About us

Quantum thermalization, localization, and constrained dynamics with interacting ultracold atoms

FOR 5522 investigates the out-of-equilibrium physics of closed quantum many-body systems and their thermalization properties. We use a combined effort of experiments with ultracold atoms in optical lattices and theoretical approaches. Our team involves researchers from the Universities of Augsburg, Göttingen, München, and Tübingen, Technical University of Munich, the Max-Planck Institute for Quantum Optics, Garching, and the Max-Planck Institute for the Physics of Complex Systems, Dresden, as well as two Mercator fellows from the University of Ljubljana, Slovenia, and Stanford University, U.S.A.

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Ergodic systems

Eigenstate Thermalization Hypothesis
Transport
Anomalous Diffusion

Figure taken from: Phys. Rev. A 90, 033606 (2014)

Ergodic closed systems are those that thermalize under their own dynamics, i.e., independent of initial conditions, the time-dependent expectation values of local observables are equal to the thermal expectation values at practically all times. The best-accepted criterion to decide whether a given system is ergodic is the eigenstate thermalization hypothesis (ETH, see Deutsch Phys. Rev. A 43, 2046 (1991) and Srednicki, Phys. Rev. E 50, 888 (1994)) which implies that expectation values computed in eigenstates of generic systems are thermal. Therefore, we define ergodicity of a quantum system as the validity of ETH. The second important notion is quantum chaos: in essentially all generic basis sets, the eigenstates of Hamiltonians have the properties of those of random matrices.

Our research in the context of ergodic systems focuses on the relevant time scales, commonly referred to as Thouless times, the calculation of transport properties, the comparison of notions of many-body baths, and minimal models for ergodicity and quantum chaos based on quantum circuits.

Constrained Dynamics

Hilbert Space Fragmentation
Kinetically Constrained Models
Lattice Gauge Theories

Picture from F. Pollmann

Quantum systems with constrained dynamics summarily describe systems where typically transitions between states are not simply single-particle processes but depend on the many-body sector. Physical systems that cause such constraints are dipole conservation and the gauge constraints in lattice gauge theories, yet a large class of models called kinetically constrained models is inherited from classical models (e.g., from spin glasses). Systems with constraints can cause the emergence of quantum scars, tower of eigenstates with sub-volume law scaling and typically a constant energy difference. Alternatively, Hilbert-space fragmentation can occur where in certain basis sets, exponentially many disconnected sub-blocks emerge. These systems can be either realizations of weak or strong nonergodic behavior. Our research on systems with constrained dynamics aims at developing setups with experimental realizations, understanding the crossover between weak ergodicity and ETH on the one hand and with MBL on the other hand, and finally, elucidating their unusual transport properties.

Quantum thermalization in closed systems: From theory to experiments

Many-Body Localization

Uncorrelated Disorder
Stark-MBL
New Forms of MBL

Figure taken from: Science 352, 1547 (2016)

The best-studied candidate system for nonergodic dynamics is many-body localization (MBL). In this putative state of matter, all eigenstates violate ETH and memory of initial conditions would never be lost, even in local measurements. In its standard incarnation, this interacting state of matter is stabilized by disorder and MBL emerges as adiabatically out of an Anderson insulator and is characterized by particle-like conserved quantities (often called l-bits). While quantum gas experiments demonstrated metastable dynamics of interacting atoms in the presence of disorder consistent with MBL, the stability of MBL is still under debate. Our research aims at exploring the boundaries of the stability of MBL and more importantly, we are investigating novel forms of localization that can arise due to linear potentials (Stark-MBL) and in fractonic systems.

Quantum Gas Experiments

Rb Quantum Gas Microscope
Cs Quantum Gas Microscope
Yb LGT experiment
Er-Li mixture

Picture from C. Groß

Closed quantum systems are best realized in quantum simulators. Our platform of choice are ultra-cold atoms in optical lattices. The basic interactions are short-range and therefore, the relevant models are Hubbard models and derivatives. We extensively use the technology of quantum gas microscopy with three different atomic species. Rubidium is the best studied system while Cesium and Ytterbium offer additional tunability via additional internal states and Feshbach resonances. These systems are well suited to study relaxation dynamics, transport, disorder physics and constrained dynamics by utilizing superlattice techniques, additional potentials and local addressing and readout. In parallel, we work with mixtures of two species with an extreme mass imbalance, specifically Erbium and Lithium, which we plan to utilize to study slow dynamics due to this mass-imbalance.

Steering Committee

Picture from S. Hardt

Name	Institution	Function
Daniel Adler	MPQ Garching	Student Representative
Monika Aidelsburger	LMU Munich	Equal Opportunities, Diversity, Gender Equality
Christian Groß	Universität Tübingen	-
Fabian Heidrich-Meisner	Universität Göttingen	Spokesperson
Markus Heyl	Universität Augsburg	RDM Representative
Frank Pollmann	TU Munich	-