Free space quantum communication

Free space quantum communication, or transmission of quantum information from one place to another through the atmosphere, can be realized using the two-dimensional, polarization degree of freedom of photons. However, higher-dimensional quantum systems, also referred to as qudits, present several advantages over simple two-level systems (qubits). The first benefit of high-dimensional states is their capability of naturally increasing the information encoded in a single carrier. Moreover, when compared to qubits, qudits are more robust against quantum cloning and, thus, they allow to enhance the security of quantum key distribution (QKD). Some promising QKD protocols are based on quantum entanglement. In this case, the presence of an eavesdropper can be detected via Bell inequalities, which are the more violated the larger the dimensionality of the employed entangled states. Therefore, entangled qudits can be used to outperform two-dimensional QKD schemes.

Photonic orbital angular momentum (OAM) states are suitable candidates for the realization of such qudits. OAM spans a discrete, infinite-dimensional Hilbert space. However, the advantages associated with OAM can be nullified by a turbulent atmosphere, because the defining feature of OAM-carrying light beams, namely their helical wavefront, is fragile with respect to turbulence-induced refractive index fluctuations.

We theoretically study the potential of adaptive optics (AO) to protect entanglement of high-dimensional photonic OAM states against turbulence-induced phase distortions. Furthermore, we explore the alternative possibility of high-dimensional spatial encoding — into highly transmissive eigenmodes of a random realization of atmospheric turbulence. 

Contact:  Vyacheslav Shatokhin

Open quantum systems

• Markovian and non-Markovian quantum dynamics in nonequilibrium many-body systems
• Detection and control of quantum correlations in open systems
• Foundations of quantum thermodynamics

We study the foundations of the quantum dynamics of open systems, i.e., quantum systems coupled to an environment, which leads to a large variety of phenomena such as dissipation, decoherence, equilibration and thermalization. Current research topics are, in particular, Markovian and non-Markovian quantum processes, dynamical detection of quantum correlations and entanglement, and control in complex systems. The most important achievements in recent years are the characterization, classification and quantification of quantum memory effects through the flow of information between an open quantum system and its environment, and the development of various schemes for the detection of quantum correlations by local operations. These theoretical results have led to a series of applications and experimental realisations, e.g. in quantum optics and quantum information, photonics, trapped-ion systems, condensed matter and quantum metrology.

Contact: Heinz-Peter Breuer

First detected arrival times

Here, the temporal aspects of quantum transport are addressed. This is particularly important in the context of quantum search algorithms. The question of when a quantum particle or system arrives at a target position requires a careful operational definition. This means that the observer must fix a detection protocol beforehand. They must explicitly decide at which epochs a detection of the system at the target is attempted. In the stroboscopic protocol, for example, detection is attempted with a fixed frequency until it is successful for the first time, thus defining the "first detected arrival time". Due to the very nature of quantum measurements, the previous unsuccessful detection attempts modify the system state. Furthermore, the first detection time is a random variable whose distribution is sought after. We investigate how the initial quantum state of the system, the structure of the target subspace and most importantly the details of the system's energy spectrum influence the distribution and the moments of the first detection time.

Contact: Christoph Dittel

Multiparticle Entanglement

Entanglement in composite quantum systems is considered one of the most fundamental properties of quantum mechanics. It allows for the violation of Bell inequalities, thus proving its inherent non-classical nature, and forms the basis of many applications that have been developed in the field of quantum information. Among the latter are quantum cryptography or computation protocols which rely on the presence of entanglement in order to establish an advantage over their classical counterparts.

While the theory of entanglement among two particles is reasonably well understood, open questions remain when considering systems of many, possibly interacting particles. In this regime, the characterization of different classes of multiparticle entangled quantum states is more demanding due to the increasing complexity of the underlying Hilbert spaces with growing particle numbers. Furthermore, the certification of the presence of specific types of multiparticle entanglement is challenged by the enormous dimensions of these Hilbert spaces. 

In our group we are concerned with the development of novel statistical methods for the characterization of multiparticle quantum systems. For instance, by exploiting protocols based on randomized measurements, one can overcome some of the outlined difficulties and verify the presence of different types of multiparticle entanglement.

Contact: Andreas Ketterer

Quantum Computation

Quantum computation describes the implementation of algorithms using quantum mechanical systems and their ability to exhibit interference. Expectations placed on this technology were fueled by the discovery of a (small) number of quantum algorithms which can solve particular problems faster than any classical computer. A famous example is Shor’s algorithm which theoretically allows to factor large numbers efficiently, a task that so far gives any classical computer a hard time.

However, practical implementations of quantum algorithms remain challenging due to the fragility of quantum systems under environmental influences. Circumventing this problem requires appropriate error correction procedures which are out of reach with current technology. Therefore, some contemporary approaches to quantum computing combine noisy intermediate-scale quantum devices and classical computing units with the hope to find possible advantages without the need of expensive error correction.

We investigate these hybrid algorithms, with a focus on a detailed understanding of quantum information processing and its role for quantum computational models. Inter alia, we perform numerical studies to uncover the basic properties of various algorithms with respect to information theoretic quantities such as the production of entanglement or the speed of convergence.

Contact: Andreas Ketterer, Christoph Dittel

Localization and multifractality

The dynamical properties of a quantum system are encoded in the eigenstates of the Hamiltonian that governs it. Typical examples are the Bloch states in a perfect crystal, which describe an electron moving through the material, and the localized states in a disordered potential, which are confined to a finite number of lattice sites and hence do not support transport.

