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arXiv:1104.5210 · Physical Review Letters

Doublon Relaxation in the Bose-Hubbard Model

Alexander L. Chudnovskiy, Dimitri M. Gangardt, Alex Kamenev

Published Feb 24, 2012• 26 citations
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Abstract

The decay of a high-energy double occupancy state, doublon, in a narrow-band lattice requires the creation of a coherent many-particle excitation. This leads to an exponentially long relaxation time of such a state. We show that, if the average occupation number is sufficiently small, the corresponding exponent may be evaluated exactly. To this end we develop the quasiclassical approach to calculation of the high-order tree-level decay amplitudes.

DOI
10.1103/physrevlett.108.085302

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The decay of a high-energy double occupancy state, doublon, in a narrow-band lattice requires the creation of a coherent many-particle excitation. This leads to an exponentially long relaxation time of such a state. We show that, if the average occupation number is sufficiently small, the corresponding exponent may be evaluated exactly. To this end we develop the quasiclassical approach to calculation of the high-order tree-level decay amplitudes.
Two fermions occupying the same site of a lattice model with strongly repulsive Hubbard-type interaction UUU form a doublon, a long-living excitation, the decay of which is suppressed because of energy conservation. By means of an exact-diagonalization approach based on the Krylov-space technique, we study the dynamics of a single doublon, of two doublons, and of a doublon in the presence of two additional fermions prepared locally in the initial state of the extended Hubbard model. The time dependence of the expectation value of the double occupancy at the different sites of a large one-dimensional lattice is analyzed by perturbative arguments. In this way the spatiotemporal evolution of the doublon can be understood. The initial decay takes place on a short time scale 1/U1/U1/U, and the long-time average of the decayed fraction of the total double occupancy scales as 1/U21/{U}^{2}1/U2. We demonstrate how the dynamics of a doublon in the initial state is related to the spectrum of two-fermion excitations obtained from linear-response theory, we work out the difference between doublons composed of fermions vs doublons composed of bosons, and we show that despite the increase of phase space for inelastic decay processes, the stability of a doublon is enhanced by the presence of additional fermions on an intermediate time scale.
We investigate the decay of artificially created double occupancies in a repulsive Fermi-Hubbard system in the strongly interacting limit using diagrammatic many-body theory and experiments with ultracold fermions in optical lattices. The lifetime of the doublons is found to scale exponentially with the ratio of the on-site repulsion to the bandwidth. We show that the dominant decay process in presence of background holes is the excitation of a large number of particle-hole pairs to absorb the energy of the doublon. We also show that the strongly interacting nature of the background state is crucial in obtaining the correct estimate of the doublon lifetime in these systems. The theoretical estimates and the experimental data are in agreement.
The interband dynamics of a two-band Bose–Hubbard (BH) model is studied with strongly correlated bosons forming single-site double occupancies referred to as doublons. Our model for resonant doublon interband coupling exhibits interesting dynamical features such as quantum Zeno effect, the generation of states such as a two-band Bell-like state and an upper-band Mott-like state. The evolution of the asymptotic state is controlled here by the effective opening of one or both of the two bands, which models decay channels.
We investigate the decay of highly excited states of ultracold fermions in a three-dimensional optical lattice. Starting from a repulsive Fermi-Hubbard system near half filling, we generate additional doubly occupied sites (doublons) by lattice modulation. The subsequent relaxation back to thermal equilibrium is monitored over time. The measured absolute doublon lifetime covers 2 orders of magnitude. In units of the tunneling time h/J it is found to depend exponentially on the ratio of on-site interaction energy U to kinetic energy J. We argue that the dominant mechanism for the relaxation is a simultaneous many-body process involving several single fermions as scattering partners. A many-body calculation is carried out using diagrammatic methods, yielding fair agreement with the data.
The fate of a local two-hole doublon excitation in the one-dimensional Fermi-Hubbard model is systematically studied for strong Hubbard interaction UUU in the entire filling range using the density-matrix renormalization group (DMRG) and the Bethe ansatz. For strong UUU, two holes at the same site form a compound object whose decay is impeded by the lack of phase space. Still, a partial decay is possible on an extremely short time scale where phase-space arguments do not yet apply. We argue that the initial decay and the resulting intermediate state are relevant for experiments performed with ultracold atoms loaded into an optical lattice as well as for (time-resolved) CVV Auger-electron spectroscopy. The detailed discussion comprises the mixed ballistic-diffusive real-time propagation of the doublon through the lattice, its partial decay on the short time scale as a function of filling and interaction strength, as well as the analysis of the decay products, which are metastable on the intermediate time scale that is numerically accessible and which show up in the two-hole excitation (Auger) spectrum. The ambivalent role of singly occupied sites is key to understanding the doublon physics; for high fillings, ground-state configurations with single occupancies are recognized to strongly relax the kinematic constraints and to open up decay channels. For fillings close to half-filling, however, their presence actually blocks the doublon decay. Finally, the analysis of the continua in the two-hole spectrum excludes a picture where the doublon decays into unbound electron holes for generic fillings, different from the limiting case of the completely filled band. We demonstrate that the decay products as well as the doublon propagation should rather be understood in terms of Bethe ansatz eigenstates.
We study the out-of-equilibrium dynamics of a dilute, lattice-confined Bose-Fermi mixture initialized in a highly excited state consisting of boson-fermion pairs (doublons) occupying single lattice sites. This system represents a paradigmatic case for studying relaxation dynamics in strongly correlated systems, and provides a versatile platform for studying thermalization and localization phenomena. We provide analytical expressions for the short-time decay of isolated doublons and small doublon clusters due to the competition between tunneling and interparticle interactions. We also discuss a mechanism for long-time decay that crucially depends on the quantum statistics of the particles constituting the doublon, namely, the conversion of pairs of neighboring doublons into an unpaired fermion and a site with a fermion and two bosons. Building on these insights, we develop a cluster expansion method to describe the dynamics in extended systems and compare it to numerically exact matrix product state simulations in one dimension. Finally, we discuss how our predictions can be observed in experiments with ultracold heteronuclear molecules.