## Research Highlights of the Department of Physics

### Topological protection versus degree of entanglement of two-photon light in photonic topological insulators

*In a joint effort, researchers from the Humboldt-Universität zu Berlin, the Max Born Institute (Berlin) and the University of Central Florida (USA), have revealed the necessary conditions for the robust transport of entangled states of two-photon light in photonic topological insulators, paving the way the towards noise-resistant transport of quantum information. The results have appeared in Nature Communications.*

Originally discovered in condensed matter systems, topological insulators are two-dimensional materials that support scattering-free (uni-directional) transport along their edges, even in the presence of defects and disorder. In essence, topological insulators are finite lattice systems where, given a suitable termination of the underlying infinite lattice, edge states are formed that lie in a well-defined energy gap associated with the bulk states, i.e. these edge states are energetically separated from the bulk states, see Fig 1.

Figure 1: Topological insulators are finite-sized lattice systems (a) that exhibit eigenspectra where (b) the eigenenergies of bulk states (c) exhibit a band gap that (d) contains the eigenenergies of so-called edge states.

Importantly, single-particle edge states in such systems are topologically protected from scattering: they cannot scatter into the bulk due to their energy lying in the gap, and they cannot scatter backwards because backward propagating edge states are either absent or not coupled to the forward propagating edge states.

The feasibility of engineering complex Hamiltonians using integrated photonic lattices, combined with the availability of entangled photons, raises the intriguing possibility of employing topologically protected entangled states in optical quantum computing and information processing (Science 362, 568, (2018), Optica 6, 955 (2019)).

Achieving this goal, however, is highly nontrivial as topological protection does not straightforwardly extend to multi-particle (back-)scattering. At first, this fact appears to be counterintuitive because, individually, each particle is protected by topology whilst, jointly, entangled (correlated) particles become highly susceptible to perturbations of the ideal lattice. The underlying physical principle behind this apparent ‘discrepancy’ is that, quantum-mechanically, identical particles are described by states that satisfy an exchange symmetry principle.

In their work, the researchers make several fundamental advances towards understanding and controlling topological protection in the context of multi-particle states:

- First, they identify physical mechanisms which induce a vulnerability of entangled states in topological photonic lattices and present clear guidelines for maximizing entanglement without sacrificing topological protection.
- Second, they stablish and demonstrate a threshold-like behavior of entanglement vulnerability and identify conditions for robust protection of highly entangled two-photon states.

To be precise, they explore the impact of disorder onto a range of two-photon states that extend from the fully correlated to the fully anti-correlated limits, thereby also covering a completely separable state. For their analysis, they consider two topological lattices, one periodic and one aperiodic. In the periodic case they consider the Haldane model, and for the aperiodic case a square lattice, whose single-particle dynamics corresponds to the quantum Hall effect, is studied.

The results offer a clear roadmap for generating robust wave packets tailored to the particular disorder at hand. Specifically, they establish limits on the stability of entangled states up to relatively high degrees of entanglement that offer practical guidelines for generating useful entangled states in topological photonic systems. Further, these findings demonstrate that in order to maximize entanglement without sacrificing topological protection, the joint spectral correlation map of two-photon states must fit inside a well-defined topological window of protection, Fig. (2).

Figure 2: In order to identify the topological window of protection, the researchers considered a spectrally broad product state as initial state and propagate it through an ensemble of 1000 random Haldane lattices. (a) Depicts the spectral correlation map for the initial state and in (b) the ensemble-average of the spectral correlation maps inside the edge-edge subspace after the propagation through the ensemble of disordered lattices is shown. It is found that the only two-photon amplitudes that survive the scattering induced by the disorder lie in the region indicated by the black square which is the protection window. Finally, (c) and (d) display, respectively, the edge-mode content E and the product of the edge-mode content with the Schmidt-number E · S_{N} as a function of the variances of the initial states.