Multifractal analysis is a powerful tool to study the statistical properties of the eigenstates. The concept of multifractality was introduced already by Mandelbrot and it was soon realised that it described wave functions at the localisation-delocalisation transition. There, the wave function is invariant upon coarse graining and can then be described by a set of scaling exponents (which make it multifractal).

In our group we use multifractal analysis to distill the general features of complex many-body systems in different regimes of, e.g., interactions, disorder or dissipation.

Contact: Edoardo Carnio

Nonlinear spectroscopy

Linear absorption spectroscopy can only reveal spectral properties of the system under investigation. However, it cannot yield information on dynamical processes and transport properties. In nonlinear spectroscopy the sample is exposed to a succession of pulses, and their time delays are varied. This has proven enormously successful in the identification of energy transport pathways in many systems ranging from quantum dots to molecular aggregates in photosynthetic complexes.

We develop novel techniques to refine and extend the possibilities to interrogate a quantum system with nonlinear spectroscopy, for instance by using quantum light. We also investigate how nonlinear spectroscopy can be applied to cold synthetic matter, such as trapped ions. In these systems, complex quantum systems can be simulated under well-controlled conditions. It is further possible to apply laser pulses onto individual ions, providing a spatial resolution within the nonlinear spectra which is not available in experiments on molecular aggregates.

Contact: Edoardo Carnio, Vyacheslav Shatokhin

Optimized multi-layered photonic structures

The term upconversion denotes processes which convert two low-energy photons into one photon with higher energy, and can be used in a wide range of optical applications. One promising concept is to combine upconverter materials with silicon solar cells to improve their efficiency by utilizing the full range rather than only a fraction of the solar spectrum. The quantum yield, which quantifies the overall efficiency of an upconverter material, is determined by an interplay of emission rates, energy transfer processes, local irradiance and local density of states. Embedding the upconverter material in photonic dielectric nanostructures allows one to affect all of these determining factors and thus to influence and improve the overall efficiency of the upconversion process.

By quantifying the structure's influence on the basic underlying processes, we develop models that allow to optimize structures for upconversion efficiency. In particular, we consider arbitrary finite multilayered dielectric stacks and utilize methods from macroscopic QED to calculate energy transfer rates, the local density of states and the structure’s influence on spontaneous emission and absorption rates of the upconverter ions. For example, by tuning the thickness of each individual layer in a multi-layered photonic structure, it is possible to trap incident photons of a given wavelength inside this structure, and considerably increase the local irradiance. Our models, rooted in analytical methods in combination with numerical optimization algorithms, allow us to propose specific designs optimized for upconversion efficiency.

To utilize our results for practical applications and to compare our predictions with experimental data, we collaborate with experimentalists at Fraunhofer Institute for Solar Energy Systems.

Contact: Fabian Spallek

Many-particle interference

The dynamics of many identical particles such as photons or cold atoms is characterized by unique interference effects. For example, two indistinguishable photons impinging on opposite sides of a semi-transparent mirror always emerge on the same side, as if tossing two coins either gave two heads or two tails, but never one head and one tail.

As the number of particles and the size of the interferometer grows, a rapidly increasing number of many-particle paths contribute coherently to a given output event. By fixing the symmetry of the input state and interferometer, one can still ensure that these many-particle paths interfere destructively, such that the corresponding output is suppressed. On the other hand, for interferometers with no particular symmetry, the large number of alternative evolutions which need to be taken into account can make calculations exceedingly difficult. Protocols such as Boson Sampling exploit this complexity to demonstrate a computational advantage of quantum over classical devices.

 The physics becomes even richer if we include additional degrees of freedom of the particles. On the one hand, these can act as (possibly ambiguous) labels and partially suppress interference effects. Such a theory of partially distinguishable particles is therefore essential to correctly describe actual experiments, which unavoidably involve partially distinguishable particles. On the other hand, if they can be controlled, these extra degrees of freedom can be used to tailor the many-particle interference. In this context, we touch upon fundamental questions about the notion(s) of entanglement for identical particles.

Moving away from the traditional picture of photons scattering in interferometers, we also want to understand how many-particle interference manifests itself in the non-equilibrium behavior of interacting systems, for example cold atoms in optical lattices.

 Contact: Christoph Dittel, Gabriel Dufour

Transport in disordered networks

We investigate the statistical properties of transport through disordered, finite quantum networks. For example, photosynthetic complexes like the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria are very efficient in transferring the energy of absorbed photons into the reaction center, where it is converted into chemical energy. The FMO complex consists of seven (or eight) molecules, which can be modeled as a quantum network of two-level systems coupled to each other by dipole-dipole interactions. However, biological systems are characterized by a large variability between individual realizations and a strong coupling to environmental degrees of freedom such as vibrations. We are therefore looking for transfer mechanisms which exploit the  coupling to the environment and simple design principles which ensure high transfer efficiencies on short time scales in spite of disorder.

Contact: Edoardo Carnio, Gabriel Dufour

Coherent wave transport in linear and nonlinear disordered media

Transport of waves through disordered media gives rise to surprising interference effects such as weak localization, coherent backscattering, and Anderson (or strong) localization. Additionally, wave transport and multiple scattering may also be affected by nonlinearities, e.g. due to an intensity-dependent refractive index (in the case of light scattering) or due to interactions between atom. Our aim is to understand how the nonlinearity interplays with the above-mentioned disorder phenomena.

For this purpose, we have developed a nonlinear diagrammatic theory, and applied it in order to evaluate the effect of nonlinearities on the coherent backscattering interference. Depending on the type of nonlinearity, scattering into the exact backward direction may be enhanced or diminished by the nonlinearity. Under appropriate circumstances, nonlinearity may even turn constructive into destructive interference.

Contact: Vyacheslav Shatokhin, Edoardo Carnio