Michael Knap

Collective Quantum Dynamics

Technical University Munich

Physics Department and Institute for Advanced Study

James-Franck-Str. 1

85748 Garching


Group webpage


Research focus: ultracold quantum gases, strongly correlated quantum matter, quantum dynamics, many-body localization

Collective Quantum Dynamics

The research in our group focuses on condensed matter theory and clusters around a variety of questions on non-equilibrium dynamics in ultracold quantum gases, trapped ions, superconducting qubits, and correlated quantum materials. Interactions and correlations in such systems often manifest in striking and novel properties, which emerge from the collective behavior of the quantum particles. Our group develops both analytical and numerical techniques to elucidate the effects of strong interactions. An important factor of our research is also its immediate relevance for experiments, which leads to a close collaboration with various experimental groups.

Correlated quantum systems out of equilibrium

Recent conceptional and technical progress makes it possible to prepare and explore strongly-correlated non-equilibrium quantum states of matter. The tremendous level of control and favorable time scales achieved in experiments with synthetic quantum matter, such as ultracold atoms, trapped ions, or superconducting qubits renders these systems as ideal candidates to explore non-equilibrium quantum dynamics. Furthermore, very powerful experimental techniques have been developed to study dynamic processes in condensed matter systems as well. These techniques are based on pump-probe spectroscopy on time scales reaching down to sub-femtoseconds. Such technology therefore makes it possible to manipulate and control material properties.

We develop both analytical and numerical techniques to explore the far-from-equilibrium quantum dynamics of these systems. The techniques range from non-equilibrium field theories to exact numerical calculations based on matrix product states. We study fundamental questions including thermalization in closed quantum systems, emergent phenomena in periodically driven Floquet systems, dynamic phase transitions, intertwined order far-from-equilibrium, and the competition between coherence and dissipation.

Selected Publications

  • Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system. Simon A. Weidinger, Michael Knap, Sci. Rep. 7, 45382 (2017). DOI: 10.1038/srep45382
  • Scrambling and thermalization in a diffusive quantum many-body system. A. Bohrdt, C. B. Mendl, M. Endres, M. Knap. [arXiv:1612.02434]
  • Ultrafast many-body interferometry of impurities coupled to a Fermi sea. M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Walraven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, E. Demler, Science 354, 96 (2016). DOI: 10.1126/science.aaf5134
  • Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions. Mehrtash Babadi, Eugene Demler, Michael Knap, Phys. Rev. X 5, 041005 (2015). DOI: https://doi.org/10.1103/PhysRevX.5.041005

Disordered many-body systems

Disorder has a drastic influence on transport properties. In the presence of a random potential a system of interacting electrons can become insulating; a phenomenon known as many-body localization. However, even beyond the vanishing transport such systems have very intriguing properties. For example, many-body localization describes an exotic phase of matter, which is robust to small changes in the microscopic Hamiltonian. Moreover, fundamental concepts of thermodynamics break down in the many-body localized phase. We study how these particular properties can be characterized by interferometric techniques, explore distinct experimental signatures of disordered systems, and analyze the transition from the localized to the delocalized phase.

Selected Publications

  • Periodically Driving a Many-Body Localized Quantum System. Pranjal Bordia, Henrik Lüschen, Ulrich Schneider, Michael Knap, Immanuel Bloch Nature Phys. AOP (2017). DOI: 10.1038/nphys4020
  • Noise-induced subdiffusion in strongly localized quantum systems. Sarang Gopalakrishnan, K. Ranjibul Islam, Michael Knap. [arXiv:1609.04818]
  • Anomalous diffusion and Griffiths effects near the many-body localization transition. Kartiek Agarwal, Sarang Gopalakrishnan, Michael Knap, Markus Mueller, Eugene Demler, Phys. Rev. Lett. 114, 160401 (2015). DOI: 10.1103/PhysRevLett.114.160401


Many-body chaos near a thermal phase transition

A. Schuckert, M. Knap.

SciPost Physics 7, 022 (2019).

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We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.

DOI: 10.21468/SciPostPhys.7.2.022

Emergent Glassy Dynamics in a Quantum Dimer Model

J. Feldmeier, F. Pollmann, and M. Knap.

Physical Review Letters 123, 040601 (2019).

