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Frustration and topology: new frontiers for cold atomic gases in and out of equilibrium

English title Frustration and topology: new frontiers for cold atomic gases in and out of equilibrium
Applicant Huber Sebastian
Number 138960
Funding scheme SNSF Professorships
Research institution
Institution of higher education ETH Zurich - ETHZ
Main discipline Theoretical Physics
Start/End 01.11.2012 - 31.10.2016
Approved amount 1'478'541.00
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All Disciplines (2)

Discipline
Theoretical Physics
Condensed Matter Physics

Keywords (10)

Non equilibrium; Condensed matter theory; Cold atoms; Quantum Hall effect; Non-linear optics; Disorder; Geometric frustration; Dipolar molecules; Linear response; Topology

Lay Summary (English)

Lead
Lay summary

Topology

Colloquially, by a topological classification we mean that we can assign an integer property to quantum mechanical system which depends on its global strucuture only. In other words, no local probe or small local change to the system parameters can change this integer: it is topologically protected.

Traditional phases that were classified in such a topological framework include the integer  and fractional quantum Hall effects and the more recently discovered topological insulators and superconductors. All of these equillibrium systems have a finite gap between the ground state and the first excited state. This gap enables a controlled derivation of a topological field theory for the low energy behavior. From that perspective, gapless or driven systems seem not to be classifiable by a topological index.

Recent developments have shown indications of the contrary, however. In one particular case of strongly interacting lattice bosons in a weak magnetic field we could show that thegapless superfluid phase is intersected by lines of topological transitions where the Hall conductivity jumps by an integer value.

We plan to extend this exciting new direction of using standard tools known from the description of gapped topologic matter to the deeper understanding of gapless or driven quantum phases.

Out of equilibrium

The use of cold atoms in simulating interesting open questions of condensed matter physics has seen a tremendous success in recent years. One key aspect is their almost perfect isolation from the environment. What proofs to be an asset in implementing a “designed” Hamiltonian turns out to be a major obstruction to the investigation of the resulting physics.

In our research we focus on the development of the theoretical framework for new investigative tools adapted to the cold atoms setup. We are mainly interested in strongly correlated lattice systems where we showed how to extract coherence porperties from a bosonic or fermionic Mott insulator. Moreover, we pointed out how the “Higgs mode” close to a quantum phase transition can be measured. Recent experiments verified our predictions. We make use of a broad range of analytical tools, however, if necessary we develop new approaches to tackle the many-body problems at hand.

Another consequence of the high degree of isolation is the ability to study pure non-equilibrium dynamics. In the past we studied mainly one-dimensional systems, in particular coupled tubes of interacting quantum liquids that undergo quantum quenches or slow Landau-Zener dynamics.

We plan to extend these studies by investigating the non-equilibrium dynamics of strongly correlated systems, in particular their topological properties. We believe that by focusing on the peculiarities  of new engineered quantum systems like cold atoms or micro-structured solid state devices like NV centers in diamonds, coupled microwave cavities, etc., we can make new discoveries in a developing field of topological phases out of equilibrium.

Frustrated lattices

Spins fixedly arranged on lattices where not all interactions can be fulfilled simultaneously have been shown to host intriguing quantum phases . In our research we are interested in the behavior of itinerant particles on such frustrated lattices. Due to destructive interference resulting from the underlying frustration the motion of the particles can be completely quenched. Deprived of their kinetic energy, the behavior of the particles is dominated by more complex processes such as interactions or disorder. What new physics can emerge from such a situation is the main question we address with our research.

Weakly interacting bosons tend to condense in the lowest single particle state. On frustrated lattices, like the kagome net, the bosons do not find such a simple low energy state. In the absence of interactions this leads to a localized valence bond solid. When interactions are turned on, the particles delocalize and condense, a delocalized state entirely stabilized by repulsive interactions. In addition, also disorder turns out to have the quite counterintuitive effect of delocalizing the eigenstates.

