Topological Phases in Cold Atom Systems

122:026 (Nordita, Stockholm)


Nordita, Stockholm

Eddy Ardonne (Stockholm University), Jonas Larson (Stockholm University), Markus Hennrich (Stockholm University), Susanne Viefers (University of Oslo)


Nordita, Stockholm, Sweden


Topological phases play an important role in condensed matter physics for understanding quantum effects like topological insulators and the quantum Hall effect. At the same time, cold atoms and ions have developed as testbeds to study complex quantum systems and are now used to generate, visualize and understand topological quantum states and phases. This program will bring together researchers from condensed matter and atomic physics, to share their knowledge how to describe and investigate topological quantum systems and to inspire collaborations between researchers of the two fields.

To facilitate the discussion between the cold atom and condensed matter communities, we plan to discuss different topics during the workshop. The timing will depend on the mix of participants, but the preliminary schedule of topics is

  • Artificial gauge fields
  • Driven and open quantum systems
  • Topological phases and their applications


If you want to apply for participation in the program, please fill in the application form. You will be informed by the organizers shortly after the application deadline whether your application has been approved. Due to space restrictions, the total number of participants is strictly limited. (Invited participants are of course automatically approved, but need to register anyway.)

Application deadline: 31 March 2017


Nordita provides a limited number of rooms in the Stockholm apartment hotel <href="">BizApartments free of charge for accepted participants.

Invited Participants

  • M. Aidelsburger
  • J. Budich
  • N. Cooper
  • N. Gemelke
  • A. Hemmerich
  • C. Monroe
  • M. Müller
  • C. de Morais Smith
  • K. Sengstock
  • I. Spielman
    • Coffee
    • M. Burrello, One dimensional ladder limits of the quantum Hall states: the fermionic case at filling 1/2

      Helical liquids have been experimentally detected in both
      nanowires with strong spin-orbit coupling and
      multi-component ultracold atomic chains with a
      position-dependent coupling between the spin species. In
      both cases the inner degree of freedom can be considered as
      an additional space dimension, providing an interpretation
      of these systems as synthetic ladders with artificial
      magnetic fluxes determined by the spin-orbit terms.
      In the presence of interactions, non-trivial helical states
      appear for special ratios of the particle density and the
      synthetic magnetic flux, like in the two-dimensional
      fractional quantum Hall regime.
      In this talk, I characterize the helical state which appears
      in a ladder model of repulsive ultracold fermions at filling
      ν = 1/2: this state cannot be explained in terms of a simple
      fermionic Laughlin-like analog; it is generated by a gap
      arising in the spin sector of the corresponding Luttinger
      liquid and it corresponds to a Laughlin state at filling 1/8
      of bosonic pairs. I will discuss the techniques required for
      its analytical description as well as its main features,
      derived from a DMRG study.

    • K. Schoutens, Many-body strategies for multi-qubit gates

      The standard method for implementing algorithms for quantum
      computation is
      through quantum circuits. Such circuits typically contain
      quantum gates
      involving more than a
      single or two qubits. Multi-qubit gates can be decomposed
      into 1- and
      2-qubit gates, but this is not necessarily the most
      efficient strategy. We
      present a framework for quantum control directly at the
      level of multiple
      qubits. A concrete proposal employs a so-called Krawtchouk
      qubit chain,
      which has previously been studied and experimentally
      realised in the
      context of perfect state transfer.

      Based on arXiv:1707.05144 with Koen Greenland

    • Coffee
    • G. Ortiz, Topological superfluidity with repulsive fermionic atoms

      I will discuss a novel route to topological superfluidity in
      repulsive fermionic systems.
      The physical mechanism leading to pairing, and thus
      superfluid behavior, is driven by
      local kinetic-energy fluctuations and can be realized, for
      instance, in multiband
      systems with dissimilar localization properties.
      Specifically, we propose to observe
      this phenomenon in an optical superlattice with
      alkaline-earth fermionic atoms, e.g.
      Yb or Sr, carefully engineered to host itinerant and
      spatially localized atoms whose
      quantum fluctuations mediate an attractive interaction
      between itinerant ones. This
      mechanism gives rise to a topological $p$-wave superfluid
      state in quasi-one-dimensional
      wires, and a chiral p_x+ip_y superfluid in two dimensions.
      Most importantly, we have
      developed several experimental probes to characterize the
      superfluid state, including
      momentum-resolved RF spectroscopy and an analog of the
      Edelstein magneto-electric