##### Publication

Konrad Tschernig, Álvaro Jimenez-Galán, Demetrios N. Christodoulides, Misha Ivanov, Kurt Busch, Miguel A. Bandres, Armando Perez-Leija

Publication 30 March 2021, Nature Communications 12, Article number: 1974 (2021)

##### Contact

Theoretical Optics & Photonics Group

### Stability of non-supersymmetric solutions of string theory

One of string theory's most prominent predictions is that our universe has extra spatial dimensions that we do not observe directly. Instead, these extra dimensions are curled up into a small compact space. In order to yield any meaningful physics, these "compactifications" must be stable, much like a ball in a valley of a hill is stable since if it is pushed slightly to the side, it will roll-back to its initial position. By contrast, if the ball is at the top of a hill, a small push to the side will cause the ball to roll down the hill and far away from its original unstable position. Similarly, in an unstable compactification, a small deformation of the shape of the extra dimensions of string theory will cause the extra dimensions to rapidly expand to large size or even to collapse and form a rip in space. Typically, string compactifications are unstable, unless they possess supersymmetry, an elegant symmetry arising in string theory but which is not observed in the real world.

Adolfo Guarino (University of Oviedo), Emanuel Malek (Humboldt-Universität zu Berlin) and Henning Samtleben (École Normale Supérieure de Lyon) proved the stability of 7 non-supersymmetric solutions of string theory, consisting of a 4-dimensional negatively curved spacetime, called anti-de Sitter space, and 6 curled up dimensions making up a spherical shape. These form the first examples of stable string theory solutions containing anti-de Sitter space. While these solutions cannot be used to directly model our universe, they could provide the first models for 3-dimensional non-supersymmetric condensed matter systems via the "holographic principle". Moreover, this class of solutions are a stepping stone towards better understanding non-supersymmetric solutions of string theory in general.

##### Publication

Stable Nonsupersymmetric Anti–de Sitter Vacua of Massive IIA Supergravity

Adolfo Guarino, Emanuel Malek, Henning Samtleben

Publication 10 February 2021, Phys. Rev. Lett. 126 (2021) 061601

##### Contact

Emmy Noether Research Group "String Theory Flux Vacua"

### Sharing is Caring! Discovering the materials of the future with FAIR data management and AI

*Panel discussion with Prof Claudia Draxl (HU) and Prof Matthias Scheffler (HU and Fritz Haber Institute of the Max Planck Society), moderated by Prof Peter Frensch (HU, Vice President for Research) at the Berlin Science Week 2020*

Many products owe their function to novel materials, but how can we find materials that perform particularly well and enable new technologies? By making smarter use of our knowledge!

Huge amounts of scientific data are generated worldwide, but much of it is considered waste because this data does not serve the specific research project. However, it could contain valuable information for other research approaches. This calls for a rethink: Recycle the Waste!

At this year's Berlin Science Week, Claudia Draxl and Matthias Scheffler demonstrated that this approach can only be realized with Artificial Intelligence and a FAIR data infrastructure. (FAIR stands for Findable, Accessible, Interoperable, and Re-purposable.) Such an infrastructure enables the productive handling of scientific data and is thus essential for the development of future technologies.

Draxl and Scheffler have already established such an infrastructure for computational materials science: The NOMAD Lab is the world's largest database of material properties, which now contains 100 million calculations. Draxl and Scheffler are even going one step further. As part of the NOMAD Center of Excellence, they are developing computational materials science into new applications, preparing it for the coming generation of high-performance computers (exascale computers).

##### More Information

Video of the panel discussion in German

##### Contact

The Novel Materials Discovery (NOMAD) Laboratory

The NOMAD Center of Excellence

### Density fluctuations in amorphous silicon discovered

**For the first time, it has been possible to identify atomic substructures in amorphous silicon with a resolution of 0.8 nanometres using X-ray and neutron scattering at BESSY II and BER II. Such a-Si:H thin films have been used for decades in solar cells, TFT displays, and detectors. The results show that three different phases form within the amorphous matrix, which dramatically influences the quality and lifetime of the semiconductor layer. The structural elucidation was achieved in a collaboration between the Department of Physics of the HU, the Helmholtz-Zentrum Berlin and the Technical Universities of Eindhoven and Delft.**