We are currently working on trying to understand the combined effect of both disorder and interaction on frustrated lattices. This seems to be an intractable problem as the interplay of disorder and interaction is an outstanding open theoretical problem. However, the peculiar structure of the frustrated geometry has a chance to give way to a controlled approach.

Our research is aimed at finding interesting new stable phases of matter. The recent developments in the design of complicated lattice structures for cold atoms further motivates our work. In particular it has been demonstrated that one can implement an optical kagome lattice.





Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
Classification of topological phonons in linear mechanical metamaterials
Süsstrunk Roman, Huber Sebastian D. (2016), Classification of topological phonons in linear mechanical metamaterials, in Proceedings of the National Academy of Sciences, 201605462-201605462.
Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models
Huber Sebastian (2016), Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models, in Physical Review B, 94, 245149.
Phase transitions in a Bose-Hubbard model with cavity-mediated global-range interactions
Dogra N., Brennecke F., Huber S. D., Donner T. (2016), Phase transitions in a Bose-Hubbard model with cavity-mediated global-range interactions, in Physical Review a, 94(2), 023632.
Single spin probe of many-body localization
van Nieuwenburg Evert P. L., Huber Sebastian D., Chitra R. (2016), Single spin probe of many-body localization, in Physical Review B, 94(18), 180202.
Topological mechanics
Huber Sebastian D. (2016), Topological mechanics, in Nature Physics, 12(7), 621-623.
Exploring Competing Density Order in the Ionic Hubbard Model with Ultracold Fermions
Messer Michael, Desbuquois Remi, Uehlinger Thomas, Jotzu Gregor, Huber Sebastian, Greif Daniel, Esslinger Tilman (2015), Exploring Competing Density Order in the Ionic Hubbard Model with Ultracold Fermions, in Physical Review Letters, 115(11), 115303.
Incompressible Polaritons in a Flat Band
Biondi Matteo, van Nieuwenburg Evert P. L., Blatter Gianni, Huber Sebastian D., Schmidt Sebastian (2015), Incompressible Polaritons in a Flat Band, in Physical Review Letters, 115(14), 143601.
Observation of phononic helical edge states in a mechanical topological insulator
Suesstrunk Roman, Huber Sebastian D. (2015), Observation of phononic helical edge states in a mechanical topological insulator, in Science, 349(6243), 47-50.
Sign reversal of the Hall response in a crystalline superconductor
Berg E., Huber S.D., Lindner N.H. (2015), Sign reversal of the Hall response in a crystalline superconductor, in Physical Review B (Condensed Matter and Materials Physics), 91(2), 024507-8.
Topological bands with a Chern number C=2 by dipolar exchange interactions
Peter David, Yao Norman Y., Lang Nicolai, Huber Sebastian D., Lukin Mikhail D., Buechler Hans Peter (2015), Topological bands with a Chern number C=2 by dipolar exchange interactions, in Physical Review a, 91(5), 053617.
Z2 slave-spin theory of a strongly correlated Chern insulator
Prychynenko Diana, Huber Sebastian (2015), Z2 slave-spin theory of a strongly correlated Chern insulator, in Physica B, 481, 53.
Classification of mixed-state topology in one dimension
van Nieuwenburg Evert P. L., Huber Sebastian D. (2014), Classification of mixed-state topology in one dimension, in Physical Review B, 90(7), 075141.
Majorana modes and p-wave superfluids for fermionic atoms in optical lattices
Buehler A., Lang N., Kraus C. V., Moeller G., Huber S. D., Buechler H. P. (2014), Majorana modes and p-wave superfluids for fermionic atoms in optical lattices, in Nature Communications, 5, 5504.
Measuring topological invariants in small photonic lattices
Bardyn C-E, Huber S. D., Zilberberg O. (2014), Measuring topological invariants in small photonic lattices, in New Journal of Physics, 16, 123013.
Nonequilibrium functional renormalization for driven-dissipative Bose-Einstein condensation
Sieberer L. M., Huber S. D., Altman E., Diehl S. (2014), Nonequilibrium functional renormalization for driven-dissipative Bose-Einstein condensation, in Physical Review B, 89(13), 134310.
Dynamical Critical Phenomena in Driven-Dissipative Systems
Sieberer Lukas, Huber Sebastian David, Altman Ehud, Diehl Sebastian (2013), Dynamical Critical Phenomena in Driven-Dissipative Systems, in Phys. Rev. Lett., 110, 195301.
Geometry induced pair condensation
Tovmasyan Murad, van Nieuwenburg Evert P.L., Huber Sebastian David (2013), Geometry induced pair condensation, in Phys. Rev. B, 88, 220510R.
Reply to "Comment on 'Z(2)-slave-spin theory for strongly correlated fermions"'
Rueegg Andreas, Huber Sebastian D., Sigrist Manfred (2013), Reply to "Comment on 'Z(2)-slave-spin theory for strongly correlated fermions"', in Physical Review B, 87(3), 037102.
Reply to “Comment on ‘Z2-slave-spin theory for strongly correlated fermions'”
Rüegg Andreas, Huber Sebastian David, Sigrist Manfred (2013), Reply to “Comment on ‘Z2-slave-spin theory for strongly correlated fermions'”, in Phys. Rev. B, 87, 037102.

