Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0905.2963 · Physical Review Letters

Observation of Elastic Doublon Decay in the Fermi-Hubbard Model

Niels Strohmaier, Daniel Greif, Robert Jördens, Leticia Tarruell, Henning Moritz, Tilman Esslinger, Rajdeep Sensarma, David Pekker, Ehud Altman, Eugene Demler

Published Feb 22, 2010• 258 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.104.080401

Related papers

Lifetime of double occupancies in the Fermi-Hubbard model

Rajdeep Sensarma, David Pekker, Ehud Altman +7 more

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.

arXiv:1001.3881•Physical Review B•Dec 3, 2010•137 citations

Doublon dynamics of Bose-Fermi mixtures in optical lattices

Martin Gärttner, Arghavan Safavi-Naini, Johannes Schachenmayer +1 more

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.

arXiv:1908.04757•Physical Review A•Nov 8, 2019•10 citations

Doublon dynamics in the extended Fermi-Hubbard model

Felix Hofmann, Michael Potthoff

Two fermions occupying the same site of a lattice model with strongly repulsive Hubbard-type interaction $U$ 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 $1/U$, and the long-time average of the decayed fraction of the total double occupancy scales as $1/{U}^{2}$. 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.

arXiv:1202.5149•Physical Review B•May 15, 2012•53 citations

Filling-dependent doublon dynamics in the one-dimensional Hubbard model

Roman Rausch, Michael Potthoff

The fate of a local two-hole doublon excitation in the one-dimensional Fermi-Hubbard model is systematically studied for strong Hubbard interaction $U$ in the entire filling range using the density-matrix renormalization group (DMRG) and the Bethe ansatz. For strong $U$, 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.

arXiv:1611.05388•Physical review. B./Physical review. B•Jan 31, 2017•20 citations

Doublon dynamics and polar molecule production in an optical lattice

Jacob P. Covey, Steven A. Moses, Martin Gärttner +8 more

Polar molecules in an optical lattice provide a versatile platform to study quantum many-body dynamics. Here we use such a system to prepare a density distribution where lattice sites are either empty or occupied by a doublon composed of an interacting Bose-Fermi pair. By letting this out-of-equilibrium system evolve from a well-defined, but disordered, initial condition, we observe clear effects on pairing that arise from inter-species interactions, a higher partial-wave Feshbach resonance and excited Bloch-band population. These observations facilitate a detailed understanding of molecule formation in the lattice. Moreover, the interplay of tunnelling and interaction of fermions and bosons provides a controllable platform to study Bose-Fermi Hubbard dynamics. Additionally, we can probe the distribution of the atomic gases in the lattice by measuring the inelastic loss of doublons. These techniques realize tools that are generically applicable to studying the complex dynamics of atomic mixtures in optical lattices.

arXiv:1511.02225•Nature Communications•Apr 14, 2016•48 citations

Detecting the tunneling rates for strongly interacting fermions on optical lattices

Alberto Anfossi, Luca Barbiero, Arianna Montorsi

Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large on-site repulsion $U$, the model is shown to reproduce the $t$-$J$ Hamiltonian, in which the $J$ coefficient of the Heisenberg term depends on the particle-assisted tunneling rate $g$: explicitly, $J=4{g}^{2}/U$. At half-filling, $g$ drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms ($g=0$) to the antiferromagnetic Mott insulator of the standard Hubbard case ($g=t$). This is observed already in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of $g$.

arXiv:1002.1814•Physical Review A•Apr 26, 2010•1 citation
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.
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.
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.
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.
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.
Polar molecules in an optical lattice provide a versatile platform to study quantum many-body dynamics. Here we use such a system to prepare a density distribution where lattice sites are either empty or occupied by a doublon composed of an interacting Bose-Fermi pair. By letting this out-of-equilibrium system evolve from a well-defined, but disordered, initial condition, we observe clear effects on pairing that arise from inter-species interactions, a higher partial-wave Feshbach resonance and excited Bloch-band population. These observations facilitate a detailed understanding of molecule formation in the lattice. Moreover, the interplay of tunnelling and interaction of fermions and bosons provides a controllable platform to study Bose-Fermi Hubbard dynamics. Additionally, we can probe the distribution of the atomic gases in the lattice by measuring the inelastic loss of doublons. These techniques realize tools that are generically applicable to studying the complex dynamics of atomic mixtures in optical lattices.
Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large on-site repulsion UUU, the model is shown to reproduce the ttt-JJJ Hamiltonian, in which the JJJ coefficient of the Heisenberg term depends on the particle-assisted tunneling rate ggg: explicitly, J=4g2/UJ=4{g}^{2}/UJ=4g2/U. At half-filling, ggg drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms (g=0g=0g=0) to the antiferromagnetic Mott insulator of the standard Hubbard case (g=tg=tg=t). This is observed already in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of ggg.