Silicon does not have to be crystalline, but can also be produced as an amorphous thin film. If additional hydrogen is incorporated during the production of these thin layers, so-called a-Si:H layers are formed. Such a-Si:H thin films have been used for decades for various applications, for example as contact layers in highly efficient tandem solar cells made of perovskite and silicon. In this study, it was shown that the a-Si:H network is by no means a homogeneously amorphous material. The amorphous matrix is interspersed with nanometre-sized areas of varying local density, from cavities to areas of extremely high order. It was possible to experimentally observe and quantitatively measure these inhomogeneities in differently produced a-Si:H thin films. To do this, the results of complementary analytical methods were combined to form an overall picture.

At the nanometer scale, voids corresponding to slightly more than 10 missing atoms were discovered. These voids arrange themselves with a distance of about 1.6 nanometres. In addition, nanometre-sized regions were discovered in which silicon atoms are better ordered compared to the surrounding material. These densely ordered domains (DOD) contain hardly any hydrogen. The DODs form aggregates of up to 15 nanometres in diameter. The DOD regions are able to reduce mechanical stress in the material and thus contribute to the stability of the a-Si:H thin film. The voids on the other hand, can promote electronic degradation of the semiconductor layers

Targeted optimization of manufacturing processes with regard to the substructures now discovered could enable new applications such as optical waveguides for programmable photonic systems or a future silicon battery technology.

Structural model of highly porous a-Si:H, which was deposited very quickly, calculated based on measurement data. Densely ordered domains (DOD) are drawn in blue and cavities in red. The grey layer represents the disordered a-Si:H matrix. The round sections show the nanostructures enlarged to atomic resolution (below, Si atoms: grey, Si atoms on the surfaces of the voids: red; H: white) Figure: Eike Gericke/HZB

##### Publication

Quantification of nanoscale density fluctuations in hydrogenated amorphous silicon

Eike Gericke, Jimmy Melskens, Robert Wendt, Markus Wollgarten, Armin Hoell, Klaus Lips

Publication 29 October 2020 Phys. Rev. Lett. 125 (2020) 18, 185501

Print Version of the Cover (pdf)

##### Contact

Prof. Simone Raoux, Institute for Nanospectroscopy, HZB

### Quantum microscopy reveals invisible bio-features

Researchers from Humboldt-Universität zu Berlin and the Experimental and Clinical Research Center in Berlin show how quantum light can help the field of bioimaging. In their new experiment, featured on the cover of "Science Advances", the team uses entangled photons to image a bio-sample probed by "invisible" light without ever looking at that light. This avoids the usually severe problems that stem from poor performance and high price of broadband mid-IR light sources and cameras. Instead, the researchers only use a normal laser and commercial CMOS camera. This makes their mid-IR microscopy technique not only robust, fast and low noise, but also cost-effective - making it highly promising for real-world applications. They show this by taking microscopic images of a tissue sample from a mouse heart.

Figure: Quantum microscopy of a mouse heart. Entangled photons allow for the making of a high-resolution mid-IR image, using a visible light (CMOS) camera and ultralow illumination intensities. In the picture, absorption (left) and phase information (right) from a region in a mouse heart. The yellow scale bar corresponds to 0.1 mm which is about the width of a human hair.

##### More Information

News of the Humboldt-Universität zu Berlin

##### Publication

Microscopy with undetected photons in the mid-infrared

Inna Kviatkovsky, Helen M. Chrzanowski, Ellen G. Avery, Hendrik Bartolomaeus, Sven Ramelow