Collaboration

Group / person Country
Types of collaboration
Prof. Gianni Blatter, ETH Zürich Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel
Prof. Chiara Daraio Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
Prof. Yaron Silberberg, The Weizmann Institut of Science Israel (Asia)
- in-depth/constructive exchanges on approaches, methods or results
Prof. Tilman Esslinger, ETH Zürich Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
Prof. Florian Marquardt Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
Prof. Paolo Ermanni Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
Dr. Netanel Lindner, Californian Institute of Technology United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
Prof. Hans-Peter Büchler, University of Stuttgart Germany (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Prof. Massimo Inguscio, LENS Florence Italy (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Prof. Gil Refael, Californian Institute of Technology United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Aspen Center for theoretical Physics Talk given at a conference Classification of mixed density matrices 01.09.2014 Aspen, United States of America Huber Sebastian;
Summer School: Topological aspects of condensed matter physics Poster Chern numbers from transfer matrices 04.08.2014 Les Houches, France Süsstrunk Roman;
Summer Course of the International School of Physics "Enrico Fermi": Quantum Matter at Ultracold Temperatures Poster Flat band condensation 30.06.2014 Varenna, Italy Tovmasyan Murad;
Quantum Effects in Low-Dimensional Systems Poster Various 29.06.2014 Copenhagen, Denmark Süsstrunk Roman; Van Nieuwenburg Everard Pieter Lodewijk;
Higgs Modes in Condensed Matter and Quantum Gases Talk given at a conference Amplitude modes in cold atoms 23.06.2014 Kyoto, Japan Huber Sebastian;
BEC2013 Frontiers in quantum gases Talk given at a conference Geometry induced pair condensation 08.09.2013 Sant Feliu, Spain Huber Sebastian;
Flat Bands: Design, Topology, and Correlations, International focus workshop Talk given at a conference Bose condensation and its suppression in flat bands 04.03.2013 Dresden, Germany Huber Sebastian;


Self-organised

Title Date Place
Quantum Correlations out of equilibrium 05.11.2014 Zürich, Switzerland

Associated projects

Number Title Start Funding scheme
166157 Frustration and topology: new frontiers for cold atomic gases in and out of equilibrium 01.11.2016 SNSF Professorships

Abstract

My research proposal covers three independent areas of theoretical quantum condensed matter physics. First, I intend to continue my research on the dynamical investigation of cold-atoms systems where I contributed over the years. Second, I propose to investigate the combined effect of disorder, interactions and geometric frustration where I expect novel quantum phases and transitions to appear. Last, I plan to further investigate the physics of topological transitions in the Hall conductivity for lattice bosons.
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