From Institute for Theoretical Physics II / University of Erlangen-Nuremberg

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Research topics Marquardt group: Theoretical quantum dynamics at the interface of nanophysics and quantum optics

In our research, we apply tools from condensed matter theory and from quantum optics to a range of questions involving quantum dynamics out of equilibrium. In our approach, we often try to identify the salient features of experimentally relevant situations and condense them into minimalist models which can then be attacked with all the state-of-the-art theoretical tools.


The wave-particle duality is at the heart of quantum physics. Matter waves show interference patterns. However, local interactions destroy interference effects, giving rise to classical-like particle dynamics. This is known as decoherence and it has important implications both for the foundations of quantum mechanics and for possible applications. We have studied decoherence especially in settings relevant to the quantum transport of electrons, where many-body effects and the Pauli principle change the usual story of a single particle coupled to some bath. To this end, we exploit techniques from many-body theory like path-integrals, diagrammatic perturbation theory and exactly solvable models such as Luttinger liquids. In addition, decoherence is of crucial importance for current challenges in quantum optics and optomechanics (see below).

Quantum electrodynamics in superconducting circuits

Systems of superconducting qubits coupling to on-chip microwave resonators have seen enormous progress in the past 10 years, with coherence times increasing by at least four orders of magnitude. They are now seen as one of the main candidates for quantum computers and simulators. In the past years, we have e.g. proposed an on-chip detector of single microwave photons or the measurement-based generation of entanglement. At present, multi-qubit circuits are becoming possible. Here we have been the first to propose a design for a two-dimensional “cavity grid”, coupling many qubits and resonators. Recently, we started exploring how multi-qubit systems could be exploited for quantum simulations of interesting many-body models, e.g. with regard to possible phase transitions of matter-radiation systems, or for implementing interacting quantum field theories.

Many-body dynamics in non-equilibrium

Systems of ultracold atoms have become a unique tool to study many-body physics, since they are well isolated and parameters can be tuned quickly on the time-scales of motion. Recently, we have started studying the possibilities afforded by the novel site-resolved detection of individual atoms. In this context, we have predicted a many-body Zeno effect occuring for interacting atoms in an optical lattice being observed repeatedly and a protocol for measuring spatial current patterns and correlations. In another development, we have proposed how to use tunnel-coupled clouds of cold atoms to generate a quantum simulator for testing structure formation in interacting quantum field theories, including the effects of cosmological expansion, which is relevant for the early universe.

Cavity optomechanics: Interaction between nanomechanics and light

In recent years, this topic directly at the interface of light and matter has become our main focus. The following text provides a bird's eye view of our research in this area. For more in-depth information, you could go to the following review-style publications (or the Springer book published in 2014, see the publications page):

  • A simple, brief overview: F. Marquardt and S. M. Girvin, Physics 2, 40 (2009) Journal PDF
  • An extended, fairly complete and up-to-date review: Cavity Optomechanics (to be published in Reviews of Modern Physics 2014); Markus Aspelmeyer, Tobias J. Kippenberg, and Florian Marquardt, arxiv:1303.0733 Journal PDF

The past years have seen an explosion of interest in the interaction of light with nanomechanical motion. Typical systems contain a laser-driven optical cavity, being coupled via radiation forces to mechanical motion (like that of a moveable mirror). The goals of this field range from foundational questions to applications in quantum information processing and in the ultrasensitive detection of mass, force, position and acceleration. We have contributed to the initial developments of this field by predicting the nonlinear dynamics and the formation of hybrid photon-phonon states in the strong coupling regime, as well as by pointing out the requirements for ground-state laser cooling.

More recently, we have gone beyond the canonical optomechanical system and studied systems where many optical and mechanical modes couple to each other, forming optomechanical arrays and circuits. There, we are studying the many-body dynamics of photons and phonons interacting with each other, possibilities for mechanical quantum state processing, classical synchronization physics, and questions related to enhancing the coupling strengths.

Light and sound can interact via radiation forces. This interaction becomes particularly strong when both light and sound are confined to micron-scale dimensions. Such a situation can be realized nowadays in photonic crystals, i.e. slabs of dielectric material with a periodic pattern of holes. The main idea is to introduce artificially engineered defects into the pattern. These give rise to localized optical modes. At the same time, localized vibrational modes will develop at the same defect sites. The vibrations will couple to the light field via radiation pressure, and the tight localization leads to strong interactions. A displacement by about a nanometer can give rise to an optical frequency shift of 100 GHz. Such setups have been employed recently in the field of cavity optomechanics to laser-cool a nanomechanical vibrational mode to near the quantum ground state and to investigate other quantum effects.

