Condensed matter theory is currently moving from its traditional role of modelling and interpreting existing matter to an active design and control of physical many-body quantum processes with desired physical properties. This is a strong requirement for the quantum technologies that will shape our future.
Luckily this is accompanied by many new challenges of fundamental character that, since they are different from the traditional questions in physics, will lead to a leap forward in our basic understanding of quantum matter. Our research is focused on this aspect: it is driven only by curiosity, but gently directed towards the needs of future technology.
The picture above shows on the left the main topics of our current research and on the right the goal to bring all these topics to use for the general idea of quantum information processing. The lines and dots indicate the connections between the different topics on which we have been working recently. A few examples of how this looks in practice are described below.
The biggest enemy of quantum computing is decoherence, the uncontrolled degrading of a well defined quantum superposition. This occurs because a quantum system is always embedded in a wider environment with a macroscopic number of degrees of freedom. The latter lead to a destructive interference for any interaction with the system and this feeds back as the phenomenon of decoherence.
Since this acts as a drain of quantum information large efforts are made to isolate the system from the environment, to suppress environments or to use special driving protocols to undo some decoherence processes. But it is also interesting to ask how exactly the decoherence builds up, if we can use this phase to learn something about the system or the environment and if there is a way to use it for quantum information processing.
One example is a spin in a metal as shown in the figure on the right. In its pure quantum form this corresponds to the Kondo model, beyond the Kondo regime this is the basis for magnetic resonance techniques in the solid state. Most properties of such a system are thus known since long. However, mostly left aside was the regime of very short time scales in which the spin and a part of the metallic environment have a joint coherent evolution, in which in particular coherent excitations in the metal act back on the spin dynamics. The coherent many-body effect of a local excitation, such as from a spin flip, on the environment runs under the name of orthogonality catastrophe or Fermi edge singularity and we have worked on extending the techniques to access this physics for various situations over many years. Very recently we have also set up an approach allowing us to systematically investigate the backaction on the spin as well. We are now working towards using these approaches as tools for gaining information on correlated systems and towards understanding how quantum information can propagate coherently through an otherwise incoherent environment.
Topological phases and topological excitations have become a topic of massive research activity over the last years. Topology refers here to a classification of quantum states that is not directly measurable through a local observable but which has consequences whenever a system of one topological class has an interface to a system with a different topological class. The most prominent interface effect is the appearance of conducting interface states between two topological insulators or topological superconductors.
Based on the maxim of designing rather than discovering we are investigating how the interaction between two quantum systems can be tailored to provide new, and especially topological effects. An important insight is that if we start from a sufficiently complex but conventional quantum state, the topological properties can be changed by projecting out a part of the wave function. Such a projection can occur through the interaction between two systems and in the best case the result is robust in the sense that no fine tuning is required. An example is shown on the right in which nuclear spins in a one-dimensional conductor order in a spiral pattern due to their interaction with the electrons, but in turn scattering on this pattern causes the opening of a gap in the electron bands as well and what is left as conducting states is known as a helical conductor. The robustness comes in because the combined state is self-stabilising through the feedback mechanism indicated in the figure.
Helical conductors are an important component to obtain further topological states. For instance, when a helical conductor is brought in contact with a superconductor, the Cooper pairs from the superconductor are projected onto one half of their wave function component when they tunnel into the conductor by proximity effect. The resulting induced superconductivity has then a changed topology class, and the interesting topological interface properties arise in the form of Majorana bound states at the ends of the conductor (the interface to the vacuum), as illustrated in the figure next. We are currently exploring how the underlying physics can be used further to obtain topological textures directly in the superconducting substrates.
One of the prime applications of topological quantum states will be with quantum computation, and much research worldwide is focused on this aspect, in addition to the question of how to obtain and manipulate topological phases. Less explored, and the topic of this branch of our research, is to use topological states as a pathway to new physical phenomena.
For instance, a most interesting situation arises in the system shown to the right. A topological superconductor (TSC) with two Majorana bound states as consequence of its topological class is left ungrounded that it acts as a capacitor. In such a situation it is possible to tune the energy levels of the Majorana states to form a low-energy two-level system similar to a magnetic moment. This resembles the Kondo model which describes an isolated magnetic moment that is screened by a complicated modification of the state of nearby conducting electrons. The Kondo model been used as the archetype of strong correlation physics over many decades.
A similar model is realised here with the Majorana modes. However, in contrast to the Kondo system, in which the renormalisation by the interactions leads either to a strongly or a very weakly correlated phase, we find an unusual intermediate behaviour, which from a merger of Kondo and Majorana we have named Kondorana. This state is a novel many-body state that extends across metallic, Majorana and superconducting electrons and complements the family of Kondo related models in a most curious way.
In a follow-up work we have investigated a similar set-up under driven situations and could identify a rich dynamics brough in by the Majorana states. Through these examples it has become clear that using topological excitations as an interface to novel phenomena has a large potential as the next step in topological physics research. In addition it is a very fruitful playground to explore how complicated many-body physics can be set up step by step by adding further interactions and interfaces.
The controlled generation and detection of entanglement is necessary if we want to use a quantum state for application. In a nanostructure, this task typically refers to controlling the entanglement of selected pairs of electrons. Such pairs must be generated by a source, for which a promising candidate is a Cooper pair splitter. The latter is a system as shown in the figure to the right, consisting of a superconductor that naturally contains pairs of spin-entangled electrons in the form of Cooper pairs. The superconductor is connected to two quantum dots, and the injection of a Cooper pair (hourglass shape in the figure) into the double quantum dot system is tuned such that preferably one electron of the pair is injected into the left dot, and the other electron into the right dot. Such split pairs supposedly maintain their entanglement, yet a direct proof by an experiment that this is indeed the case is very challenging and could not be realised so far.
To overcome the difficulties inhibiting the progress so far, we have suggested a new setup of a Cooper pair splitter, in which spin filters are placed directly at the superconductor (and we showed that this is achievable actually with ordinary carbon nanotubes as sketched in the figure). We demonstrated that a proof of entanglement can be given by standard transport measurements of the conductances of the Cooper pair splitter without the requirement of measuring noise correlators. Necessary instead is some tunability of the spin filter settings, which for the carbon nanotubes is an intrinsic property, accessible by applying a constant magnetic field B and controlling resonant electron transport by quantum dot side gates (see the figure).