    • A. Trombettoni, Junctions of weakly-coupled strongly-interacting ultracold systems

      After briefly reviewing the use of ultracold atoms for the
      implementation of quantum devices, I discuss two examples of
      junctions made by strongly interacting systems weakly
      coupled between them. I present in the first part of the
      talk recent results on the Josephson dynamics of two
      ultracold fermionic gases at the unitary limit weakly linked
      by a controllable barrier [1]. In the second part I discuss
      properties of 1D Bose gases and then of junctions of
      Tonks-Girardeau gases. When three Tonks-Girardeau gases are
      coupled, one can exactly map their Hamiltonian by means of a
      suitable Jordan-Wigner transformation into the Hamiltonian
      of the multichannel Kondo model. I will also show recent
      results on the experimental realization of Y-geometries with
      holographic traps [2].

      [1] G. Valtolina, A. Burchianti, A. Amico, E. Neri, K.
      Xhani, J. A. Seman, A. Trombettoni, A. Smerzi, M. Zaccanti,
      M. Inguscio, and G. Roati, "Josephson effect in fermionic
      superfluids across the BEC-BCS crossover", Science 350, 1505
      [2] F. Buccheri, G. Bruce, A. Trombettoni, D. Cassettari, H.
      Babujian, V. Korepin, and P. Sodano, "Holographic optical
      traps for atom-based topological Kondo devices", New J.
      Phys. 18, 075012 (2016).

    • Coffee
    • J. Budich, Topological Insulators far from Equilibrium


    • G. Martone, Quantum phases and excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate in a one-dimensional optical lattice

      Spin-orbit-coupled quantum gases are characterized by a rich
      phase diagram, with the appearance of novel quantum phases
      having intriguing static and dynamic features.
      In this talk I shall discuss the effect of a periodic
      potential generated by a one-dimensional optical lattice on
      the properties of a S=1/2 spin-orbit-coupled Bose gas.
      Because of the interplay between the modified band structure
      and the two-body interaction the ground state exhibits a
      mixed regime, where the condensate wave function
      is given by a superposition of multiple Bloch-wave
      components, and an unmixed one, in which the atoms occupy a
      single Bloch state. Magnetic phase transitions between
      polarized and unpolarized states can be induced by tuning
      the Raman coupling and the lattice strength, with the
      emergence of a quantum tricritical point whose existence
      is a consequence of the spin-dependent interaction. At the
      dynamic level, I shall illustrate the behavior of the phonon
      and roton modes of the excitation spectrum,
      pointing out the instabilities occurring when a phase
      transition is approached.

    • Reception outside NORDITA building
    • Coffee
    • N. Cooper, Superradiance-induced particle flow via dynamical gauge coupling

      Superradiance-induced particle flow via dynamical gauge coupling

    • Coffee
    • R. Kraus, Localization transition in presence of cavity backaction

      We study the localization transition of an atom confined by
      an external optical lattice in a high-finesse cavity. The
      atom-cavity coupling yields an effective secondary lattice
      potential, whose wavelength is incommensurate with the
      periodicity of the optical lattice. The cavity lattice can
      induce localization of the atomic wave function analogously
      to the Aubry-André localization transition. Starting from
      the master equation for the cavity and the atom we perform a
      mapping of the system dynamics to a Hubbard Hamiltonian,
      which can be reduced to the Harper's Hamiltonian in
      appropriate limits. We evaluate the phase diagram for the
      atom ground state and show that the transition between
      extended and localized wavefunction is controlled by the
      strength of the cavity nonlinearity, which determines the
      size of the localized region and the behaviour of the
      Lyapunov exponent. The Lyapunov exponent, in particular,
      exhibits resonance-like behaviour in correspondence with the
      optomechanical resonances. Finally we discuss the
      experimental feasibility of these predictions.

