The groups participating in the ExQM School focus on seven primary research areas between the broader field of quantum optics, numerical tensor networks methods and theoretical quantum information. The individual focus areas are:
Another major advantage of cold atoms for elucidating many-body phenomena is the possibility to change parameters characterising the relative strength of kinetic and interaction energy dynamically. It paves the way to study real-time dynamics of strongly correlated systems in a controlled way, a simple example being the quantum quench of the system from the superfluid to the Mott-insulator regime. One of the future challenges amounts to cool strongly interacting bosonic and fermionic spin mixtures below the super-exchange energy scale for observing magnetically ordered quantum phases, for which new cooling schemes have been proposed.
Primary Working Groups and PhD Students: Research Group Bloch: Michael Lohse
Networks of these entities would be particularly well suited for accessing the strongly correlated regime and for investigating quantum many-body dynamics of interacting particles under the influence of driving and dissipation. Solid state quantum circuits with multiple drives are another attracting system. E.g., superconducting quantum bits strongly coupled to a resonator field mode and subjected to multiple classical drives can be used for quantum simulations of relativistic quantum physics (e.g. dynamics of the Dirac equations, Klein paradox). The key advantage is the controllability of the relevant physical parameters via the strength of the longitudinal and two transverse drives. Moreover, quantum bits with two-tone multiple drives can be used for quantum simulation of strong and ultra-strong coupling dynamics.
Primary Working Groups and PhD Students: Research Group Gross: Michael Fischer
The extension to 2D quantum systems is more difficult and a key challenge of current computational physics in spite of the impressive results already obtained. DMRG methods have been applied to spin systems, bosonic and fermionic systems with equal success. This has become particularly obvious in the simulation of non-equilibrium properties of 1D quantum systems in scenarios with both pure and mixed states as well as in the presence or absence of dissipation.
The Cirac group devised a new variational algorithm to find a matrix product operator (MPO) description for the steady states of dissipative one dimensional systems described by a master equation [PRL 114, 220601 (2015)], which allows immediate application to explore dissipative phase transitions. – Moreover, numerical applications of matrix product states to lattice gauge theories have produced results of unprecedented numerical accuracy, which the Cirac group extended to the real time evolution of a non-Abelian theory. This allows to include the study of the string breaking phenomenon in the presence of fully dynamical fermions, beyond the reach of the most traditional lattice methods.
Primary Working Groups and PhD Students: Research Group Cirac; Research Group Schollwöck: Claudius Hubig
Furthermore, it is feasible to study both one- and two-dimensional finite systems, the latter with near-linear scaling of computational cost in the larger of the two dimensions. By numerically including more symmetries of the system in question, that cost can additionally be reduced further and with new parallelisation techniques, large-scale calculations become more and more viable. Lastly, as a generalisation of the MPS structure to two or more dimensions, Projected Entangled Pair States (PEPS) are a straightforward generalisation of MPS with great potential for improvements in the future.
The three approaches — embedding techniques, large-scale MPS-DMRG calculations and improvements for PEPS-based methods — each offer the possibility to study quantum states at high numerical accuracy and sufficiently-large system sizes to allow for scaling to the thermodynamic limit. Together, they combine into an arsenal of numerical methods with the potential to unravel many standing problems in condensed-matter physics like the nature of high temperature superconductivity or solving the doped Fermi-Hubbard model.
The Schollwöck group has developed very powerful impurity solvers based on matrix product states for simulations of correlated materials both in and out of equilibrium in combination with the dynamical mean-field theory (DMFT). By a complete revision of its MPS codes (large scale parallelization and asynchronous memory management, improved convergence schemes and quantum-information driven rephrasing of the Hamiltonians) it is now also able to access very large 2D cylinders of Hubbard or frustrated Heisenberg models.
Primary Working Groups and PhD Students: Research Group König
The field has developed very dynamically now providing links to important areas including high-dimensional big data, (quantum) machine learning, and neural networks. ExQM will extend its research activities to encompass functions with matrix and tensor arguments for numerical applications in quantum dynamics and quantum simulation. Recent developments provided new insight to study the interrelation of tensor networks and neural networks in view of possible applications in machine learning and quantum simulation.
Primary Working Groups and PhD Students: Research Group Huckle: Moritz August
Primary Working Groups and PhD Students: Research Group Schuch
We plan to generate a single photon from a quantum dot and subsequently store it in an atomic system. The development of such technologies is highly demanding since the spectral properties must be tailored to match each other. Connecting several such systems leads to a few-body system. As another example of a few-body system, schemes for the generation of entangled states of three or more photons will be conceived and implemented. Furthermore, the interaction between Rydberg atoms in a BEC, a genuine form of many-body quantum matter, can be exploited for processing quantum information. Combination of this interaction with an atom-light interface offers a way to process photonic quantum information.
Primary Working Groups and PhD Students:Research Group Rempe: Stephan Welte
These technologically relevant systems rely on quantum operations such as controlling electronic charge or spin degrees of freedom in coupled quantum dots, manipulating the dynamics of Josephson junctions, and using spin chains as quantum communication channels. Laser-written waveguides offer— for the first time—the potential to design 3D photonic structures, which in turn enable an entire new regime in all-optical quantum simulation.
Primary Working Groups and PhD Students: Research Group Weinfurter: Lukas Knips
Primary Working Groups and PhD Students: Research Group Finley: Jakob Wierzbowski