In our research, we are exploring the possibilities that could be realized in the future, based on this platform. We imagine going from the situation of a single optical and vibrational mode to a whole array (or circuit) of such modes, realizing “optomechanical arrays”. Photons and phonons are able to ‘hop’ between the localized modes, because the evanescent tails of those nearby modes have a non-vanishing overlap. At the same time, at each localized site, they feel the mutual interaction. The appropriate conceptual framework to describe this situation would be a tight-binding model, as it is known from condensed matter physics (but replacing electrons by photons). In contrast to the situation in solids, however, the optomechanical array is strongly out of equilibrium, being continuously driven by a laser. This basic model of interacting photons and phonons on a lattice has a very rich phenomenology, which will be addressed in this talk.

The radiation pressure interaction is initially nonlinear (with the force depending on the light intensity instead of the amplitude). However, in many cases, it is possible to focus on the small intensity fluctuations. These fluctuations of the light field can couple coherently to the phonons, and the coupling strength can be tuned by the overall laser power. In this sense, an optomechanical array becomes similar to optical lattices for atoms, i.e. a periodic lattice whose properties can be tuned via the laser beam.

We have explored the tuneable bandstructure of photons interacting with phonons on such a lattice. For example, polaritons can form, i.e. hybrid excitations made from light field fluctuations and phonons. In addition, interesting instabilities can arise that eventually lead to nonlinear behaviour. When one allows the lattice structure to go beyond a simple Bravais lattice, it is possible to encounter other situations reminiscent of important condensed matter phenomena. On a honeycomb lattice, both photons and phonons produce the type of bandstructure known for electrons in graphene. That is, at special points the bandstructure resembles that of massless relativistic particles, such that energy vs. momentum forms a Dirac cone. We have started to describe the transport of photon-phonon Dirac polaritons, analyzing both edge states and Klein tunneling.

When the laser field is allowed to be time-dependent, it can be used to engineer an artificial magnetic field for photons or phonons, based on the optomechanical interaction. That means, photons (or phonons) start to feel arbitrary phase factors when hopping from site to site. This gives rise to quantum-Hall effect type edge states, which in this case turn out to be robust against disorder. Other situations can be engineered as well, based on these laser-tuneable phase factors for phonons or photons hopping between different sites.

Some (older) additional information

OptomechanicsButton.png Optomechanics - Light interacting with nanomechanical motion has become a research topic drawing a lot of attention recently. Read more about our theory contributions in that domain DecoherenceButton.png Decoherence - A quantum system interacting with a noisy environment suffers decoherence, i.e. interference effects are destroyed. This is a topic important both for fundamental reasons (quantum-classical transition, quantum measurement, characterizing interaction effects), as well as for possible applications (sensitive measurements and quantum information processing). CircuitQEDButton.png Quantum electrodynamics in superconducting circuits - Microwave radiation interacting with a superconducting artificial atom on a chip.

Research topics Reinhard group

Metallic Clusters - Metallic clusters are microscopically small drops of two to a few thousand metal atoms. Such systems lie between the atom and the bulk solid state.

See also the website of the Erlangen-Toulouse collaboration

Atomic Nuclei - In the research areas mentioned so far the atomic nucleus can be treated as a charged point. At higher spatial resolution, below 10-14 m, one has to account for its structure, consisting of interacting protons and neutrons. Quite similar as the metallic clusters the nucleus is a finite many-body system, a drop, whose structure is strongly determined by quantum shell effects and surface forces. Enhanced stability at certain magic proton and/or neutron numbers allows the existence of exotic unstable nuclei which can be produced in reactors or by accelerators. Exotic isotopes of known elements, i.e. extremely neutron- or proton rich nuclei play an important role in the nucleosynthesis in stars. There is also the quest for yet unknown superheavy elements with Z > 112. The new reactor in Garching is excellently suited for further experimental research in this area. This allows an improvement of the theories for the structure of the atomic nucleus and its dynamics.