    • L. Mazza, Majorana zero modes in earth-alkaline(-like) one-dimensional quantum gases

      In this seminar, I discuss the problem of creating Majorana
      zero modes in a cold-atom system, which is naturally
      number-conserving, and without assuming the presence of a
      I begin by presenting a model of interacting fermions in a
      two-leg ladder supporting zero-energy Majorana edge modes.
      The model has a quasi-exactly solvable line for all possible
      densities of fermions described by a topologically
      non-trivial ground state wave-function which can be fully
      In the second part of the seminar, I argue that all the
      necessary ingredients for the appearance of Majorana zero
      modes in number-conserving ladders are naturally present in
      one-dimensional Ytterbium gases (and more generally in
      earth-alkaline(-like) atomic gases), which are currently
      studied in several state-of-the-art experiments. I support
      the claim with extensive numerical simulations.

      [1] Iemini, Mazza, Rossini, Fazio, and Diehl, Phys. Rev.
      Lett. 115, 156402 (2015).
      [2] Iemini, Mazza, Fallani, Zoller, Fazio, and Dalmonte,
      Phys. Rev. Lett. 118, 200404 (2017).

    • Coffee
    • N. Gemelke, TBA


    • Coffee
    • F. Kunst, Anatomy of Topological Flat and Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices

      The main feature of topological phases is the presence of
      robust boundary states, which appear
      for example in the form of chiral edge states in Chern
      insulators and open Fermi arcs on the
      surfaces of Weyl semimetals. Even though, non-interacting,
      topological systems can be
      straightforwardly described in fully periodic systems, the
      understanding of the corresponding
      boundary states has almost exclusively relied on numerical
      studies. In our work, we present a
      general method on how to find exact, analytical solutions
      for topological as well as trivial
      boundary states using a generic tight-binding model on a
      large class of geometrically frustrated
      lattices without the necessity of having to fine-tune
      hopping amplitudes. Our method is inspired
      by a similar approach that has been used in the past to
      construct, topologically-trivial, flat band
      models from local constraints on ‘line graphs’, in which
      case fine-tuning is required in the sense
      that hopping is strictly local. We expand on this work by
      considering a larger class of lattices,
      finding solutions for both topologically trivial and
      non-trivial bands, and going beyond the need
      for fine-tuning. This class of lattices are highly suited to
      be realized in cold atom systems. In this
      sense, it is likely that our work will contribute to both
      the research fields of flat-band physics and
      that of topological matter, as well as advance the
      cross-fertilization between them. In this talk, I
      will present a number of examples to illustrate our
      discoveries, some of which are
      experimentally relevant such as the derivation of exact
      solutions for Fermi arcs in the recently
      synthesized slabs of pyrochlore iridates.

    • Coffee
    • C. Repellin, Creating a bosonic fractional quantum Hall state by pairing fermions

      We numerically study the behavior of spin-1/2 fermions on a
      two-dimensional square lattice subject to a uniform magnetic
      field, where opposite spins interact via an on-site
      attractive interaction. The single-particle Hamiltonian is
      the Harper-Hofstadter model which was recently realized in
      several cold atomic gas experiments using artificial gauge
      fields. In this context, a Feschbach resonance can be used
      to implement a highly tunable on-site interaction. Starting
      from the non-interacting case where each spin population is
      prepared in a quantum Hall state with unity filling, we
      follow the evolution of the system as the interaction
      strength is increased. Above a critical value and for
      sufficiently low flux density, we observe the emergence of a
      twofold quasidegeneracy accompanied by the opening of an
      energy gap to the third level. Analysis of the entanglement
      spectra shows that the gapped ground state is the bosonic
      1/2 Laughlin state. Our work therefore provides compelling
      evidence of a topological phase transition from the
      fermionic integer quantum Hall state to the bosonic Laughlin
      state at a critical attraction strength. I will present the
      numerical signatures of these two phases, and analyze the
      equilibrium properties of the phase transition. Finally, I
      will discuss some preliminary results concerning the
      dynamics of the phase transition.