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We consider the quench dynamics of a two-dimensional quantum dimer model and determine the role of its kinematic constraints. We interpret the nonequilibrium dynamics in terms of the underlying equilibrium phase transitions consisting of a Berezinskii-Kosterlitz-Thouless (BKT) transition between a columnar ordered valence bond solid (VBS) and a valence bond liquid (VBL), as well as a first-order transition between a staggered VBS and the VBL. We find that quenches from a columnar VBS are ergodic and both order parameters and spatial correlations quickly relax to their thermal equilibrium. By contrast, the staggered side of the first-order transition does not display thermalization on numerically accessible timescales. Based on the model’s kinematic constraints, we uncover a mechanism of relaxation that rests on emergent, highly detuned multidefect processes in a staggered background, which gives rise to slow, glassy dynamics at low temperatures even in the thermodynamic limit.

DOI: 10.1103/PhysRevLett.123.040601

String patterns in the doped Hubbard model

C. S. Chiu, G. Ji, A. Bohrdt, M. Xu, M. Knap, E. Demler, F. Grusdt, M. Greiner, D. Greif.

Science 365, 251-256 (2019).

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Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.

DOI: 10.1126/science.aav3587

Classifying snapshots of the doped Hubbard model with machine learning

A. Bohrdt, C. S. Chiu, G. Ji, M. Xu, D. Greif, M. Greiner, E. Demler, F. Grusdt und M. Knap.

Nature Physics (2019).

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Quantum gas microscopes for ultracold atoms can provide high-resolution real-space snapshots of complex many-body systems. We implement machine learning to analyse and classify such snapshots of ultracold atoms. Specifically, we compare the data from an experimental realization of the two-dimensional Fermi–Hubbard model to two theoretical approaches: a doped quantum spin liquid state of resonating valence bond type (1,2), and the geometric string theory (3,4), describing a state with hidden spin order. This technique considers all available information without a potential bias towards one particular theory by the choice of an observable and can therefore select the theory that is more predictive in general. Up to intermediate doping values, our algorithm tends to classify experimental snapshots as geometric-string-like, as compared to the doped spin liquid. Our results demonstrate the potential for machine learning in processing the wealth of data obtained through quantum gas microscopy for new physical insights.

DOI: 10.1038/s41567-019-0565-x

Site-selectively generated photon emitters in monolayer MoS2 via local helium ion irradiation

J. Klein, M. Lorke, M. Florian, F. Sigger, J. Wierzbowski, J. Cerne, K. Müller, T. Taniguchi, K. Watanabe, U. Wurstbauer, M. Kaniber, M. Knap, R. Schmidt, J. Finley, A. Holleitner.

Nature Communications 10, Article number: 2755 (2019).

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Quantum light sources in solid-state systems are of major interest as a basic ingredient for integrated quantum photonic technologies. The ability to tailor quantum emitters via site-selective defect engineering is essential for realizing scalable architectures. However, a major difficulty is that defects need to be controllably positioned within the material. Here, we overcome this challenge by controllably irradiating monolayer MoS2 using a sub-nm focused helium ion beam to deterministically create defects. Subsequent encapsulation of the ion exposed MoS2 flake with high-quality hBN reveals spectrally narrow emission lines that produce photons in the visible spectral range. Based on ab-initio calculations we interpret these emission lines as stemming from the recombination of highly localized electron–hole complexes at defect states generated by the local helium ion exposure. Our approach to deterministically write optically active defect states in a single transition metal dichalcogenide layer provides a platform for realizing exotic many-body systems, including coupled single-photon sources and interacting exciton lattices that may allow the exploration of Hubbard physics.

DOI: 0.1038/s41467-019-10632-z

Atomtronics with a spin: Statistics of spin transport and nonequilibrium orthogonality catastrophe in cold quantum gases

J. S. You, R. Schmidt, D. A. Ivanov, M. Knap, and E. Demler.

Physical Review B 99, 214505 (2019).

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We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin population remains constant. Thus one can directly count the number of spins in each reservoir to investigate the full counting statistics of spin flips, which is notoriously challenging in solid-state devices. Moreover, using Ramsey interferometry, the dynamical impurity response can be measured. Since the impurity interacts with a many-body environment that is out of equilibrium, our setup provides a way to realize the nonequilibrium orthogonality catastrophe. Here, even for spin reservoirs initially prepared in a zero-temperature state, the Ramsey response exhibits an exponential decay, which is in contrast to the conventional power-law decay of Anderson's orthogonality catastrophe. By mapping our system to a multistep Fermi sea, we are able to derive analytical expressions for the impurity response at late times. This allows us to reveal an intimate connection of the decay rate of the Ramsey contrast and the full counting statistics of spin flips.

DOI: 10.1103/PhysRevB.99.214505

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