Publication 14 October 2020, Science Advances 6, Issue 42

##### Contact

Nonlinear Quantum Optics Group

### Hidden Symmetries in Massive Quantum Field Theory

Theoretical models with a large amount of symmetry are ubiquitous in physics and often key to developing efficient methods for complex problems. If the number of symmetries surpasses a critical threshold, a system is called integrable with a prime example being the Kepler problem of planetary motion. While integrability typically comes with a rich spectrum of mathematical methods, it is often hard to identify the underlying symmetries. For the first time quantum integrability was now discovered in the context of massive quantum field theories in four spacetime dimensions. Florian Loebbert and Julian Miczajka (both Humboldt University) together with Dennis Müller (NBI Copenhagen) and Hagen Münkler (ETH Zürich) have shown that large classes of mostly unsolved massive Feynman integrals feature an infinite dimensional Yangian symmetry - a hallmark of integrability. This mathematical structure is highly constraining and it allows to completely fix these building blocks of quantum field theory as has been demonstrated for first examples. The observed Yangian symmetry goes hand in hand with an extension of the important structure of conformal symmetry to situations including massive particles. Remarkably, this discovery suggests that similar symmetry features may also be hidden in massive versions of the celebrated holographic duality between gauge theories and gravity. These findings were recently published in Physical Review Letters 125 (2020) 9, 091602.

##### Publication

Massive Conformal Symmetry and Integrability for Feynman Integrals

Florian Loebbert, Julian Miczajka, Dennis Müller, and Hagen Münkler

Publication 25 August 2020, Phys. Rev. Lett. 125 (2020) 9, 091602

##### Contact

Quantum Field and String Theory Group

### Jetting into the dark side: a precision search for dark matter

The nature of dark matter remains one of the great unsolved puzzles of fundamental physics. Unexplained by the Standard Model, dark matter has led scientists to probe new physics models to understand its existence. Many such theoretical scenarios postulate that dark matter particles could be produced in the intense high-energy proton–proton collisions of the LHC. While the dark matter would escape the ATLAS detector unseen, it could occasionally be accompanied by a visible jet of particles radiated from the interaction point, thus providing a detectable signal.

The ATLAS Collaboration set out to find just that. Today, at the International Conference in High-Energy Physics (ICHEP 2020), ATLAS presented a new search for novel phenomena in collision events with jets and high missing transverse momentum (MET). The search was designed to uncover events that could indicate the existence of physics processes that lie outside the Standard Model and, in doing so, open a window to the cosmos.

A monojet event recorded by the ATLAS experiment in 2017, with a single jet of 1.9 TeV transverse momentum recoiling against corresponding missing transverse momentum (MET). The green and yellow bars show the energy deposits in the electromagnetic and hadronic calorimeters, respectively. The MET is shown as the red dashed line on the opposite side of the detector. (Image: ATLAS Collaboration/CERN)

##### More Information

Physics Briefing, By ATLAS Collaboration, 27th July 2020

##### Contact

Groups: Experimental Particle and Astroparticle Physics and High Energy Physics

### Direct measurement of quantum efficiency of single-photon emitters in hexagonal boron nitride

Single-photon emitters (SPEs) in two-dimensional materials are promising candidates for the future generation of quantum photonic technologies. In this work, we experimentally determine the quantum efficiency (QE) of SPEs in few-layer hexagonal boron nitride (h-BN). We employ a metal hemisphere that is attached to the tip of an atomic force microscope to directly measure the lifetime variation of the SPEs as the tip approaches the ℎ-BN. This technique enables nondestructive, yet direct and absolute measurement of the QE of SPEs. We find that the emitters exhibit very high QEs approaching (87±7)% at wavelengths of ≈580 nm, which is among the highest QEs recorded for a solid-state SPE

Schematics of an experiment to measure the quantum efficiency of a single photon emitter in a two-dimensional material: A metal sphere very close to the emitter changes the spontaneous emission rate due to a quantum electrodynamic effect thus revealing its quantum efficiency.

##### Publication

Direct measurement of quantum efficiency of single-photon emitters in hexagonal boron nitride

Niko Nikolay, Noah Mendelson, Ersan Özelci, Bernd Sontheimer, Florian Böhm, Günter Kewes, Milos Toth, Igor Aharonovich, and Oliver Benson

Optica 6 (2019), 1084-1088

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