution of a one-dimensional cloud of hard-core bosons loaded on a harmonic trap potential which is slowly released in time with a general ramp g ( t ) . After the identification of a typical length scale ℓ ( t ) , related to the time ramp, we focus our attention on the dynamics of the density profile within a first order time-dependent perturbation scheme. In the special case of a linear ramp, we compare the first order predictions to the exact solution obtained through Ermakov–Lewis dynamical invariants. We also obtain an exact analytical solution for a cloud released from a harmonic trap with an amplitude that varies as the inverse of time. In such situations, the typical size of the cloud grows with a power law governed by an exponent that depends continuously on the initial trap frequency. At a high enough initial trap amplitude, the exponent acquires an imaginary part that leads to the emergence of a log-periodic modulation of the cloud expansion.
We develop an exact approach to study the quench dynamics of hard-core bosons initially in thermal equilibrium in one-dimensional lattices. This approach is used to study the sudden expansion of thermal states after confining potentials are switched off. We find that a dynamical fermionization of the momentum distribution occurs at all temperatures. This phenomenon is studied for low initial site occupations, for which the expansion of the cloud is self-similar. In this regime, the occupation of the natural orbitals allows one to distinguish hard-core bosons from noninteracting fermions. We also study the free expansion of initial Mott insulating domains at finite temperature and show that the emergence of off-diagonal one-body correlations is suppressed gradually with increasing temperature. Surprisingly, the melting of the Mott domain is accompanied by an effective cooling of the system. We explain this phenomenon analytically using an equilibrium description based on an emergent local Hamiltonian.
We study properties of the strongly repulsive Bose gas on one-dimensional incommensurate optical lattices with a harmonic trap, which can be dealt with by use of an exact numerical method through Bose-Fermi mapping. We first exploit the phase transition of hard-core bosons in optical lattices from the superfluid to the Bose-glass phase as the strength of the incommensurate potential increases. Then we study the dynamical properties of the system after suddenly switching off the harmonic trap. We calculate the one-particle density matrices, the momentum distributions, and the natural orbitals and their occupations for both the static and dynamic systems. Our results indicate that the Bose-glass and superfluid phases display quite different properties and expansion dynamics.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.