      Ref: Creating a bosonic fractional quantum Hall state by
      pairing fermions, C. Repellin, T. Yefsah, A. Sterdyniak,

    • G. Brunn, Topological superfluid in a Fermi-Bose mixture with a high critical temperature

      We show that a two-dimensional (2D) spin-polarised Fermi gas
      immersed in a 3D Bose-Einstein condensate (BEC) constitutes
      a very promising system to realise a topological superfluid.
      The fermions attract each other via an induced interaction
      mediated by the bosons, and the resulting pairing is
      analysed with retardation effects fully taken into account.
      This is further combined with
      Berezinskii-Kosterlitz-Thouless (BKT) theory to obtain
      reliable results for the superfluid critical temperature. We
      show that both the strength and the range of the induced
      interaction can be tuned experimentally, which can be used
      to make the critical temperature approach the maximum value
      allowed by general BKT theory. Moreover, this is achieved
      while keeping the Fermi-Bose interaction weak so that
      three-body losses are small. We furthermore show that if the
      fermions are confined in two layers, they can realise a
      so-called Z_2 topological superfluid with time-reversal
      symmetry and chiral edge states in analogy with the quantum
      spin Hall state.

    • Coffee
    • K. Sengstock, Topology and dynamics in Floquet engineered optical lattices


    • Reception outside (when weather permits) the Nordita building

      Eating, drinking, enjoying the sun,...

    • Coffee
    • M. Müller, Topological Quantum Computation: From Concepts to Experiments

      Quantum computers hold the promise to allow one to solve
      problems that cannot be efficiently treated on classical
      computers. To date, the construction of a fault-tolerant
      quantum computer remains a fundamental scientific and
      technological challenge, due the influence of unavoidable
      noise which affects the fragile quantum states. In our talk,
      we will first introduce basic concepts of quantum error
      correction based on topological quantum error-correcting
      codes, which allow one to protect quantum information during
      storage and processing by distributing logical quantum
      information over quantum many-body spin systems. We
      then discuss progress on experimental quantum error
      correction, in particular the realisation of a minimal
      topological color code with trapped ions, which for the
      first time demonstrated basic quantum computations on an
      encoded qubit. In the second part, I will present recent
      theory work of our group and experimental progress towards
      fault-tolerant quantum error correction and control of
      coupled logical qubits of increasing size and robustness in
      scalable trapped-ion architectures.

    • J. Slingerland, Spin chains with stable topological zero modes.

      Ground state degeneracy is an important characteristic of
      order. It is a natural question under what conditions such
      degeneracy extends to higher energy states or even to the
      full energy
      spectrum of a model, in such a way that the degeneracy is
      when the Hamiltonian of the system is perturbed. It appears that
      Ising/Majorana wires have this property due to the presence
      of robust
      edge zero modes. Generalized wire models based on
      parafermions also
      have edge zero modes and topological degeneracy at special
      points in
      parameter space, but the stability of these modes is a much
      intricate question, and generically the zero modes are
      spoilt by the
      presence of resonances between bands in the unpertrbed
      model. Both the
      Majorana and parafermionic models are part of a large class
      of chain
      models with edge modes, based on tensor categories. It is
      natural to
      ask which of these have stable edge zero modes and/or full

    • Coffee
    • P. Laurell, Prethermal states of matter in interacting Floquet systems

      Periodically driven quantum systems are able to host novel
      phases not
      found in equilibrium, such as topological Floquet states or time
      crystals. Alternatively, one can use the periodic drive to
      new band structures or interactions. In both cases integrability
      breaking terms are generally present, and the absence of
      quantities tend to cause the system to heat up to an effectively
      infinite temperature. Thus, at first sight, it appears as if
      interacting Floquet systems have a rather limited phase
      However, it is possible to use time-dependent transformations to
      remove almost all time-dependence from the Hamiltonian,
      mapping it onto a system in thermal equilibrium. This
      approach can be
      valid up to exponentially long times, after which thermalization
      occurs. I will discuss our recent numerical results on symmetry
      breaking prethermal states in spin systems, and the
      connections to
      experimental realizations in cold atoms or solid state systems.

