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arXiv:cond-mat/0606155 · New Journal of Physics

Coherent matter waves emerging from Mott-insulators

Karen Rodríguez, Salvatore R. Manmana, Marcos Rigol, R. M. Noack, A. Muramatsu

Published Aug 30, 2006• 43 citations
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Abstract

We study the formation of (quasi-) coherent matter waves emerging from a Mott insulator for strongly interacting bosons on a one-dimensional lattice. It has been shown previously that a quasi-condensate emerges at momentum k cond = π/2 a , where a is the lattice constant, in the limit of infinitely strong repulsion (hard-core bosons). Here, we show that this phenomenon persists for all values of the repulsive interaction that lead to a Mott insulator at a commensurate filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by means of a Jordan–Wigner transformation, and the generic case is studied using a time-dependent density matrix renormalization group technique. Different methods for controlling the emerging matter wave are discussed.

DOI
10.1088/1367-2630/8/8/169

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We study the formation of (quasi-) coherent matter waves emerging from a Mott insulator for strongly interacting bosons on a one-dimensional lattice. It has been shown previously that a quasi-condensate emerges at momentum k cond = π/2 a , where a is the lattice constant, in the limit of infinitely strong repulsion (hard-core bosons). Here, we show that this phenomenon persists for all values of the repulsive interaction that lead to a Mott insulator at a commensurate filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by means of a Jordan–Wigner transformation, and the generic case is studied using a time-dependent density matrix renormalization group technique. Different methods for controlling the emerging matter wave are discussed.
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.
We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion; the asymptotic density dynamics is identical to that of initially localized, noninteracting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this nonequilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model; while being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the noninteracting limit. These results are compared to the setup of a recent experiment [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. In the latter case, the interaction quench breaks the universal dynamics in the asymptotic regime and the expansion depends on the interaction strength. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways; while the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.
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.
The single-vortex problem in a strongly correlated bosonic system is investigated self-consistently within the mean-field theory of the Bose-Hubbard model. Near the superfluid--Mott-insulator transition, the vortex core has a tendency toward the Mott-insulating phase, with the core particle density approaching the nearest commensurate value. If the nearest-neighbor repulsion exists, the charge-density wave order may develop locally in the core. The evolution of the vortex configuration from the strong- to weak-coupling regions is studied. This phenomenon can be observed in systems of rotating ultracold atoms in optical lattices and Josephson-junction arrays.
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.