Time-resolved observation of coherent multi-body interactions in quantum phase revivals

Will, Sebastian; Best, Thorsten; Schneider, Ulrich; Hackermüller, Lucia; Lühmann, Dirk-Sören; Bloch, Immanuel

doi:10.1038/nature09036

Cited by 289 publications

(389 citation statements)

References 32 publications

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“…Due to this reduced tunneling rate the density distribution is essentially frozen out during the following 40 ms magnetic field ramp (B f in = 206 − 260 G), which sets the interaction for the expansion due to the well known Feshbach resonance at B 0 = 202.1 G [37]. Combined with the strong harmonic confinement, this leads to a dephasing between different lattice sites and effectively localizes all particles to individual sites [38].…”

Section: Supplementary Information a Experimental Sequencementioning

confidence: 99%

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

et al. 2012

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Transport properties are among the defining characteristics of many important phases in condensed matter physics. In the presence of strong correlations they are difficult to predict even for model systems like the Hubbard model. In real materials they are in general obscured by additional complications including impurities, lattice defects or multi-band effects. Ultracold atoms in contrast offer the possibility to study transport and out-of-equilibrium phenomena in a clean and well-controlled environment and can therefore act as a quantum simulator for condensed matter systems. Here we studied the expansion of an initially confined fermionic quantum gas in the lowest band of a homogeneous optical lattice. While we observe ballistic transport for non-interacting atoms, even small interactions render the expansion almost bimodal with a dramatically reduced expansion velocity. The dynamics is independent of the sign of the interaction, revealing a novel, dynamic symmetry of the Hubbard model.In solid state physics, transport properties are among the key observables, the most prominent example being the electrical conductivity, which e.g. allows to distinguish normal conductors from insulators or superconductors. Furthermore, many of today's most intriguing solid state phenomena manifest themselves in transport properties, examples including high-temperature superconductivity, giant magnetoresistance, quantum hall physics, topological insulators and disorder phenomena. Especially in strongly correlated systems, where the interactions between the conductance electrons are important, transport properties are difficult to calculate beyond the linear response regime. In general, predicting out-of-equilibrium fermionic dynamics represents an even harder problem than the prediction of static properties like the nature of the ground state. In real solids further complications arise due to the effects of e.g. impurities, lattice defects and phonons. These complications render an experimental investigation in a clean and well controlled ultracold atom system highly desirable. While the last years have seen dramatic progress in the control of quantum gases in optical lattices [1-3], a thorough understanding of the dynamics in these systems is still lacking. Genuine dynamical experiments can not only uncover new dynamic phenomena but are also essential to gain insight into the timescales needed to achieve equilibrium in the lattice [4,5] or to adiabatically load into the lattice [6,7].Using both bosonic and fermionic [8-10] atoms, it has become possible to simulate models of strongly interacting quantum particles, for which the Hubbard model [11] * ulrich.schneider@lmu.de is probably the most important example. A major advantage of these systems compared to real solids is the possibility to change all relevant parameters in real-time by e.g. varying laser intensities or magnetic fields. While first studies of dynamical properties of both bosonic and fermionic quantum gases [12][13][14] have already been performed, a remaining...

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Section: Supplementary Information a Experimental Sequencementioning

confidence: 99%

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

et al. 2012

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“…The shift of the observed transition between the superfluid (SF) and the MI phases, observed experimentally in Refs. [38][39][40] (for the analogous effects with Bose-Bose mixtures and tightly trapped bosons, see [41,42]), could not be explained with this simple description. It has soon been realized that density-dependent tunneling terms as well as contributions coming from higher Bloch bands are necessary to describe the systems in question [43][44][45][46], whenever the interspecies interaction becomes strong enough.…”

Section: Introductionmentioning

confidence: 99%

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

et al. 2014

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We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the sitedependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as, the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points however, cease to exists after the addition of the hopping disorder.

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“…Our comparisons between the numerical and perturbative results accounted for first-and higher-order effective range corrections nonperturbatively by introducing the quantity E s−wave gr in Eq. (29). In the weakly-interacting regime, we find that the leading-order interplay between the spin-orbit coupling term and the effective range scales as r eff a 2 aa k 2 so (or higher order) for the ground state.…”

Section: Discussionmentioning

confidence: 87%

“…4 and 5, the quantity |(∆E (soc,a,1) gr,MJ =1/2 − E scatt )/E scatt | is smaller than 5 × 10 −3 and 4 × 10 −2 , respectively, implying that the energy shift due to the interplay between the spin-orbit coupling term and the s-wave interaction is respectively less than a percent and a few percent of the mean-field shift. While these effects are small, they can potentially be measured in "quantum phase revival experiments" analogous to those for few-atom systems in an optical lattice [29]. In that work, (28), as a function of (ksoa ho ) 2 .…”

Section: B Perturbative Treatment Of H (12)mentioning

confidence: 99%

“…Our work combines analytical and numerical approaches, and covers weak spin-orbit coupling strengths and weak to strong atom-atom interactions. Few atom systems can nowadays be prepared and probed experimentally [28,29], opening the door for developing a bottom-up understanding of cold atom systems with spin-orbit coupling. Our results provide much needed theoretical guidance for such experimental studies.…”

Section: Introductionmentioning

confidence: 99%

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Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

Yin

Gopalakrishnan²,

Blume

2014

Phys. Rev. A

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The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms and condensed matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold atom systems, giving rise to a spin-orbit coupling term with "strength" kso. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body s-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small s-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly-interacting unitary regime. We find that the interplay between the spin-orbit coupling term and the s-wave interaction generically enters, depending on the exact parameter combinations of the s-wave scattering lengths, at order k 2 so or k 4 so for the ground state and leads to a shift of the energy of either sign. While the absence of a term proportional to kso follows straightforwardly from the functional form of the spin-orbit coupling term, the absence of a term proportional to k 2 so for certain parameter combinations is unexpected. The well-known fact that the spin-orbit coupling term couples the relative and center of mass degrees of freedom has interesting consequences for the trapped two-particle systems. For example, we find that the spin-orbit coupling term turns, for certain parameter combinations, sharp crossings into avoided crossings with an energy splitting proportional to kso. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

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Time-resolved observation of coherent multi-body interactions in quantum phase revivals

Cited by 289 publications

References 32 publications

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

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