    • M. Aidelsburger Floquet engineering with interacting ultracold atoms: Floquet engineering with interacting ultracold atoms

      Floquet engineering is an important tool for the engineering
      of novel band structures with interesting properties that go
      beyond those offered by static systems. Recently, Floquet
      systems have enabled the generation of Bloch bands with
      non-trivial topological properties, such as the Hofstadter
      and Haldane model. This led to the observation of chiral
      Meissner currents and the first Chern-number measurements
      with charge-neutral atoms.
      Besides this success studies of many-body phases in driven
      systems remains experimentally challenging in particular due
      to the interplay between periodic driving an interactions.
      In a driven system energy is not conserved which can lead to
      severe heating. In order to find stable parameter regimes
      for the generation of driven many-body phases it is
      essential to develop a deeper understanding of the
      underlying processes.
      Here, I briefly review recent experimental advances in the
      generation of topological band structures in the
      non-interacting regime using Floquet engineering and present
      first studies of interacting atoms in driven 1D lattices.

    • Coffee
    • M. Tylutki, Coherent Oscillations of a Small Fermi Polaron

      We study a trapped polarized Fermi gas interacting with a single
      impurity. First, we investigate the tunnelling dynamics of the
      impurity through a potential barrier, such as one created by a
      double-well trap. We perform an exact diagonalization of the
      many-body Hamiltonian and analyze the results in a Local Density
      Approximation. Second, we consider a radio-frequency
      spectroscopy of
      our system and the resulting spectral function. These
      calculations can
      motivate future experiments, which can provide us with a further
      insight into the physics of a Fermi polaron.

    • Coffee
    • A. Quelle, TBA


    • A. Hemmerich, Topological bosons in optical lattices

      I will discuss possible schemes to implement topological
      matter with bosons condensed in metastable higher bands of
      an optical lattice.

    • Coffee
    • M. Hasan, Pushing Topologicity with Light: A Route towards Topotronics

      I will outline how strong light-matter interaction can be
      used to induce quantum phase transition between normal and
      topological phases in two-dimensional topological
      insulators. The example case is a HgTe quantum well, in
      which band inversion occurs above a critical value of the
      well-thickness, and it will be delineated that coupling
      between electron states and the E-field from an off-resonant
      laser provides a powerful tool to control topological
      transitions, even for a thickness of the quantum well that
      is below the critical value where normally topological edge
      states occur. The dependence of topological phase properties
      of the edge states, including their group velocity, will be
      discussed from an analytic perspective. I will then hint
      towards possible new experimental means with which to
      investigate topological insulators, that are discussed in
      the talk. Importantly, all the topological effects that will
      be discussed here could be realized in a controllable and
      reversible manner, simply by changing the intensity of the
      electromagnetic radiation. Technology that relies on these
      topological states will be extrapolated, hinting towards a
      possible new field of topotronics.

      I believe this will be interesting for a broad audience. For
      a detail of the talk please have a look at the arXiv version
      ( The paper is now
      being reviewed in Physical Review Letters.

    • E. Bergholtz, Fractional Chern insulators and non-Abelian twist defects

      In this talk I will discuss fractional Chern insulators with
      emphasis on the analogy with more conventional continuum
      Landau level physics — and on aspects that are qualitatively
      new in the lattice setting such as Berry curvature
      fluctuations, competing instabilities and novel collective
      states of matter emerging in bands with higher Chern number.
      I will also explain how the lattice setting naturally allows
      for exotic extrinsic wormhole-like twist defects (aka
      “genons”) that effectively increase the genus of space.

    • Reception ourside Nordita building

      Sun, snacks, socializing, ...

    • Coffee
    • J. Zheng, Effective field theory for a strong magnetic scatterer near the edge of a quantum spin Hall insulator

      We derive the effective field theory describing a classical
      impurity located near the edge of a two-dimensional quantum
      spin Hall
      insulator focusing on the regime where the impurity
      potential is larger
      than the band gap. We show that, due to the new features
      brought about by
      dimensionality, the low energy physics is universally
      described by a
      resonant level model coupled to the one-dimensional (1D)
      channel of
      interacting edge electrons. Away from resonance, the
      effective 1D model
      reduces to stuctureless impurity in a Tomonaga-Luttinger
      liquid. On the
      other hand, in the resonant regime, the transmission is
      suppressed both
      for weak to moderately attractive and repulsive interactions.

      Ref: arXiv:1609.06227