Dynamics in Correlated Quantum Matter

In our research we are interested in a variety of different quantum many-body problems at the interface between condensed matter theory, quantum simulation, and quantum information. 

This includes, in particular, the prospect for identifying emergent phenomena and universality in the dynamics of complex quantum systems with a strong focus onto current experiments in quantum simulators. 

In this context we work on a theory of dynamical quantum phase transitions which is an attempt to extend fundamental equilibrium concepts such as universality and scaling to the dynamical far-from equilibrium regime. Moreover, our research includes topics such as many-body localization in interacting strongly disordered systems, energy localization in periodically driven systems, as well as the quantification and experimental accessibility of multipartite entanglement.

Below you can find a selection of recent research conducted in this group.

Direct observation of dynamical quantum phase transitions in an interacting many-body system

Today, the equilibrium properties of quantum matter are theoretically described with remarkable success. Yet, in recentyears pioneering experiments have created novel quantum states beyond this equilibrium paradigm. Thanks to this progress, it is now possible to experimentally study exotic phenomena such as many-body localization, prethermalization, particle-antiparticle production in the lattice Schwinger model, and light-induced superconductivity. Understanding general properties of such nonequilibrium quantum states provides a significant challenge, calling for new concepts that extend important principles such as universality to the non-equilibrium realm. A general approach towards this major goal is the theory of dynamical quantum phase transitions (DQPTs), which extends the concept of phase transitions and thus universality to the nonequilibrium regime. In this letter, we directly observe the defining real-time non-analyticities at DQPTs in a trapped-ion quantum simulator for interacting transverse-field Ising models. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production. Our work advances towards experimentally characterizing nonequilibrium quantum states and their dynamics, by offering general experimental tools that can be applied also to other inherently dynamical phenomena

P. Jurcevic
H. Shen
P. Hauke
C. Maier
T. Brydges
C. Hempel
B. P. Lanyon
M. Heyl
R. Blatt
C. F. Roos

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

Physics World: one of the top-ten breakthroughs 2016

This experiment has been chosen by the magazine Physics World as one of the top ten breakthroughs in physics in the year 2016.

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories.

E. A. Martinez 
C. A. Muschik 
P. Schindler
D. Nigg
A. Erhard
M. Heyl
P. Hauke
M. Dalmonte
T. Monz
P. Zoller
R. Blatt

Observation of a dynamical topological phase transition

Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental concepts for systems far from equilibrium are just being explored, such as the recently introduced dynamical phase transition (DPT). Here we report on the first observation of a DPT in the dynamics of a fermionic many-body state after a quench between two lattice Hamiltonians. With time-resolved state tomography in a system of ultracold atoms in optical lattices, we obtain full access to the evolution of the wave function. We observe the appearance, movement, and annihilation of vortices in reciprocal space. We identify their number as a dynamical topological order parameter, which suddenly changes its value at the critical times of the DPT. Our observation of a DPT is an important step towards a more comprehensive understanding of non-equilibrium dynamics in general.

N. Fläschner 
D. Vogel 
M. Tarnowski 
B. S. Rem 
D.-S. Lühmann 
M. Heyl 
J. C. Budich 
L. Mathey 
K. Sengstock 
C. Weitenberg

Heating and many-body resonances in a periodically driven two-band system

We study the dynamics and stability in a strongly interacting resonantly driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the time evolution is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is relatively fast in these two regimes (but to different "temperatures"), in the crossover between them we find slow nonthermalizing time evolution: temporal fluctuations become strong and temporal correlations long lived. Microscopically, we trace back the origin of this nonthermalizing time evolution to the properties of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the approximate energy conservation, and thus produces thermalization to infinite temperature.

Marin Bukov 
Markus Heyl 
David A. Huse 
Anatoli Polkovnikov

Measuring multipartite entanglement through dynamic susceptibilities

Entanglement is considered an essential resource in quantum technologies, and central to the understanding of quantum many-body physics. Developing protocols to detect and quantify the entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles by means of the dynamic susceptibility—that is, with resources readily available in present cold atomic-gas and condensed-matter experiments. This establishes a connection between multipartite entanglement and many-body correlations contained in response functions, with immediate implications close to quantum phase transitions, where the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartite entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments and strongly correlated materials.

Philipp Hauke 
Markus Heyl 
Luca Tagliacozzo 
Peter Zoller

Scaling and Universality at Dynamical Quantum Phase Transitions

Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point’s universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.

Markus Heyl